# Four Fours Problem

Compiled by Paul Bourke

Contributions by Frank Primer, Chris Smith, Guido Roach, Dhruv Chand, Jim Millar, Vijay Kailas, David Bevan, Ewald R. de Wit, Martin Olivella, Heiner Marxen, Scott Forschler, Wayne Goode, Jörg Wiegels, Ben Rudiak-Gould, Charles Dillingham, Peter Karsanow, Brad McInnes, Richard Schorn, Ewart Shaw, Rick Hevener, Toufic Batouli, Sven Peterson and Rizvan Dadaev.

This classical problem is most commonly formulated as follows:

## "Given no more than four instances of the digit 4, represent all integers using a finite number of mathematical symbols and operators in common use."

The central issue then is which symbols may one use and which ones may not, the rules that will be applied to the following lists are outlined below. In situations where more than one solution can be found the challenge is to find the simplest, least number of symbols and operators as well as the simplest operators.

• Acceptable symbols and operators

```   +,-   addition subtraction
*,/   multiplication, division
sqrt,^   square root, power
!   factorial, eg: n! = n * (n-1) * (n-2) * ... * 2 * 1
.   decimal point, eg: .4
`   repeating decimal, eg: .4` = .444444444...```

• Other Symbols

Cannot use representations for other numbers, eg: use of [pi] in sin(π / 4) = 1

• Infinity

Cannot use ... to represent an infinite number of operations eg: sqrt(sqrt(sqrt(...4))) = 1

• Subfactorials

Many solutions to this problem in the past have relied on an operator called the subfactorial, defined as follows.

!n = n! (1 - 1/1! + 1/2! - 1/3! + 1/4! - ... +/-1/n!)

Note that !n is always an integer.
In particular
```   !1 = 0
!2 = 1
!3 = 2
!4 = 9```

Since the subfactorial is not considered a symbol in "common" use it will not be used here.

• Gamma function

The gamma function can be used to get an expression for 6 with only one 4.

Γ(4) = 6

Γ(√4) = 1

Nora Grider proposed a simple soloution for the elusive 113, 4(4!+4)+Γ(√4).

Gamma function will only be used here as a last resort.

• Concatenation operator

Nora Grider proposed the concatenation operator "||" which is already being used implicitely in 4||4 and 4||4||4. This can also be used as a solution for 113.

((Γ(√4)) || (Γ(√4)) || (4-Γ(√4))

• 0.4th root (Courtesy of Scott Forschler)

The 0.4th root of a number, normally written as This will be represented in the ASCII form as sqrt.4(x). It gives a shorter solution for 32, namely root.4(4) = 4^(5/2) = 32. Solutions are also listed below for 766, 770, and 772.

• Arbitrary root (Courtesy of Frank Mrazik)

An arbitrary root "b" of a number "a" may be written as root(a,b) where, in this context, a and b are made up entirely of the digit 4. This gives a four 4 solution for 657 for example.

• Percent (Courtesy of Scott Forschler)

While "%" is not strictly a mathematical symbol it is "in common use". It is shown below as alternative solutions for some numbers but still the primary solution for the problematic 113. This has been extended by Frank Mrazik to the following .4% (.004), .4'% (.00444444....), and even 4!% (0.24).

• Percent-percent (Courtesy of Frank Mrazik)

Getting a bit weird, 1%% = 1/10000. So for example 10000 = 4 / 4%%

• Summation (Courtesy of Scott Forschler)

A summation can be used to give various solutions, in particular, 303.

Because solutions based upon summations use additional symbols, namely "i", they will not be used here.

• Using five 4's

Some of the gaps in the numbers below (numbers for which a solution with only four 4's hasn't yet been found) have solutions listed that use five 4's. Note that variations of the problem allow 'free' squaring (eg: 4^2 uses only one 4). In this case those five 4 solutions that use sqrt(4) in the rules used here become solutions with four or less fours. For example, 163 = (4^2+4^2+.4'^2)/.4'^2 uses only four 4's but eight if the 2's are replaced by sqrt(4) as required here.

• 2/9 (First introduced by Richard Schorn for 113)

This and the next repeating decimals are pushing the limits of what is acceptable. In this case it is written as .(sqrt(4))' = 0.22222222... otherwise known as 2/9.

• 24/99 (Introduced by Rick Hevener)

Hardly standard but some of the difficult numbers can be solved with .(4!)' which is supposed to represent 24/99 or 0.2424242424..... For example 99 then can be solved with two 4's as 4! / .(4!)'.

• Mille (Proposed by Frank Mrazik)

Frank Mrazik proposed use of the mille notation %o to mean 1/1000. Initially used for the elusive 713.

• n!! (Proposed by Gerard Schildberger)

Double factorial !! for even and odd numbers, for example
8!! = 8 * 6 * 4 * 2
9!! = 9 * 7 * 5 * 3

For example, Jim Millar gave the following solution for 113
113 = (4!! - 4/4)!! + 4!!

A further list by Frank Mrazik.
```     8 = 4!!
15 = 5!!
48 = 6!!
105 = 7!!
384 = 8!!
945 = 9!!
3840 = 10!!
```
Including a double double !, by Frank Wrazik
```   384 = (4!!)!!
113 = ((4!!)! / (4!!)!!) + 4!!
```
• !!n (Proposed by Gerard Schildberger)

!!n = 0! + 1! + 2! + 3! + ... + n!
For example !!4 = 10

• Any number with three 4's (Contributed by Ben Rudiak-Gould)

A cute solution to any number using just 3 fours. By admitting natural logarithms "ln()" then any positive integer n can be represented as

n = -ln[ ln( sqrt(sqrt(...(sqrt(4))...))) / ln(4) ] / ln(4)

where the number of nested sqrt() functions is twice n. Or if base 4 logarithms are permitted "log4()" then the expression becomes

n = -log4(log4(sqrt(sqrt(...(sqrt(4))...))))

• Any number with two 4's (Contributed by "whetstone")

Using log10, any number can be represented using two fours and creative use of % as shown below:

```   log(srqt(4/(4%)))      = log(sqrt(100))   = log(10)  = 1
log(sqrt(4/(4%%)))     = log(sqrt(10000)) = log(100) = 2
log(sqrt(4/(4%%...%)))                               = n
```

• Any number with one 4 (Contributed by Jim Millar)

Another cunning idea sees any number created using only one 4 and a lot of nested trigonometric functions (atan and sec). The principle lies in the relationship

tan2(x)+1 = sec2(x)

from which

sec(atan(x)) = sqrt(x2+1)

Repeated and nested application k times gives

sec(atan(...(sec(atan(x))...)) = sqrt(x2+k)

So if x=4 we can get any number (greater than 4) by only using a single 4. For example 5 is represented as

sec(atan(sec(atan(sec(atan(sec(atan(sec(atan(sec(atan(sec(atan(sec(atan(sec(atan(4))))))))))))))))))

To get a particular number n requires k = n2-16 nestings. For more information, including how to derive numbers up to 4, see this description by Jim Millar.

• Primorial (Suggested by Chris Smith)

The primorial function, often written using the "#" symbol and it is the prime equivalent for factorial. So, for example, 4# is the product of the first 4 primes, 2*3*5*7=210.

(4+4/4)=3210 and (4+(4+4)/4)=30030.

• ceiling() and floor() (Suggested by Bruno Curfs)

An option that provides another solution for the pesky 113, namely the "ceiling(x)" function defined as the smallest integer greater than or equal to x. Written as //x\\, then //.4\\ = 1.

113 can be written as 4 * (4 + 4!) + //.4\\

Along the same lines, if floor(x) is the largest integer less than or equal to x, if floor(x) is written as \\x// then

113 = \\exp(4.4)// + root.4(4)

• Exactly 4 fours

A variation to the problems description above is to use exactly 4 fours. A list compiled by Sven Peterson is given here: 4_4_4_4.docx.

Suggested using 4/9900 = (4%)'% as well as other fractions, for example:

4/99900 = (.4%)'%

24/99900 = (4!‰)'%

2/9900 = (sqrt(4)%)'%

Also pointed out that from the definition of the gamma function, factorials can be defined for non-integer values, in particular

• Tetration (Suggested by Rizvan Dadaev)

Another candidate operator is tetration, repeated exponentiation. For example. 5a = a^(a^(a^(a^(a))))
See also: Tetration fractal. Here we will use the operator "^^" to represent tetration. This leads to some alternative solutions as follows.

sqrt(4)^^4 = 2^^4 = 2^(2^(2^2) = 2^16 = 65536

(sqrt(4)^^4)/4! - sqrt(.4') = 2730

(sqrt(4) /.4)^^sqrt(4) = 5^5 = 3125

(4!/4)^^sqrt(4) = 6^6 = 46656

((4!/4)^^sqrt(4) )/4! = 1944

sqrt( (sqrt(4/.4'))^^sqrt(4) ) = 19683

sqrt( (sqrt(4/.4'))^^sqrt(4) ) * .4' = 8748

sqrt( (sqrt(4/.4'))^^sqrt(4) ) * sqrt(.4') = 13122

(sqrt(4) ^^ 4) * .4 - .4 = 26214

(sqrt(4) ^^ 4) * .sqrt(4) - .sqrt(4) = 13107

(sqrt(4) ^^ 4) * (.sqrt(4))' + .4' = 14564

(sqrt(4) ^^ 4 + sqrt(4) ) * .4!' = 15888

sqrt( sqrt(sqrt(sqrt((4!/sqrt(.4'))^^sqrt(4))))/.4! ) = 6840

sqrt( sqrt(sqrt(sqrt((4!/sqrt(.4'))^^sqrt(4)))) * 4! ) = 15552

And there is a more esoteric solution for 2, namely the infinite tetration of the square root of 2.

sqrt(sqrt(4))^^(4/(4-4)) = sqrt(2)^^infinity = sqrt(2)^(sqrt(2)^(sqrt(2)^(sqrt(2)^ ... )))) = 2

The solutions so far

 ``` 0 2 4 - 4 4 (4+4) - (4+4) 1 2 4 / 4 4 (4+4) / (4+4) 2 1 sqrt(4) 4 ((4+4) ÷ sqrt(4)) / sqrt(4) 3 2 sqrt(4 / .4`) 3 4 - 4 / 4 4 (4+4+4) / 4 π 3 sqrt((-sqrt(4) / 4)!)^4 4 sqrt((sqrt(4)/4)!^4)*4 4 1 4 4 (4+4) - (sqrt(4)+sqrt(4)) 5 2 sqrt(4) / .4 4 (4+sqrt(4)) - (4/4) 6 2 4 + sqrt(4) 4 (4+sqrt(4)) / (4/4) 7 3 (4! + 4) / 4 4 4 + 4 - 4 / 4 8 2 4 + 4 4 (sqrt(4)+sqrt(4)) + (sqrt(4)+sqrt(4)) 9 2 4 / .4` 4 (4+4) + (4/4) `````` 10 2 4 / .4 4 (4+4) + (4/sqrt(4)) 11 3 44 / 4 4 (4! / sqrt(4)) - (4/4) 12 2 4! / sqrt(4) 3 4 + 4 + 4 4 (4×4) - (sqrt(4)+sqrt(4)) 13 3 (4! + sqrt(4)) / sqrt(4) 4 (4! / sqrt(4)) + (4/4) 14 3 4 * 4 - sqrt(4) 4 (4×4) - (4 / sqrt(4)) 15 3 (4 + sqrt(4)) / .4 4 4 * 4 - 4 / 4 2 sqrt(.4') / 4' % 16 2 4 * 4 4 (sqrt(4) * sqrt(4)) × (sqrt(4) * sqrt(4)) 17 4 4 * 4 + 4/4 3 (4 - .(sqrt(4))`) / .(sqrt(4))` 3 sqrt(4) + root(-sqrt(4), .4`%) 18 3 4 * 4 + sqrt(4) 2 4 / .(sqrt(4))' 4 (4 * 4) + (4 /sqrt(4)) 19 3 4! - sqrt(4) /.4 4 4! - (4 + (4/4)) 20 2 4! - 4 4 (4 * 4) + (sqrt(4)+sqrt(4)) 21 3 4! - sqrt(4) / sqrt(.4`) 4 4! - (4 - (4/4)) 22 2 4! - sqrt(4) 4 (4 * 4) + (4+sqrt(4)) 23 3 4! - 4 / 4 4 (4!-sqrt(4)) + (4/4) 24 1 4! 4 (4*4) + (4+4) 25 3 4! + 4 / 4 2 .(sqrt(4))^(-sqrt(4)) 2 sqrt(4% ^ -sqrt(4)) 4 (4!+sqrt(4)) - (4/4) 26 2 4! + sqrt(4) 4 4! + (sqrt(4) × (4/4)) 27 3 4! / (.4` * sqrt(4)) 4 4! + ((4+ sqrt(4)) / sqrt(4)) 28 2 4! + 4 4 4! + ((4 * 4) / 4) 29 3 4! + sqrt(4) / .4 4 (4!+4) + (4/4) 30 3 4! + 4 + sqrt(4) 2 sqrt(4) / sqrt(.4' %) 4 (4!+4) + (4+sqrt(4)) 31 4 4! + (4! + 4) / 4 3 (sqrt(4) + sqrt(.4' %)) / sqrt(.4' %) 32 3 4 * (4 + 4) 2 root.4(4) 4 (4*4) + (4*4) 33 4 (4!+4) + (sqrt(4) / 0.4) 3 4! + 4 / .4` 2 sqrt(.4') /(sqrt(4)%)' 34 3 4! + 4 / .4 4 (4!+sqrt(4)) + (4+4) 35 3 (4! - sqrt(.4`)) / sqrt(.4`) 4 ((4!+4) / 0.4) / sqrt(4) 36 4 4 * (4 + 4) + 4 3 4! + 4! / sqrt(4) 2 4! / sqrt(.4`) 37 3 (4! + sqrt(.4`)) / sqrt(.4`) 4 4! + ((4!+sqrt(4)) / sqrt(4)) 38 3 4! / sqrt(.4`) + sqrt(4) 4 (4!-sqrt(4)) + (4 * 4) 39 3 (sqrt(4) + 4!) / sqrt(.4`) 4 ((4 * 4) + 0.4) / 0.4 40 3 44 - 4 4 (4!+4!) - (4+4) 41 4 (4 * 4 + .4) / .4 3 (sqrt(4%) / .4`%) - 4 42 3 44 - sqrt(4) 4 (4!+4!) - (4+sqrt(4)) 43 4 44 - 4/4 3 (sqrt(4%) / .4`%) - sqrt(4) 44 2 44 4 (4!+4!) - (sqrt(4)+sqrt(4)) 45 3 (4! - 4) / .4` 2 sqrt(4) / 4' % 4 ((4 * 4) + sqrt(4)) / 0.4 46 3 44 + sqrt(4) 4 (4!+4!) - (4 / sqrt(4)) 47 4 4! + 4! - 4 / 4 3 sqrt(4) + (sqrt(4%) / .4`%) 48 2 4! + 4! 4 (4!+4!) ÷ (4/4) 49 4 4! + 4! + 4 / 4 3 .(sqrt(4))^(-sqrt(4)) + 4! 3 (sqrt(4) - 4%) / 4% 50 3 4! + 4! + sqrt(4) 2 sqrt(4) / 4 % 4 (4!+4!) + (4 / sqrt(4)) 51 4 (.4 + 4! - 4) / .4 3 (sqrt(4) + 4%) / 4% 52 3 4! + 4! + 4 4 (4!+4!) + (sqrt(4)+sqrt(4)) 53 3 (4! - .4`) / .4` 4 (4!+4!) + (sqrt(4) / .4) 54 2 4! /.4` 4 (4!+4!) + (sqrt(4)+4) 55 4 (4!/0.4) - (sqrt(2) / 0.4) 3 (4! - sqrt(4)) / .4 2 (sqrt(4))'% /(4%)'% 56 3 4! / .4 - 4 57 4 (4! + .4) / .4 - 4 3 (4 - sqrt(4%)) / sqrt(.4`%) 58 3 4! / .4 - sqrt(4) 59 3 (4! - .4) /.4 60 2 4! / .4 61 3 (4!+ .4) / .4 62 3 4! / .4 + sqrt(4) 63 3 (4! + 4) / .4` 64 2 sqrt(sqrt(sqrt(4^(4!)))) 65 3 (4! + sqrt(4)) / .4 66 3 sqrt(sqrt(sqrt(4^(4!)))) + sqrt(4) 3 44 / sqrt(.4`) 67 4 sqrt(4) + (4! + sqrt(4)) / .4 68 3 44 + 4! 69 4 (4! + 4 - .4) / .4 3 4! + (sqrt(4%) / .4`%) 70 3 (4! + 4) / .4 71 4 (4! + 4.4) / .4 72 3 4! + 4! + 4! 73 4 sqrt(sqrt(sqrt(4^(4!)))) + 4 / .4` 74 4 4! + 4! + 4! + sqrt(4) 3 (sqrt(4) / 4%) + 4! 75 4 (4! + 4 + sqrt(4)) / .4 3 4! / root(.4, 4)% 76 4 4! + 4! + 4! + 4 3 4! / .(4!) - 4! 3 (4 / 4%) - 4! 77 4 4! / (.4` * sqrt(.4`)) - 4 78 3 4! + 4! / .4` 79 4 4! + (4! - sqrt(4)) / .4 80 3 4 * (4! - 4) 81 3 (4 / .4')^sqrt(4) 82 4 4 * (4! - 4) + sqrt(4) 83 4 4! - (.4 - 4!) / .4 84 3 4! / .4 + 4! 85 4 (4! + 4 / .4) / .4 3 (.4` - sqrt(.4`%)) / .4`% 86 4 44 * sqrt(4) - sqrt(4) 3 (.4 / .4`%) - 4 87 4 4 * 4! - 4 / .4` 88 3 44 * sqrt(4) 89 4 (4! + sqrt(4)) / .4 + 4! 3 (.4 - .4`%) / .4`% 90 3 4 / (.4` - .4) 2 .4 / .4`% 91 4 4 * 4! - sqrt(4) / .4 3 (.4` - 4%) / .4`% 92 3 4 * 4! - 4 93 4 4 * 4! - sqrt(4) / sqrt(.4`) 94 3 4 * 4! - sqrt(4) 95 4 4 * 4! - 4/4 3 (4 - sqrt(4%)) / 4% 96 2 4 * 4! 97 4 4 * 4! + 4/4 3 (sqrt(.4`) - sqrt(4)%) / sqrt(.4`)% 98 3 4 * 4! + sqrt(4) 99 3 44 / .4` 2 4! / .(4!)' `````` 100 3 4 * 4! + 4 2 4! / .(4!) 2 4 / 4% 101 4 4 * 4! + sqrt(4) / .4 3 (4 + 4%) / 4% 102 4 4 * 4! + 4 + sqrt(4) 3 4! / .(4!) + sqrt(4) 3 (4 / 4%) + sqrt(4) 103 4 44 / .4` + 4 3 (sqrt(4)% + sqrt(.4`)) / sqrt(.4`)% 104 3 4 * (4! + sqrt(4)) 105 4 (44 - sqrt(4)) / .4 3 (4 + sqrt(4%)) / 4% 106 4 44 / .4 - 4 3 (4 + 4!%) / 4% 107 4 (4! + 4! - .4`) / .4` 3 (4! - .(sqrt(4))`) / .(sqrt(4))` 108 3 (4! + 4!) / .4` 2 4!/.(sqrt(4))` 109 4 (44 - .4) / .4 3 (4! + .(sqrt(4))`) / .(sqrt(4))` 3 (4% + .4`) / .4`% 110 3 44 / .4 111 4 444/4 112 3 4 * (4! + 4) 113 4 4!/.(sqrt(4))` + sqrt(4)/.4 4 (.4 - .4`%) / .4`% + 4! 4 ( sqrt(4) / .4' + sqrt(4)% ) / 4% 4 (sqrt(4) + (sqrt(4) + 4!)%) / (sqrt(4))% 3 (.(sqrt(4))' / (.(sqrt(4)) % )') + sqrt(4) 114 4 44 / .4 + 4 3 4! + (.4 / .4`%) 115 4 (44 + sqrt(4)) / .4 3 (.4` + sqrt(.4`%)) / .4`% 116 3 (sqrt(4) / .4)! - 4 117 4 (4! + 4! + 4) / .4` 118 3 (sqrt(4) / .4)! - sqrt(4) 119 4 (4! + 4! - .4) / .4 3 (4! - sqrt(4%)) / sqrt(4%) 120 2 (sqrt(4) / .4)! 121 4 (44 / 4) ^ sqrt(4) 3 (4! + sqrt(4%)) / sqrt(4%) 122 3 (sqrt(4) / .4)! + sqrt(4) 123 4 44 / .4` + 4! 124 3 (sqrt(4) / .4)! + 4 125 4 (4! - 4) / (.4 * .4) 3 sqrt(sqrt(sqrt((sqrt(4) / .4)^(4!)))) 2 sqrt(sqrt(sqrt(.(sqrt(4))))^(-4!) 126 4 4^4 / sqrt(4) - sqrt(4) 3 (4! + 4) / .(sqrt(4))` 3 (sqrt(.4`) / .4`%) - 4! 127 4 (4^4 - sqrt(4)) / sqrt(4) 128 3 4^4 / sqrt(4) 129 4 (4^4 + sqrt(4)) / sqrt(4) 130 4 4^4 / sqrt(4) + sqrt(4) 3 (sqrt(4) + 4!) / sqrt(4%) 131 4 4! / (.4 * .4`) - 4 132 4 4^4 / sqrt(4) + 4 133 4 4! / (.4 * .4`) - sqrt(4) 134 4 4! + 44 / .4 135 3 4! / (.4 * .4`) 136 4 4 * ( 4! + 4 / .4) 3 (4!% + sqrt(.4`)) / sqrt(.4`)% 137 4 4! / (.4 * .4`) + sqrt(4) 138 4 (4! * 4! - 4!) / 4 139 4 4! / (.4 * .4`) + 4 140 4 4 * 4! + 44 3 (4! + 4) / .(sqrt(4)) 3 (4 + 4!) / sqrt(4%) 141 4 (4 * 4! - sqrt(4)) / sqrt(.4`) 3 (sqrt(.4`) - 4%) / .4`% 142 4 4! * 4! / 4 - sqrt(4) 143 4 (4! * 4! - 4) / 4 144 3 4! * 4! / 4 145 4 (4 + 4! * 4!) / 4 3 (sqrt(4%) + .4`) / .4`% 146 4 4! / .4 / .4 - 4 3 (sqrt(.4`) / .4`%) - 4 147 4 (4 * 4! + sqrt(4)) / sqrt(.4`) 148 4 4 + 4! * 4! / 4 3 (sqrt(.4`) / .4`%) - sqrt(4) 149 4 (4! / .4 - .4) / .4 3 (sqrt(.4`) - .4`%) / .4`% 150 3 4! / (.4 * .4) 2 sqrt(.4') / .4' % 151 4 (4! / .4 + .4) / .4 3 (sqrt(.4`) + .4`%) / .4`% 152 4 4 * 44 - 4! 3 sqrt(4) + (sqrt(.4`) / .4`%) 153 4 (44 + 4!) / .4` 154 4 4 + 4! / .4 / .4 3 4 + (sqrt(.4`) / .4`%) 155 4 (4! / .4 + sqrt(4)) / .4 156 4 (4! + sqrt(4)) * (4 + sqrt(4)) 157 4 4^4 - 4! / .(4!)' 4 ((4% + sqrt(.4`)) / .4`%) - sqrt(4) 158 4 sqrt(sqrt(sqrt(4^4!))) / .4 - sqrt(4) 159 4 4! / .4 / .4` + 4! 3 (4% + sqrt(.4`)) / .4`% 160 3 sqrt(sqrt(sqrt(4^4!))) / .4 161 4 (sqrt(sqrt(sqrt(4^4!))) + .4) / .4 162 4 (4! * 4 - 4!) / .4` 3 4! / sqrt(.4') / .(sqrt(4))' 163 4 (4! / sqrt(.4`) + .(sqrt(4))`) / .(sqrt(4))` 4 ((4 + 4!)% + .4`) / .4`% 164 4 (sqrt(4) / .4)! + 44 165 4 44 / .4 / sqrt(.4`) 2 .4 / .(4!)' % 3 (sqrt(.4`) - sqrt(.4`)%) / .4% 166 4 4! / (sqrt(.4') * .(sqrt(4))') + 4 4 (sqrt(.4)^(-4) + sqrt(.4')) * 4! 3 (sqrt(.4`) / .4%) - sqrt(.4`) 167 4 (sqrt(.4') / .4 % ) + (sqrt(.4') / sqrt(4)) 4 .4 / (.4!' - .4!) + sqrt(4) 168 4 (4! + 4) * (4 + sqrt(4)) 169 4 (4! + sqrt(4))^sqrt(4) / 4 170 4 (44 + 4!) / .4 171 4 (.4 / .(4!)' %) + sqrt(4) + 4 4 ((4 / 4%) - 4!) / .4` 172 4 4 * 44 - 4 173 4 ((4!/4)! * .(4!)) + .(sqrt(4)) 4 (4 - (4! / .4`)%) / sqrt(4)% 174 4 4 * 44 - sqrt(4) 3 4! + (sqrt(.4`) / .4`%) 175 4 (4! + 4) / (.4 * .4) 176 3 4 * 44 177 4 ((sqrt(4) / .4)! - sqrt(4)) / sqrt(.4`) 178 4 4 * 44 + sqrt(4) 179 4 ((4! / 4)! - 4) / 4 180 3 (4 + sqrt(4))! / 4 2 .4 / .(sqrt(4))' % 181 4 ((4! / 4)! + 4) / 4 182 4 sqrt(4) + (4! / 4)! / 4 183 4 ((sqrt(4) / .4)! + sqrt(4)) / sqrt(.4`) 184 4 4 * (sqrt(4) + 44) 185 4 44.4 / .(4!) 4 44.4 / 4!% 186 4 ((4! / 4)! + 4!) / 4 187 4 (4 - .(4!) - sqrt(4) % ) / sqrt(4) % 4 (4 - (sqrt(4) + 4!)%) / sqrt(4)% 4 (4 - .(sqrt(4))') / (.(4!)' - .(sqrt(4))') 188 4 4 * (4! + 4!) - 4 3 (4 - 4!%) / sqrt(4)% 189 4 (4! / .4 + 4!) / .4` 190 4 4! (4 + 4) - sqrt (4) 3 (.4 + .4`) / .4`% 191 4 (.4' % + .4 + .4') / .4' % 192 3 4 * (4! + 4!) 193 4 (4 + .(sqrt(4))' + sqrt(.4' % )) / (sqrt(4) % )' 4 sqrt(.4`% ^ -sqrt(4)) - root(.4, 4) 194 4 4! (4 + 4) + sqrt (4) 195 4 (4! / .4` + 4!) / .4 3 (sqrt(4%) + sqrt(.4`)) / .4`% 196 4 sqrt(4) * (4 * 4! + sqrt(4)) 3 (4 / sqrt(4)%) - 4 197 4 (44 - .(sqrt(4)')) / .(sqrt(4)') 4 (4 - (4 + sqrt(4))%) / sqrt(4)% 198 4 (4! - sqrt(4)) * 4 / .4` 3 44 / .(sqrt(4)') 3 (4 / sqrt(4)%) - sqrt(4) 199 4 (44 + .(sqrt(4)')) / .(sqrt(4)') 4 4!/.(4!)' + 4!/(4!) 3 (4 - sqrt(4)%) / sqrt(4)% 200 4 4 * 44 + 4! 2 .4' / .(sqrt(4))' % 2 4 / sqrt(4)% 201 4 ((4!) - (sqrt(sqrt(sqrt(.4))))^(-4!)) * (4!) 3 (4 + sqrt(4)%) / sqrt(4)% 202 4 4^4 - 4! / .4` 3 (4 / sqrt(4)%) + sqrt(4) 203 3 (.4' + sqrt(.4') % / .(sqrt(4))' % 4 (4 + (4 + sqrt(4))%) / sqrt(4)% 204 4 4! + (4! / 4)! / 4 3 4 + (4 / sqrt(4)%) 205 4 ((sqrt(4) / 4' %) - 4) / .(sqrt(4)) 4 (4 + (.4 / 4)) / sqrt(4)% 206 4 (4! / .(4!)' + 4) * sqrt(4) 4 4 ^ 4 - (sqrt(4) / 4%) 207 4 (4 * 4! - 4) / .4` 208 4 4^4 - 4! - 4! 209 4 ((sqrt(4) / 4 % ) + sqrt(.4')) / .(4!)' 4 (4 / sqrt(4)%) + (4 / .4`) 210 4 (4! / .4 + 4!) / .4 3 (4 + sqrt(4%)) / sqrt(4)% 211 4 ((.4 * 4!) - .sqrt(4))') / 4' % 4 4 ^ 4 - (sqrt(4%) / .4`%) 212 4 4^4 - 44 3 (4 + 4!%) / sqrt(4)% 213 4 (4! * sqrt(4) - sqrt(.4')) / .(sqrt(4))' 4 (4 + (sqrt(4) + 4!)%) / sqrt(4)% 214 4 4! * 4 / .4` - sqrt(4) 215 4 (4 * 4! - .4`) / .4` 216 3 4 * 4! / .4` 217 4 (4 * 4! + .4') / .4' 218 4 4! * 4 / .4` + sqrt(4) 219 4 (root.4(4/.4')) - 4! 220 4 44 * sqrt(4) / .4 3 44 / sqrt(4%) 221 4 (44 + .(sqrt(4))) / .(sqrt(4) 3 sqrt(.4`% ^ -sqrt(4)) - 4 222 4 444 / sqrt(4) 223 4 ((4! / .(4!)) / .4') - sqrt(4) 3 sqrt(.4`% ^ -sqrt(4)) - sqrt(4) 224 4 (4 + 4) * (4! + 4) 3 (4 / sqrt(4)%) + 4! 225 4 ((sqrt(4) + 4) / .4)^sqrt(4) 2 sqrt(.4`% ^ -sqrt(4)) 226 4 ((4! / .(4!)) + .4') / .4' 3 sqrt(.4% ^ -sqrt(4)) - 4! 227 4 ((4! / .(4!)) / .4') + sqrt(4) 3 sqrt(4) + sqrt(.4`% ^ -sqrt(4)) 228 4 4^4 - 4! - 4 229 4 ((4! / .(4!)) / .4') + 4 3 4 + sqrt(.4`% ^ -sqrt(4)) 230 4 (4 * 4! - 4) / .4 231 4 (sqrt(4) + 4! / .4') / .(4!)' 4 ((4 / .4`%) + 4!) / 4 232 3 4^4 - 4! 233 4 (4! / .(sqrt(4))') + sqrt(sqrt(sqrt(.(sqrt(4)))) ^ (- 4!) 4 4 + 4 + sqrt(.4`% ^ -sqrt(4)) 234 4 4^4 - 4! + sqrt(4) 235 4 (4 * 4! - sqrt(4)) / .4 236 4 4^4 - 4! + 4 237 4 (4 * 4) - .(sqrt(4)) / sqrt(.4' %) 4 ((4 * 4) - sqrt(4%)) / sqrt(.4`%) 238 4 4! * 4 /.4 - sqrt(4) 239 4 (4 * 4! - .4) / .4 240 3 4 * 4! / .4 241 4 (4 * 4! + .4) / .4 242 4 4! * 4 / .4 + sqrt(4) 243 4 sqrt(4) * 4! / (.4` * .4`) 3 root(sqrt(4%), sqrt(4 / .4`)) 244 4 4^4 - 4! / sqrt(4) 245 4 (4 * 4! + sqrt(4)) / .4 246 4 4^4 - 4 / .4 3 sqrt(.4% ^ -sqrt(4)) - 4 247 4 4^4 - 4 / .4` 248 4 4^4 - 4 - 4 3 sqrt(.4% ^ -sqrt(4)) - sqrt(4) 249 4 ((4!/.4) - .(4!)) / .(4!) 3 4! + sqrt(.4`% ^ -sqrt(4)) 250 4 (4 * 4! + 4) / .4 2 sqrt(.4% ^ -sqrt(4)) 251 4 4^4 - sqrt(4) / .4 252 3 4^4 - 4 253 4 4^4 - sqrt(4) / sqrt(.4`) 254 3 4^4 - sqrt(4) 255 4 4^4 - 4/4 256 2 4^4 257 4 4^4 + 4/4 258 3 4^4 + sqrt(4) 259 4 4^4 + sqrt(4) / sqrt(.4`) 260 3 4^4 + 4 261 4 4^4 + sqrt(4) / .4 262 4 4^4 + 4 + sqrt(4) 263 4 (sqrt(sqrt(sqrt(4^4!))) - .(4!)') / .(4!)' 4 (sqrt(4) - (4! + sqrt(.4`))%) / sqrt(.4`)% 264 4 44 * (4 + sqrt(4)) 3 (sqrt(4) - 4!%) / sqrt(.4`)% 265 4 4^4 + 4 / .4` 266 4 4^4 + 4 / .4 267 4 (root.4(4/.4')) + 4! 268 4 4^4 + 4! / sqrt(4) 269 4 ((sqrt(4) / .4)! - .4`) / .4` 270 3 (sqrt(4) / .4)! / .4` 271 4 ((sqrt(4) / .4)! + .4`) / .4` 272 4 4^4 + 4 * 4 273 4 ((4! / .4) + .4') / .(sqrt(4))' 4 ((sqrt(4) - sqrt(4)%) / sqrt(.4`)%) - 4! 274 4 (sqrt(4) / .4)! / .4` + 4 3 4! + sqrt(.4% ^ -sqrt(4)) 275 4 44 / .4 / .4 2 sqrt(.4') / .(4!)' % 276 4 4^4 + 4! - 4 3 (sqrt(4) / sqrt(.4`)%) - 4! 277 4 ((sqrt(.4') + .(sqrt(4))' % ) / .(sqrt(4))' % ) - 4! 4 ((sqrt(4) + sqrt(.4`)%) / sqrt(.4`)%) - 4! 278 4 4^4 + 4! - sqrt(4) 279 4 ((sqrt(4) / .4)! + 4) / .4` 4 (((sqrt(sqrt(sqrt(.4))))^(-4!)) - (4)) * (4!) 280 3 4^4 + 4! 281 4 .(sqrt(4))^(-sqrt(4)) + 4^4 4 4 ^ 4 + sqrt(4% ^ -sqrt(4)) 282 4 4^4 + 4! + sqrt(4) 283 4 (sqrt(.4') - 4 % + .(sqrt(4))' % / .(sqrt(4))' % 4 sqrt (.4') / .4!'% + 4 + 4 284 4 4^4 + 4! + 4 285 4 (sqrt(sqrt(sqrt(4^4!))) - .4') / .(sqrt(4))' 4 (4! + (.4 / .4`%)) / .4 286 4 (4! * 4! / sqrt (4)) - sqrt (4) 287 4 (4! * 4! - sqrt(4)) / sqrt(4) 288 3 (4 + sqrt(4))! * .4 289 4 (sqrt(4) + 4! * 4!) / sqrt(4) 290 4 (4! * 4! / sqrt (4)) + sqrt(4) 3 (sqrt(4) - sqrt(.4`%)) / sqrt(.4`)% 291 4 (sqrt(sqrt(sqrt(4^4!))) + .4') / .(sqrt(4))' 4 (sqrt(4 * .4`) - 4%) / .4`% 292 4 (4! * 4! / sqrt (4)) + 4 293 4 ((sqrt(.4') - sqrt(4) % ) / .(sqrt(4))' % ) + sqrt(4) 4 ((sqrt(4) - sqrt(4)%) / sqrt(.4`)%) - 4 294 4 (sqrt(4) / .4)! / .4` + 4! 3 (sqrt(4) - 4%) / sqrt(.4`)% 295 4 ((sqrt(4) / .4)! - sqrt(4)) / .4 296 4 (sqrt(4) / .4)! / .4 - 4 3 (sqrt(4) / sqrt(.4`)%) - 4 297 4 4! / .(4!)' * sqrt(4 / .4') 3 (sqrt(4) - sqrt(4)%) / sqrt(.4`)% 298 4 (sqrt(4) / .4)! / .4 - sqrt(4) 3 (sqrt(4) / sqrt(.4`)%) - sqrt(4) 299 4 ((sqrt(4) / .4)! - .4) / .4 3 (sqrt(4) - sqrt(.4`)%) / sqrt(.4`)% 300 3 (sqrt(4) / .4)! / .4 2 sqrt(.4') / .(sqrt(4))' % 2 sqrt(4) / sqrt(.4`)% 301 4 (.4 + (sqrt(4) / .4)!) / .4 3 (sqrt(4) + sqrt(.4`)%) / sqrt(.4`)% 302 4 sqrt(4) + (sqrt(4) / .4)! / .4 3 sqrt(4) + (sqrt(4) / sqrt(.4`)%) 303 4 ((4! / sqrt(4)) + .(4!)') / .4'% 3 (sqrt(4) + sqrt(4)%) / sqrt(.4`)% 304 4 4^4 + 4! + 4! 3 4 + (sqrt(4) / sqrt(.4`)%) 305 4 (sqrt(4) + (sqrt(4) / .4)!) / .4 306 4 (4 + sqrt(sqrt(sqrt(4^4!)) / .(sqrt(4))' 3 (sqrt(4) + 4%) / sqrt(.4`)% 307 4 (.(4!) + .4' - .(sqrt(4))' % ) / .(sqrt(4))' % 4 4 + ((sqrt(4) + sqrt(4)%) / sqrt(.4`)%) 308 4 (4 + (sqrt(.4') / .4' % )) * sqrt(4) 309 4 (sqrt(.4' * 4) + 4 % ) / .4' % 310 4 (4 + (sqrt(4) / .4)!) / .4 3 (sqrt(4) + sqrt(.4`%)) / sqrt(.4`)% 311 4 (sqrt(.4') + (4 % )' - sqrt(4) % ) / .(sqrt(4))' % 4 (sqrt(sqrt(4) - 4%) / .4`%) - 4 312 4 (4 + sqrt(4))! * .4 + 4! 313 4 (.(sqrt(4)) + (.(sqrt(4)) ^ -(sqrt(sqrt(sqrt((4!))))) / .4 4 (sqrt(sqrt(4) - 4%) / .4`%) - sqrt(4) 314 4 ((sqrt(.4') - sqrt(4)' % ) / .(sqrt(4)' % ) + 4! 4 4 + ((sqrt(4) + sqrt(.4`%)) / sqrt(.4`)%) 315 4 (4! / sqrt(.4' %)) - (sqrt(4) / 4' %) 3 sqrt(sqrt(4) - 4%) / .4`% 316 4 4^4 + 4! / .4 317 4 ((sqrt(.4') + 4 % - .(sqrt(4))' % ) / .(sqrt(4))' % 4 sqrt(4) + (sqrt(sqrt(4) - 4%) / .4`%) 318 4 (4 + sqrt(4))! * .4` - sqrt(4) 319 4 (sqrt(sqrt(sqrt(4 ^ 4!)))) - .(sqrt(4))) / .(sqrt(4)) 4 4 + (sqrt(sqrt(4) - 4%) / .4`%) 320 3 (4 + sqrt(4))! * .4` 321 4 (sqrt(sqrt(sqrt(4 ^ 4!) + .(sqrt(4))) / .(sqrt(4) 4 ((sqrt(.4`) / .4%) - 4!) / .4` 322 4 (4 + sqrt(4))! * .4` + sqrt(4) 323 4 ((sqrt(.4') - .(sqrt(4))' % ) / .(sqrt(4))' % ) + 4! 4 ((sqrt(4) - sqrt(.4`)%) / sqrt(.4`)%) + 4! 324 4 (4 * 4 + sqrt(4))^sqrt(4) 3 (sqrt(4) / sqrt(.4`)%) + 4! 325 4 (4! + sqrt(4))! / (4!)! / sqrt(4) 326 4 (4! - sqrt(4)) / sqrt(.4' %)) - 4 327 4 ((sqrt(sqrt(sqrt(.4))))^(-4!) - sqrt(4)) * 4! 328 4 (4! / sqrt(.4' % )) - root.4(4) 329 4 (4! - (sqrt(4) + sqrt(.4' %))) / sqrt(.4' %) 330 4 (root.4(4) / .4) / .(4!)' 3 (4! - sqrt(4)) / sqrt(.4`%) 331 4 (sqrt(.4' %) - sqrt(4) + 4!) / sqrt(.4' %) 332 4 (4! / sqrt(.4' %)) - (4 + 4!) 333 4 (4! - sqrt(4) + .(sqrt(4))) / sqrt(.4' % ) 3 (sqrt(.4`) - sqrt(.4`%)%) / sqrt(4%)% 334 4 (4! / sqrt(.4' %)) - (sqrt(4) + 4!) 3 (sqrt(.4`) / sqrt(4%)%) + sqrt(.4`) 335 4 (4! / sqrt(.4' %)) - .(sqrt(4)) ^ - (sqrt(4)) 4 (4 + sqrt(4)%) / (sqrt(4) / .4)!%% 336 4 4! * (4! + 4) / sqrt(4) 3 (4! / sqrt(.4`%)) - 4! 337 4 ((4! + sqrt(.4' % )) / sqrt(.4' % )) - 4! 338 4 (4! + sqrt(4))^sqrt(4) / sqrt(4) 339 4 ((sqrt(.4') / 4' % ) + sqrt(.4' % )) / 4' %) 340 4 (4! / sqrt(.4' %)) - (4! - 4) 4 (sqrt (sqrt (sqrt (4 ^ 4!))) + 4) / .sqrt (4) 341 4 (sqrt(4) - .4' - 4 % ) / .4' % 342 4 (root(.(sqrt(4))' ,4) * sqrt(.4')) + sqrt(.4') 4 (4 - sqrt(4%)) * .4 / .4`% 343 4 sqrt(sqrt(sqrt((sqrt(4) + sqrt(4) / .4))))^4! 344 4 (4 + sqrt(4))! * .4` + 4! 345 4 (4! / sqrt(.4' %)) - (sqrt(.4') / 4' %) 346 4 ((4! - sqrt(.4')) / sqrt(.4' % )) - 4 347 4 ((4! - sqrt(.4') - .(sqrt(4))) / sqrt(.4' % ) 4 (4! - (sqrt(4%) + sqrt(.4`))) / sqrt(.4`%) 348 4 ((4! / 4)! - 4!) / sqrt(4) 349 4 ((4! - sqrt(.4') - sqrt(.4' % )) / sqrt(.4' % ) 350 4 (4! - (4 / .4)) / 4% 3 (sqrt(4) - .4`) / .4`% 4 (4! /. 4 + 4!) / .4! 351 4 4! / sqrt(sqrt(sqrt(.4^(4!)))) - 4! 352 4 44 * (4 + 4) 353 4 ((4! - sqrt(.4') + .(sqrt(4))) / sqrt(.4' % ) 4 ((4! - sqrt(4%)) / sqrt(.4`%)) - 4 354 4 (sqrt(4) / .4' %) - (4 * 4!) 3 (4! - .4) / sqrt(.4`%) 355 4 4^4 + 4! / .(4!)' 4 ((4 * .4`) - sqrt(4%)) / .4`% 356 4 (4! / 4)! / sqrt(4) - 4 3 (4! / sqrt(.4`%)) - 4 357 3 (4! - .(sqrt(4))) / sqrt(.4' %) 3 (4! - sqrt(4%)) / sqrt(.4`%) 358 4 ((4! / 4)! - 4) / sqrt(4) 3 (4! / sqrt(.4`%)) - sqrt(4) 359 4 ((4! / 4)! - sqrt(4)) / sqrt(4) 3 (4! - sqrt(.4`%)) / sqrt(.4`%) 360 3 (sqrt(4) + 4)! / sqrt(4) 2 4! / sqrt(.4' % ) 361 4 (sqrt(4) + (4! / 4)!) / sqrt(4) 3 (4! + sqrt(.4`%)) / sqrt(.4`%) 362 4 ((4! / 4)! + 4) / sqrt (4) 3 sqrt(4) + (4! / sqrt(.4`%)) 363 4 44 * sqrt(4) / .(4!)' 3 (4! + sqrt(4%)) / sqrt(.4`%) 364 4 4 + (4! / 4)! / sqrt(4) 3 4 + (4! / sqrt(.4`%)) 365 4 (4! / sqrt(.4' %)) + (sqrt(4) / .4) 366 4 (4! / sqrt(.4' %)) + (4! / 4) 3 (4! + .4) / sqrt(.4`%) 367 4 (4! + sqrt(.4') - .(sqrt(4))) / sqrt(.4' % ) 4 4 + ((4! + sqrt(4%)) / sqrt(.4`%)) 368 4 4 * (4 * 4! - 4) 369 4 .(sqrt(4))^(-4) - 4^4 4 4% ^ -sqrt(4) - 4 ^ 4 370 4 (4! / sqrt(.4' %)) + (4 / .4) 3 (4! + sqrt(.4`)) / sqrt(.4`%) 371 4 4! / sqrt(sqrt(sqrt(.4^(4!)))) - 4 372 4 (4! + (4! / 4)!) / sqrt(4) 373 4 4! / sqrt(sqrt(sqrt(.4^(4!)))) - sqrt(4) 374 4 (.(sqrt(4)) ^ - (sqrt(4)) - (sqrt(.4' %)) / sqrt(.4' %) 4 ((sqrt(4) - .4`) / .4`%) + 4! 375 4 .4 * 4! / .4^4 3 4! / sqrt(sqrt(sqrt(.4 ^ (4!))) 376 4 (4! - 4)^sqrt(4) - 4! 377 4 4! / sqrt(sqrt(sqrt(.4^(4!)))) + sqrt(4) 378 4 (4^4 - 4) / sqrt(.4`) 379 4 4! / sqrt(sqrt(sqrt(.4^(4!)))) + 4 380 4 4 * 4 * 4! - 4 381 4 (4^4 - sqrt(4)) / sqrt(.4`) 382 4 4 * 4 * 4! - sqrt(4) 383 4 (4^4 - sqrt(.4`)) / sqrt(.4`) 384 3 4 * 4 * 4! 385 4 (4^4 + sqrt(.4`)) / sqrt(.4`) 386 4 4 * 4 * 4! + sqrt(4) 387 4 (4^4 + sqrt(4)) / sqrt(.4`) 388 4 4 * 4 * 4! + 4 389 4 (sqrt(4) + 4! - sqrt(.4`%)) / sqrt(.4`%) 390 4 (4^4 + 4) / sqrt(.4`) 3 (sqrt(4) + 4!) / sqrt(.4`%) 391 4 (sqrt(.4' %) + sqrt(4) + 4!) / sqrt(.4' %) 392 4 4 * (4 * 4! + sqrt(4)) 393 4 (.(sqrt(4)) + sqrt(4) + 4!) / sqrt(.4' %) 4 (sqrt(4) + 4! + sqrt(4%)) / sqrt(.4`%) 394 4 ((4*4!) / .(4!)') - sqrt(4) 4 ((4 * 4) - 4!%) / 4% 395 4 ((4*4!) - .(4!)') / .(4!)' 4 ((4 * 4) - sqrt(4%)) / 4% 396 4 (4! - 4)^sqrt(4) - 4 3 ((4*4!) / .(4!)') 3 (sqrt(4) - 4!%) / .4`% 397 4 ((4*4!) + .(4!)') / .(4!)' 4 (sqrt(4) - (4! - .4`)%) / .4`% 398 4 (4! - 4)^sqrt(4) - sqrt(4) 399 4 (4! / sqrt(sqrt(sqrt(.4^(4!))))) + 4! 400 3 (4! - 4)^sqrt(4) 401 4 (.(4!) + (4! * 4)) / .(4!) 4 ((4 * 4) + 4%) / 4% 402 4 (4! - 4)^sqrt(4) + sqrt(4) 403 4 ((sqrt(4) - .(sqrt(4))) / .4' % ) - sqrt(4) 3 (4 + 4)!% - sqrt(4%) 404 4 (4! - 4)^sqrt(4) + 4 405 4 (4 + sqrt(4))! / 4 / .4` 3 (sqrt(4) - sqrt(4%)) / .4`% 406 4 ((sqrt(4) - .(sqrt(4)) + .4' % ) / .4' % 4 (sqrt(4) / .4`%) - 44 407 4 ((sqrt(4) - .(sqrt(4))) / .4' % ) + sqrt(4) 4 4 + (4 + 4)!% - sqrt(4%) 408 4 4 * 4 * 4! + 4! 409 4 ((sqrt(4) - .(sqrt(4))) / .4' % ) + 4 4 ((4 * .4`) + 4%) / .4`% 410 4 ((4 * 4) + .4) / 4% 411 4 ((sqrt(4) - sqrt(.4' % )) / .4' % ) - 4! 412 4 ((4! / .(4!)') + 4) * 4 4 (4 + 4 + 4!%) / sqrt(4)% 413 4 root(.(sqrt(4))' ,4) - (4! / .(4!)') 414 4 ((4*4!) - 4) / .(sqrt(4)') 4 (sqrt(4) - (4 * 4)%) / .4`% 415 4 (sqrt(4) - .(sqrt(4)) + 4' % ) / .4' % 4 ((4 / 4%) - .4) / 4!% 4 (4! /. 4! - .4) / .4! 416 4 4 * 4 * (4! + sqrt(4)) 417 4 (4 - .(sqrt(4)) + 4!) / sqrt(.4'%) 4 ((sqrt(4) - 4%) / .4`%) - 4! 418 4 (sqrt(4) / .4' %) - root(.4,4) 419 4 (4 + 4! - sqrt(.4' %)) / sqrt(.4' %) 420 4 444 - 4! 3 (4 + 4!) / sqrt(.4`%) 421 4 (sqrt(.4') + 4 + 4!) / sqrt(.4' %) 4 4 ^ 4 + .4 / .4!'% 422 4 (sqrt(4) / .4' %) - (4 + 4!) 423 4 (((sqrt(sqrt(sqrt(.4))))^(-4!)) + (sqrt(4))) * (4!) 424 4 (4! - 4)^sqrt(4) + 4! 425 4 ((sqrt(4) - .4' % ) / .4' % ) - 4! 426 4 4! * (4! - .4^(-sqrt(4))) 3 (sqrt(4) / .4`%) - 4! 427 4 ((sqrt(4) + .4' % ) / .4' % ) - 4! 4 (4 + 4)!% + 4! - .sqrt(4) 428 4 (4*4!) / .sqrt(4)' - 4 4 sqrt(4) + (sqrt(4) / .4`%) - 4! 429 4 ((4*4!) - .4') / .(sqrt(4))' 4 (4! + (sqrt(.4`) / .4%)) / .4` 430 4 (4*4!) / .sqrt(4)' - sqrt(4) 4 ((4 / .4`) - .4) / sqrt(4)% 431 4 ((4*4!) - .sqrt(4)') / .sqrt(4)' 4 ((sqrt(4) - sqrt(.4`%)) / .4`%) - 4 432 4 4! * (4 * 4 + sqrt(4)) 3 (4*4!) / .sqrt(4)' 433 4 ((4*4!) + .sqrt(4)') / .sqrt(4)' 4 ((sqrt(4) - sqrt(.4`%)) / .4`%) - sqrt(4) 434 4 (4*4!) / .sqrt(4)' + sqrt(4) 4 (sqrt(4) / .4`%) - (4 * 4) 435 4 ((4*4!) + .4') / .(sqrt(4))' 3 (sqrt(4) - sqrt(.4`%)) / .4`% 436 4 (4*4!) / .sqrt(4)' + 4 4 4 * (4% + .4`) / .4`% 437 4 ((sqrt(4) - 4 %) / .4' % ) - 4 438 4 (sqrt(4) / .4' %) - (4! / sqrt(4)) 4 sqrt(4) /. 4'% - 4! / sqrt(4) 439 4 ((sqrt(4) - 4 % ) / .4' % ) - sqrt(4) 440 4 444 - 4 3 (sqrt(4) - 4!%) / .4% 441 4 (4! - sqrt(4) / sqrt(.4`))^sqrt(4) 3 (sqrt(4) - 4%) / .4`% 442 4 444 - sqrt(4) 443 4 ((sqrt(4) - 4 % ) / .4' % ) + sqrt(4) 444 3 444 445 4 (sqrt(4) / .4' %) - (sqrt(4) / .4) 446 4 444 + sqrt(4) 3 (sqrt(4) / .4`%) - 4 447 4 ((sqrt(4) / .4'% ) - (sqrt(4 / .4') 4 (4! /.4! - sqrt(.4 ')) / .sqrt(4)' 448 4 444 + 4 3 (sqrt(4) / .4`%) - sqrt(4) 449 4 (4! / .(sqrt(4))' - .(4!)) / .(4!) 3 (sqrt(4) - .4`%) / .4`% 450 4 (4! / 4)! / 4 / .4 2 sqrt(4) / .4' % 451 4 (4! / .(sqrt(4)) + .(4!)) / .(4!) 3 (sqrt(4) + .4`%) / .4`% 452 4 root(.(sqrt(4))' ,4) - (4! / .4) 3 sqrt(4) + (sqrt(4) / .4`%) 453 4 ((4! / .(4!)) + sqrt(.4')) / .(sqrt(4))' 4 4 + ((sqrt(4) - .4`%) / .4`%) 454 4 (4! / .(4!) / .(sqrt(4))') + 4 3 4 + (sqrt(4) / .4`%) 455 4 (sqrt(4) / .4' %) + (sqrt(4) / .4) 456 4 4! * (4! - sqrt(4) / .4) 457 4 ((sqrt(4) + 4 % ) / .4' % ) - sqrt(4) 458 4 (4*4!) / .sqrt(4)' + 4! 4 4 + 4 + (sqrt(4) / .4`%) 459 4 ((4! / .(4!)) + sqrt(4)) / .(sqrt(4))' 3 (sqrt(4) + 4%) / .4`% 460 4 (4! - sqrt(4))^sqrt(4) - 4! 3 (4!% + sqrt(.4`%)) / sqrt(.4`%)% 461 4 ((sqrt(4) + 4 % ) / .4' % ) + sqrt(4) 462 4 (4! - sqrt(4))! / (4! - 4)! 463 4 ((sqrt(4) + 4 % ) / .4' % ) + 4 464 4 (4^4 - 4!) * sqrt(4) 465 4 (sqrt(4) / .4' %) + (sqrt(.4') / 4' %) 3 (sqrt(4) + sqrt(.4`%)) / .4`% 466 4 (sqrt(4) / .4' %) + (4 * 4) 467 4 ((sqrt(4) + sqrt(.4' % )) / .4' % ) + sqrt(4) 468 4 444 + 4! 469 4 ((sqrt(4) + sqrt(.4' % )) / .4' % ) + 4 470 4 (sqrt(4) / .4' %) + (4! - 4) 4 (4! * 4 - sqrt (4)) / .sqrt(4) 471 4 (((sqrt(sqrt(sqrt(.4))))^(-4!)) + (4)) * (4!) 472 4 (4! - 4) * (4! - .4) 473 4 ((sqrt(4) - .4' % ) / .4' % ) + 4! 474 4 (4! / .(4!) / .(sqrt(4))') + 4! 3 (sqrt(4) / .4`%) + 4! 475 4 ((4! / .(4!)') - 4) / .(sqrt(4)) 4 (sqrt(4) - (.4 / 4)) / .4% 476 4 4! * (4! - 4) - 4 3 (sqrt(4) / .4%) - 4! 477 4 4! * 4! - 4! / .(4!)' 4 (4 + 4!%) / (sqrt(4) * .4`)% 478 4 4! * (4! - 4) - sqrt(4) 479 4 (4 * 4!) - .(sqrt(4)) / .(sqrt(4)) 4 ((4 * 4!) - sqrt(4%)) / sqrt(4%) 480 3 4! * (4! - 4) 481 4 (4 * 4!) + .(sqrt(4)) / .(sqrt(4)) 4 ((4 * 4!) + sqrt(4%)) / sqrt(4%) 482 4 sqrt(4) + 4! * (4! - 4) 483 4 (4! / .(sqrt(4))' - sqrt(.4')) / .(sqrt(4))' 4 ((sqrt(4) + 4%) / .4`%) + 4! 484 3 (4! - sqrt(4))^sqrt(4) 485 4 ((4! / .(sqrt(4))') - .(sqrt(4))') / .(sqrt(4))' 4 (sqrt(4) - (4 + sqrt(4))%) / .4% 486 4 4 * 4! / (.4` * .4`) 487 4 (((4! / .(sqrt(4))') + .(sqrt(4))') / .(sqrt(4))' 488 4 sqrt(4) * 4 ^ 4 - 4! 489 4 ((4! / .(sqrt(4))') + sqrt(.4') / .(sqrt(4))' 4 (sqrt(4) - 4.4%) / .4% 490 4 (4! / .(sqrt(4))' / .(sqrt(4))') + 4 3 (sqrt(4) - 4%) / .4% 491 4 ((sqrt(4) / .4)! / .(4!)' - 4 4 (sqrt(4) / .4%) - (4 / .4`) 492 4 root(.(sqrt(4))' ,4) - (4 / .(sqrt(4))) 4 (sqrt(4) / .4%) - (4 + 4) 493 4 ((sqrt(4) / .4)! / .(4!)' - sqrt(4) 4 ((sqrt(4) - sqrt(4)%) / .4%) - sqrt(4) 494 4 (((sqrt(4) / .4)! - .(4!)') / .(4!)' 4 (sqrt(4) / .4`%) + 44 495 4 (4! - sqrt(4)) / (.4` - .4) 3 ((sqrt(4) / .4)! / .(4!)' 3 (sqrt(4) - sqrt(4)%) / .4% 496 4 4 * (4 + (sqrt(4) / .4)!) 3 (sqrt(4) / .4%) - 4 497 4 ((sqrt(4) / .4)! / .(4!)' + sqrt(4) 4 ((sqrt(4) + .4%) / .4%) - 4 498 4 ((4! / .(4!) - .4) / .(sqrt(4)) 3 (sqrt(4) / .4%) - sqrt(4) 499 4 ((sqrt(4) / .4)! / .(4!)' + 4 3 (sqrt(4) - .4%) / .4% 500 4 4 * sqrt(sqrt(sqrt((sqrt(4) / .4)^4!))) 2 sqrt(4) / .4% 501 4 ((sqrt(4) / .4)! + .(4!)) / .(4!) 3 (sqrt(4) + .4%) / .4% 502 4 root(.(sqrt(4))' ,4) - (4 /.4) 3 sqrt(4) + (sqrt(4) / .4%) 503 4 root(.(sqrt(4))' ,4) - (4 / .4') 4 4 + ((sqrt(4) - .4%) / .4%) 504 4 (4^4 - 4) * sqrt(4) 3 4 + (sqrt(4) / .4%) 505 4 .(sqrt(4))^(-4) - (sqrt(4) / .4)! 3 (sqrt(4) + sqrt(4)%) / .4% 506 4 root(.(sqrt(4))' ,4) - (4 / sqrt(.4')) 4 4 + sqrt(4) + (sqrt(4) / .4%) 507 4 root(.(sqrt(4))' ,4) - (sqrt(4) / .4) 4 sqrt(4) + ((sqrt(4) + sqrt(4)%) / .4%) 508 4 4^4 * sqrt(4) - 4 509 4 root(.(sqrt(4))' ,4) - (sqrt(4 / .4')) 4 (4 / .4`) + (sqrt(4) / .4%) 510 4 sqrt(4) * 4^4 - sqrt(4) 3 (sqrt(4) + 4%) / .4% 511 4 root(.(sqrt(4))' ,4) - (4 / 4) 4 (4.4% + sqrt(4)) / .4% 512 3 sqrt(4) * 4^4 2 root(.(sqrt(4))',4) 513 4 root(.(sqrt(4))' ,4) + (4 / 4) 4 (sqrt(4) + root(sqrt(4%), 4)) / sqrt(4) 514 4 sqrt(4) * 4 ^ 4 + sqrt(4) 515 4 root(.(sqrt(4))' ,4) + (sqrt(4 / .4')) 4 ((4 + sqrt(4))% + sqrt(4)) / .4% 516 4 sqrt(4) * 4 ^ 4 + 4 517 4 root(.(sqrt(4))' ,4) + (sqrt(4) / .4)) 518 4 root(.(sqrt(4))' ,4) + (4 / sqrt(.4')) 4 ((4 + sqrt(4))!%% + sqrt(4)) / .4% 519 4 ((sqrt(4) / .4)! / .(4!)' + 4! 4 ((sqrt(4) - sqrt(4)%) / .4%) + 4! 520 4 sqrt(4) * (4 + 4^4) 521 4 root(.(sqrt(4))' ,4) + (4 / .4') 522 4 (4^4 - 4!) / .4` 523 4 ((sqrt(4) - .4 % ) / .4 % ) + 4! 524 4 4! * (4! - sqrt(4)) - 4 3 (sqrt(4) / .4%) + 4! 525 4 (4! - sqrt(.4`)) / (.4` - .4) 526 4 4! * (4! - sqrt(4)) - sqrt(4) 527 4 ((4! - sqrt(.4')) / 4' % ) + sqrt(4) 528 3 (4! - sqrt(4)) * 4! 529 4 (4! - 4 / 4) ^ sqrt(4) 530 4 sqrt(4) + 4! * (4! - sqrt(4)) 531 4 (4! - .4) / (.4` - .4) 532 4 4!^sqrt(4) - 44 533 4 (4! * .4' - sqrt(.4)%) / sqrt(4)% 534 4 root(.(sqrt(4))' ,4) + (4! - sqrt(4)) 4 (4 - 44%) / sqrt(.4`)% 535 4 (4! - .(sqrt(4))') / (.4' - .4) 4 4% ^ -sqrt(4) - (.4 / .4`%) 536 4 sqrt(4) * 4 ^ 4 + 4! 537 4 ((sqrt(4) / .4')! - .4') / .(sqrt(4))' 4 (4 - (sqrt(4)% + .4)) / sqrt(.4`)% 538 4 4! / (.4` - .4) - sqrt(4) 539 4 (((sqrt(4) / .4)! - .(sqrt(4)')) / .(sqrt(4)') 4 (sqrt(4) + .4 - .4`%) / .4`% 540 3 4! / (.4` - .4) 2 4! / 4' % 541 4 (((sqrt(4) / .4)! + .(sqrt(4)')) / .(sqrt(4)') 4 (sqrt(4) - 4% + .4`) / .4`% 542 4 4! / (.4` - .4) + sqrt(4) 543 4 ((sqrt(4) / .4)! + .4') / .(sqrt(4))' 4 (4 + sqrt(4)% - .4) / sqrt(.4`)% 544 4 4! / (.4` - .4) + 4 545 4 (4! + .(sqrt(4))') / (.4' - .4) 4 (4! - sqrt(4)%) / 4.4% 546 4 ((4! - sqrt(4)) / 4%) - 4 547 4 (4! + .(sqrt(4))') / 4' % ) + sqrt(4) 548 4 4!^sqrt(4) - 4! - 4 549 4 (4! + .4) / (.4` - .4) 550 4 4!^sqrt(4) - 4! - sqrt(4) 3 (4! - sqrt(4)) / 4% 551 4 4! * 4! - .(sqrt(4))^(-sqrt(4)) 4 (4! - sqrt(4) + 4%) / 4% 552 3 4!^sqrt(4) - 4! 553 4 ((4! + sqrt(.4')) / 4' % ) - sqrt(4) 4 (sqrt(sqrt(sqrt(4!^4!))) * 4)% + 4% 554 4 4!^sqrt(4) - 4! + sqrt(4) 555 4 (4! + sqrt(.4`)) / (.4` - .4) 556 4 4!^sqrt(4) - 4! + 4 557 4 ((4! + sqrt(.4')) / 4' % ) + sqrt(4) 558 4 (4! - sqrt(.4`)) * 4! - sqrt(4) 559 4 (sqrt(4) + .(4!) - .4 % ) / .4 % 4 (sqrt(4) + (4! - .4)%) / .4% 560 3 (4! - sqrt(.4`)) * 4! 561 4 .(sqrt(4))^(-4) - (sqrt(sqrt(sqrt(4^4!) 4 (sqrt(4) + (4! + .4)%) / .4% 562 4 (4! - sqrt(.4`)) * 4! + sqrt(4) 563 4 ((4! - 4' % ) / 4' % ) + 4! 564 4 4!^sqrt(4) - 4! / sqrt(4) 3 (4 - 4!%) / sqrt(.4`)% 565 4 .(sqrt(4))^(-4) - (4! / .4) 4 4% ^ -sqrt(4) - (4! / .4) 566 4 4!^sqrt(4) - 4 / .4 567 4 (4^4 - 4) / .4' 568 4 4!^sqrt(4) - 4 - 4 569 4 ((4! + .(sqrt(4))') / 4' % ) + 4! 4 (4 - (sqrt(4%) + sqrt(.4`)%)) / sqrt(.4`)% 570 4 4!^sqrt(4) - 4 - sqrt(4) 3 (4 - sqrt(4%)) / sqrt(.4`)% 571 4 4!^sqrt(4) - sqrt(4) / .4 572 3 4!^sqrt(4) - 4 573 4 4!^sqrt(4) - sqrt(4 / .4`) 574 3 4!^sqrt(4) - sqrt(4) 575 4 4!^sqrt(4) - 4/4 576 2 4!^sqrt(4) 577 4 4!^sqrt(4) + 4/4 578 3 4!^sqrt(4) + sqrt(4) 579 4 4!^sqrt(4) + sqrt(4) / sqrt(.4`) 580 3 4!^sqrt(4) + 4 581 4 4!^sqrt(4) + sqrt(4) / .4 582 4 4!^sqrt(4) + 4 + sqrt(4) 583 4 ((sqrt(4) + 4!) / 4' % ) - sqrt(4) 3 (4! - .4') / (4%)' 584 4 4!^sqrt(4) + 4 + 4 585 4 (4^4 + 4) / .4` 586 4 4!^sqrt(4) + 4 / .4 587 4 ((sqrt(4) + 4!) / 4' % ) + sqrt(4) 588 4 4!^sqrt(4) + 4! / sqrt(4) 3 (4! - .4!') / (4%)' 589 4 .(sqrt(4))^(-4) - (4! / sqrt(.4')) 4 (4! - 44%) / 4% 590 4 (4! + sqrt(.4`)) * 4! - sqrt(4) 3 (4! - .4) / 4% 591 4 (4! / 4%) - (4 / .4') 592 3 4! (sqrt(.4') + 4!) 593 4 .(sqrt(4))^(-4) - root(.4,4) 4 4% ^ -sqrt(4) - root(.4, 4) 594 4 (4! + sqrt(.4`)) * 4! + sqrt(4) 3 4! - .(4!)) / 4 % 3 (4! - 4!%) / 4% 595 4 (4!/4)! - sqrt(sqrt(sqrt(.(sqrt(4)))))^(-4!) 3 (4! - sqrt(4%)) / 4% 596 4 4!^sqrt(4) + 4! - 4 3 (4! / 4%) - 4 597 4 .(sqrt(4))^(-4) - (4! + 4) 3 (4 - sqrt(4)%) / sqrt(.4`)% 598 4 4!^sqrt(4) + 4! - sqrt(4) 3 (4! / 4%) - sqrt(4) 599 4 .(sqrt(4))^(-4) - (4! + sqrt(4)) 3 (4! - 4%) / 4% 600 3 4!^sqrt(4) + 4! 2 4! / 4% 601 4 (sqrt(4) / .4)^4 - 4! 3 (4! + 4%) / 4% 602 4 4!^sqrt(4) + 4! + sqrt(4) 3 sqrt(4) + (4! / 4%) 603 4 .(sqrt(4))^(-4) - (4! - sqrt(4)) 3 (4 + sqrt(4)%) / sqrt(.4`)% 604 4 4!^sqrt(4) + 4! + 4 3 4 + (4! / 4%) 605 4 .(sqrt(4))^(-4) - (4! - 4) 3 (4! + sqrt(4%)) / 4% 606 4 (4! + .(4!)' + .(4!)') / .4'% 3 (4! + 4!%) / 4% 607 4 (4 % + .(4!) + 4!) / 4 % 4 ((4 + 4!)% + 4!) / 4% 608 4 (4! + sqrt(.4`) + sqrt(.4`)) * 4! 609 4 .(sqrt(4))^(-4) - (4 * 4) 4 (4 / .4`) + (4! / 4%) 610 4 ((sqrt(4) / .4)! + sqrt(4)) / .(sqrt(4)) 3 (4! + .4) / 4% 611 4 root(.(sqrt(4))' ,4) + (4! / .(4!)') 4 (4! + 44%) / 4% 612 4 4! * (4! + sqrt(.4`) / .4`) 613 4 .(sqrt(4))^-(4) - (4! / sqrt(4)) 4 4% ^ -sqrt(4) - (4! / sqrt(4)) 614 4 ((4! - .4) / 4 % ) + 4! 615 4 .(sqrt(4))^(-4) - (4 / .4) 4 (4 + (.4 / 4)) / sqrt(.4`)% 616 4 4^4 / .4 - 4! 617 4 .(sqrt(4))^(-4) - (4 + 4) 4 4% ^ -sqrt(4) - (4 + 4) 618 4 (4! / 4 % ) + (4 / .(sqrt(4))') 4 4! + ((4! - 4!%) / 4%) 619 4 .(sqrt(4))^(-4) - (4 / sqrt(.4')) 4 4% ^ -sqrt(4) - (4 + sqrt(4)) 620 4 4!^sqrt(4) + 44 621 4 (sqrt(4) / .4)^4 - 4 3 4% ^ -sqrt(4) - 4 622 4 4! * (4! + sqrt(4)) - sqrt(4) 623 4 (sqrt(4) / .4)^4 - sqrt(4) 3 4% ^ -sqrt(4) - sqrt(4) 624 3 4! * (4! + sqrt(4)) 625 3 (sqrt(4) / .4) ^ 4 2 .(sqrt(4))^-(4) 2 4% ^ -sqrt(4) 626 4 sqrt(4) + 4! * (4! + sqrt(4)) 4 (4! + sqrt(4) )! / (4!)! - 4! 627 4 sqrt(4) + (sqrt(4) / .4)^4 3 sqrt(4) + 4% ^ -sqrt(4) 628 4 4 + 4! * (4! + sqrt(4)) 629 4 4 + (sqrt(4) / .4)^4 3 4 + 4% ^ -sqrt(4) 630 4 (4 / .4')! / (4! * 4!) 3 (4 + sqrt(4%)) / sqrt(.4`)% 631 4 .(sqrt(4))^(-4) + (4 / sqrt(.4')) 4 4 + sqrt(4) + 4% ^ -sqrt(4) 632 4 root(.(sqrt(4))' ,4) + (sqrt(4) / .4)! 4 (4! / 4%) + root(.4, 4) 633 4 .(sqrt(4))^(-4) + 4 + 4 4 4 + 4 + 4% ^ -sqrt(4) 634 4 .(sqrt(4))^(-4) + (4 / .4') 4 4! + ((4! + .4) / 4%) 635 4 (4^4 - sqrt(4)) / .4 636 4 4^4 / .4 - 4 3 (4 + 4!%) / sqrt(.4`)% 637 4 .(sqrt(4))^-(4) + (4! / sqrt(4)) 4 (4! / sqrt(4)) + 4% ^ -sqrt(4) 638 4 4^4 / .4 - sqrt(4) 639 4 (4^4 - .4) / .4 640 3 4^4 / .4 641 4 (.4 + 4^4) / .4 642 4 sqrt(4) + 4^4 / .4 643 4 .(sqrt(4)) ^ (- 4) + (4 / .(sqrt(4))') 4 ((sqrt(4%) - 4!)% + sqrt(.4`)) / sqrt(.4`%)% 644 4 4 + 4^4 / .4 645 4 (sqrt(4) + 4^4) / .4 646 4 (4! + sqrt(4))! / (4!)! - 4 647 4 .(sqrt(4))^(-4) + (4! - sqrt(4)) 4 4! - sqrt(4) + 4% ^ -sqrt(4) 648 4 (sqrt(4) + 4)^4 / sqrt(4) 649 4 4! + (sqrt(4) / .4)^4 3 4! + 4% ^ -sqrt(4) 650 3 (4! + sqrt(4))! / (4!)! 651 4 (4! + sqrt(4))! + (4!)!) / (4!)! 652 4 (4! + sqrt(4))^sqrt(4) - 4! 653 4 .(sqrt(4))^(-4) + 4! + 4 4 4 + 4! + 4% ^ -sqrt(4) 654 4 4 + (4! + sqrt(4))! / (4!)! 655 4 (.(sqrt(4)) + sqrt(4) + 4!) / 4 % 4 (sqrt(4) + 4! + sqrt(4%)) / 4% 656 4 4! * (4! + 4 - sqrt(.4`)) 657 4 (4!) * (4!) + root( - (sqrt(.4')), .4'))) 658 4 (44 / sqrt(.4' % )) - sqrt(4) 659 4 (44 - sqrt(.4' %)) / sqrt(.4' %) 660 4 (4! / 4)! - 4! / .4 3 44 / sqrt(.4`%) 661 4 .(sqrt(4))^(-4) + (4! / sqrt(.4')) 4 (44 + sqrt(.4`%)) / sqrt(.4`%) 662 4 (44 / sqrt(.4' %)) + sqrt(4) 663 4 (44 + .(sqrt(4))) / sqrt(.4' %) 4 (sqrt(4%) + 44) / sqrt(.4`%) 664 4 4! + 4^4 / .4 665 4 (4! / 4' %) + (.(sqrt(4)) ^ - (sqrt(sqrt(sqrt(4!))))) 4 ((4 * sqrt(.4`)) - sqrt(.4`)%) / .4% 666 4 444 / sqrt(.4`) 3 (.4` / sqrt(.4`%)%) - sqrt(.4`) 667 4 (sqrt(4) - sqrt(.4') +(sqrt(.4' % ) % ) / .(sqrt(4)) % 4 (4 + sqrt(4%)%) / (4! / .4)%% 668 4 4! * (4! + 4) - 4 669 4 .(sqrt(4))^(-4) + 44 4 4% ^ -sqrt(4) + 44 670 4 4! * (4! + 4) - sqrt(4) 671 4 (sqrt(4) / .4' % / sqrt(.4')) - 4 672 4 (4 + 4)! /4! * .4 3 4! * (4! + 4) 673 4 .(sqrt(4))^(-4) + (4! * sqrt(4)) 4 (4! / (4 - .4`)%) - sqrt(4) 674 4 (4! + sqrt(4))^sqrt(4) - sqrt(4) 675 4 (sqrt(4) / .4)! / (.4 * .4`) 3 4! / (4 - .4`)% 676 3 (4! + sqrt(4))^sqrt(4) 677 4 (sqrt(4) / .4' % / sqrt(.4')) + sqrt(4) 678 4 (4! + sqrt(4))^sqrt(4) + sqrt(4) 679 4 .(sqrt(4))^(-4) + (4! / .4') 4 4 + (4! / (4 - .4`)%) 680 4 (4! + sqrt(4))^sqrt(4) + 4 681 4 ((sqrt(4) / 4' %) + .4) / sqrt(.4' %) 682 4 (sqrt(4) - .4' - 4 % ) / .(sqrt(4))' % 4 (root(sqrt(4%), 4) * sqrt(.4`)) - sqrt(.4`) 683 4 ((.(4!)' + (4 % )') / (4 % % )') - 4! 4 (.4! + (4%)' - .4'%) / (4%)'% 684 4 4! * (4! + sqrt(4) / .4`) 685 4 .(sqrt(4))^(-4) + (4! / .4) 4 (4! / .4) + 4% ^ -sqrt(4) 686 4 ((.(4!) + sqrt(.4' % ) / (4 % )' % ) - 4 4 root(sqrt(.4`), sqrt(4) - 4%) / .4% 687 4 (((sqrt(.4') / .(4!)% )% ) - .(sqrt(4)% ) / .4 % 4 (sqrt(.4') / .4!'% - .sqrt (4) ) /.4 688 4 (4! + 4 + sqrt(.4`)) * 4! 689 4 .(sqrt(4))^(-4) + sqrt(sqrt(sqrt(4)^4!))) 690 4 (4! / 4)! - ((sqrt(4) / sqrt(.4' %)) 691 4 (sqrt(4) - .4' - sqrt(4) % ) / .(sqrt(4))' % 692 4 (4 + sqrt(4))! - 4! - 4 693 4 ((sqrt(.4') / .4' % ) + 4) / .(sqrt(4))' 694 4 (4 + sqrt(4))! - 4! - sqrt(4) 695 4 (4! / 4)! - .(sqrt(4))^(-sqrt(4)) 4 (4 + 4! - sqrt(4%)) / 4% 696 3 (4 + sqrt(4))! - 4! 697 4 (sqrt(4) - .4' - sqrt(.4') % ) / .(sqrt(4))' % 4 (4 - sqrt(4)% + sqrt(.4`)) / sqrt(.4`)% 698 4 (4 + sqrt(4))! - 4! + sqrt(4) 699 4 (sqrt(.4') / .4' % / .(sqrt(4))') + 4! 4 (4 + 4! - 4%) / 4% 700 4 (4^4 + 4!) / .4 3 (4 + 4!) / 4% 701 4 (sqrt(sqrt(sqrt(.(sqrt(4))))^(-4!))) + 4! * 4! 4 (4 + 4! + 4%) / 4% 4 sqrt(((4! +4)! + (4!)!) / (4!)!) 702 4 (4!/4)! - (4/.(sqrt(4))') 4 ((4 + 4!) / 4%) + sqrt(4) 703 4 (sqrt(4) - .4' + sqrt(.4') % ) / .(sqrt(4))' % 4 (4 + sqrt(4)% + sqrt(.4`)) / sqrt(.4`)% 704 4 4 * 4 * 44 705 4 (sqrt(sqrt(sqrt(4/.4')))^(4!)) - 4! 706 4 (.(4!) + 4 + 4!) / 4 % 4 4 ^ 4 + (sqrt(4) / .4`%) 707 4 (sqrt(4) - .4') / ((4! - sqrt(4)) % % )' 4 (4 + .4!') / (.4!%)' * .4 708 4 (4 + sqrt(4))! - 4! / sqrt(4) 709 4 (sqrt(4) - .4' + sqrt(4) % ) / .(sqrt(4))' % 710 4 (4 + sqrt(4))! - 4 / .4 711 4 (4 + sqrt(4))! - 4 / .4` 712 4 (4 + sqrt(4))! - 4 - 4 713 4 ((.(4!) - sqrt(.4' % )) / .(4!)' %o ) - sqrt(4) 5 (sqrt(sqrt(sqrt(4/.4')))^(4!)) - (4 * 4) 4 (.(sqrt(4)) '+ sqrt(.4'%)) / (4%)'% - sqrt(4) 714 4 (4 + sqrt(4))! - 4 - sqrt(4) 715 4 (4 + sqrt(4))! - sqrt(4) / .4 716 3 (4 + sqrt(4))! - 4 717 4 (4 + sqrt(4))! - sqrt(4) / sqrt(.4`) 718 3 (4 + sqrt(4))! - sqrt(4) 719 4 (4 + sqrt(4))! - 4/4 720 2 (4 + sqrt(4))! 721 4 (4 + sqrt(4))! + 4/4 722 3 (4 + sqrt(4))! + sqrt(4) 723 4 (4 + sqrt(4))! + sqrt(4) / sqrt(.4`) 724 3 (4 + sqrt(4))! + 4 725 4 (4 + sqrt(4))! + sqrt(4) / .4 726 4 (4 + sqrt(4))! + 4 + sqrt(4) 727 4 (sqrt(sqrt(sqrt(4/.4')))^(4!)) - sqrt(4) 728 4 (4 + sqrt(4))! + 4 + 4 729 4 (4 + sqrt(4))! + 4 / .4` 3 sqrt(sqrt(sqrt((4/.4')^4!))) 730 4 (4 + sqrt(4))! + 4 / .4 731 4 (sqrt(sqrt(sqrt(4/.4')))^(4!)) + sqrt(4) 732 4 (4 + sqrt(4))! + 4! / sqrt(4) 733 4 (sqrt(sqrt(sqrt(4/.4')))^(4!)) + 4 734 4 ((.4' + (4%)') / sqrt(.4' % ) % ) + sqrt(.4') 4 (sqrt(4) - .4!) / (.4!)% + sqrt(.4') 735 4 (sqrt(.4') / 4' % ) + (4! / 4)! 736 4 (4 + sqrt(4))! + 4 * 4 737 4 (.4' + .(sqrt(4))' % ) / (.(4!)' %o ) / .4) 4 root (. (sqrt(4)) ', 4) + sqrt(.4'%) ^ (-sqrt(4)) 738 4 (4 / .(sqrt(4))') + (4! / 4)! 4 (root(-sqrt(4), .4`%) - 4!%) / sqrt(4)% 739 4 ((.(4!) - sqrt(.4' % )) / .(4!) %o ) + 4! 4 (.(sqrt(4)) '+ sqrt(.4'%)) / (4%)'% + 4! 740 4 (4 + sqrt(4))! + 4! - 4 741 4 (4 - sqrt(.4') - 4 % ) / .4' % 742 4 (4 + sqrt(4))! + 4! - sqrt(4) 743 4 (.(sqrt(4))' + (4!) %o / .(sqrt(4))') / (.4') %o 4 (sqrt(4 /.4'%) + (sqrt(4(%)') / (4%)' 744 3 (4 + sqrt(4))! + 4! 745 4 .(sqrt(4))^(-4) + (sqrt(4) / .4)! 4 (sqrt(4 / .4`) - sqrt(4)%) / .4% 746 4 (4 + sqrt(4))! + 4! + sqrt(4) 747 4 ((sqrt(4) / .4 %) - sqrt(4)) / sqrt(.4') 748 4 (4 + sqrt(4))! + 4! + 4 749 4 ((sqrt(4) / .4 %) - sqrt(.4')) / sqrt(.4') 750 4 (sqrt(4) / .4)! / .4 / .4 3 sqrt(4 / .4`) / .4% 3 (root(-.sqrt(4), .sqrt(4)))*.4! 751 4 ((sqrt(4) / .4 %) + sqrt(.4')) / sqrt(.4') 752 4 (sqrt(4) + 4)! + root.4(4) 753 4 (sqrt(sqrt(sqrt(4/.4')))^(4!)) + 4! 754 4 (sqrt(4) / .4 %) / sqrt(.4')) + 4 4 root (-.sqrt (4), .sqrt (4) ) * .4! + 4 755 4 (4 - .(sqrt(4)) - .4') / .4' % 4 (4 - (sqrt(4%) + .4`)) / .4`% 756 4 (4! + 4)! / (4! + sqrt(4))! 757 4 (.(sqrt(4))' - ((4!) %o / .4')) / .(sqrt(4))' %o 4 (.4! + sqrt(.4'%)) / (4%)'% - sqrt(4) 758 4 (root(.(sqrt(4))',4) % - sqrt(.4' % )) / sqrt(.4') % 759 4 (4- sqrt(.4') + 4 % ) / .4' % 760 4 (4! + 4)^sqrt(4) - 4! 761 4 (sqrt(4) / .(4!)' % ) - sqrt(sqrt(sqrt(4 ^ (4!)))) 762 4 (root(.(sqrt(4))' ,4) - 4) / sqrt(.4') 4 (root(-sqrt(4), .4`%) + 4!%) / sqrt(4)% 763 4 (.4! + sqrt(.4'%)) / (4%)'% + 4 4 (.4! '+ sqrt(.4'%)) / (4%)'% - sqrt(4) 764 4 (4 + sqrt(4))! + 44 765 4 (root(.(sqrt(4))' ,4) - sqrt(4)) / sqrt(.4') 4 (4 - (4! / .4)%) / .4`% 766 4 root.4(4)*4! - sqrt(4) 767 4 (root(.(sqrt(4))' ,4) - sqrt(.4')) / sqrt(.4') 768 4 (4 + 4) * 4! * 4 3 root.4(4) * 4! 769 4 (root(.(sqrt(4))' ,4) + sqrt(.4')) / sqrt(.4') 770 4 root.4(4)*4! + sqrt(4) 771 4 (root(.(sqrt(4))' ,4) + sqrt(4)) / sqrt(.4') 772 4 root.4(4)*4! + 4 773 4 ((sqrt(4) - .4') / (.(sqrt(4)) % )') - 4 774 4 (4 + sqrt(4))! + 4! / .4` 775 4 (sqrt(.4') / .4' % ) + .(sqrt(4)) ^ (- 4) 4 (4 - (.4 / .4`)) / .4% 776 4 ((4 - .4') / .4' % ) - 4! 777 4 (sqrt(4) / .(4!)' % ) - (4! + 4!) 3 (sqrt(4) - .4') / (sqrt(4%)%)' 778 4 ((sqrt(4) - .4') / .(sqrt(4)) % ) + .(sqrt(4))' 779 4 (.(4!) - sqrt(.4'%) - .(sqrt(4))'%o) / .(sqrt(4))'%o 4 (sqrt(4) - .4') / (.sqrt (4)%)' + sqrt (4) 780 4 (4! + 4)^sqrt(4) - 4 781 4 (sqrt(4) / .(4!)' % ) - 44 782 4 (4! + 4)^sqrt(4) - sqrt(4) 783 4 ((sqrt(.4') / .4' % ) + 4!) / .(sqrt(4))' 4 (4 + sqrt(4%)%) / (.4` + sqrt(.4`%))% 784 3 (4! + 4)^sqrt(4) 785 4 (4 - .4' - sqrt(.4' %)) / .4' % 786 4 (4! + 4)^sqrt(4) + sqrt(4) 787 4 (sqrt(.4') / .(4!)' % ) + root(.(sqrt(4))',4) 788 4 (4! + 4)^sqrt(4) + 4 789 4 (sqrt(4) - .(4!) - sqrt(.4') % ) / .(sqrt(4))' % 790 4 (4 - .4' - 4' % ) / .4' % 791 4 (4 - .4' - 4 % ) / .4' % 792 4 (4! - sqrt(4)) * 4! / sqrt(.4`) 3 (sqrt(4) - (4!)%) / (.(sqrt(4))')% 793 4 (sqrt(4) - .(4!) + .(sqrt(4))' % ) / .(sqrt(4))' % 4 (sqrt(4) / .4!'%) - root (.4, 4) 794 4 (sqrt(4) - .(4!)) / .(sqrt(4))' % ) + sqrt(4) 4 (root(.4, 4) - 4!%) / 4% 795 4 (4 - sqrt(.4') - .4) / .4' % 796 4 ((4 - .4') / .4' % ) - 4 797 4 (sqrt(4) - .(sqrt(4))' - sqrt(.4') % / .(sqrt(4))' % 798 4 ((4 - .4') / .4' % ) - sqrt(4) 799 4 (4 - .4' - .4' % ) / .4' % 800 4 sqrt(4) * (4! - 4)^sqrt(4) 3 root(.4, 4) / 4% 801 4 (4 - .4' + .4' % ) / .4' % 802 4 ((4 - .4') / .4' % ) + sqrt(4) 803 4 (sqrt(4) - .(sqrt(4))' + sqrt(.4') % / .(sqrt(4))' % 804 4 ((4 - .4') / .4' % ) + 4 805 4 (root .4,(4) + .(sqrt(4)) / 4 % 4 (sqrt(4%) + root(.4, 4)) / 4% 806 4 ((4 - .4) / .4' % ) - 4 807 4 ((4! / 4' %) - sqrt(4)) / sqrt(.4') 808 4 (4! + 4)^sqrt(4) + 4! 809 4 ((4! / 4' %) - sqrt(.4')) / sqrt(.4') 810 4 4! / sqrt(.4`) / (.4` - .4) 3 (4 - .4) / .4`% 811 4 ((4! / 4' %) + sqrt(.4')) / sqrt(.4') 812 4 ((4! / 4' %) / sqrt(.4')) + sqrt(4) 813 4 ((4! / 4'%) + sqrt(4)) / sqrt(.4') 814 4 ((4! / 4' %) / sqrt(.4')) + 4 815 4 (4! / sqrt(.4') + .(sqrt(4))') / 4' % 4 (4 - .4` + sqrt(.4`%)) / .4`% 816 4 4! * (4! + 4 / .4) 817 4 (sqrt(4) / .(4!)' % ) - (4 + 4) 818 4 (sqrt(4) - .(sqrt(4))' + 4 % ) / .(sqrt(4))' % 819 4 (4! / .(4!)' + (4!/4)! 4 (4 / sqrt(.4'))! + 4! / .(4!)' 4 (4 + 4% - .4) / .4`% 820 4 (4! / .(4!)) + (4!/4)! 4 ((4 * 4) + .4) / sqrt(4)% 821 4 (.4' / .(sqrt(4))' % / .(4!)') - 4 3 sqrt(4)/.(4!)'% - 4 822 4 ((4 - .(4!)) / .4' % ) - 4! 4 ((4 - 4!%) / .4`%) - 4! 823 4 (.4' / .(sqrt(4))' % / .(4!)') - sqrt(4) 3 sqrt(4)/.(4!)'% - sqrt(4) 824 4 ((4 - .4') / .4' % ) + 4! 3 (sqrt(4) - .(4!)'%) / .(4!)'% 825 4 ((4!/.(4!)' / .(4!)) * sqrt(4) 3 sqrt(4) / (.(4!)' - .(4!)) 2 sqrt(4) / .(4!)'% 2 sqrt(4) / .(4!)' % 4 ((4 / .4`) + 4!) / 4% 826 4 ((4 - .(sqrt(4))' / .4' % ) - 4! 4 (4! * 4!) + sqrt(.4% ^ -sqrt(4)) 3 (sqrt(4) + .(4!)'%) / .(4!)'% 827 4 (.4' / .(sqrt(4))' % / .(4!)') + sqrt(4) 3 sqrt(4)/.(4!)'% + sqrt(4) 828 4 (4! * 4! - 4!) / sqrt(.4`) 829 4 (.4' / .(sqrt(4))' % / .(4!)') + 4 3 sqrt(4)/.(4!)'% + 4 830 4 (sqrt(4) + sqrt(.4' % ) - .(sqrt(4))') / .(sqrt(4))' % 4 ((4 / 4!%) - sqrt(.4`%)) / sqrt(4)% 831 4 ((4 - .(sqrt(4)) / .4' % ) - 4! 4 ((4 - sqrt(4%)) / .4`%) - 4! 832 4 4! * 4! + 4^4 833 4 ((4 / 4!%) - sqrt(.4`)%) / sqrt(4)% 834 4 (4! / 4' % / sqrt(.4')) + 4! 3 sqrt(4)/.(4!)% + sqrt(.4') 835 4 ((.4' / .(sqrt(4))' % ) + .4) / .(4!) 4 ((4 / sqrt(4)%) + .4) / 4!% 3 (sqrt(4) + .4%) / .(4!)% 836 4 ((.4' + (sqrt(4))' % ) / .(sqrt(4))' % ) * 4 837 4 (4 - .(4!) - 4 %) / .4' % 4 (4 - (4 + 4!)%) / .4`% 838 4 sqrt(.4') + 4 + (sqrt(4) / .(4!) % ) 839 4 ((sqrt(4) + .4 % ) / .(4!) % ) + 4 840 4 (4 + 4)! / (4! + 4!) 841 4 (4! + sqrt(4) / .4)^sqrt(4) 842 4 ((4 - .(4!)) / .4' % ) - 4 4 ((4 - 4!%) / .4`%) - 4 843 4 (sqrt(4) / .(4!)' % ) + (4 / .(sqrt(4))') 844 4 ((4 - .(4!)) / .4' % ) - sqrt(4) 4 ((4 - 4!%) / .4`%) - sqrt(4) 845 4 sqrt(sqrt(sqrt(.(sqrt(4))))^(-4!)) + (4 / sqrt(.4'))! 4 (4 - (4! + .4`)%) / .4`% 846 4 (4! + (4! / 4' %)) / sqrt(.4') 3 (4 - 4!%) / .4`% 847 4 (4 - .(4!) + .4' % ) / .4' % 4 (4 - (4! - .4`)%) / .4`% 848 4 4! * (4! - .4`) / sqrt(.4`) 849 4 (4 - .(sqrt(4))' - .4' % ) / .4' % 3 sqrt(4)/.(4!)'% + 4! 850 4 ((4 - .(4!)) / .4' % ) + 4 4 ((4 / .4) + 4!) / 4% 3 (4 - .(sqrt(4))') / .4'% 851 4 (4 - .(sqrt(4))' + .4' % ) / .4' % 4 ((4 - sqrt(4%)) / .4`%) - 4 852 4 ((4 - .(sqrt(4))') / .4' % ) + sqrt(4) 4 (4 / .4`%) - (sqrt(4) * 4!) 853 4 ((4 - .(sqrt(4))) / .4' % ) - sqrt(4) 4 ((4 - sqrt(4%)) / .4`%) - sqrt(4) 854 4 ((4 - .(sqrt(4)) - .4' % ) / .4' % 4 (4 + 4!% - .4`) / .4`% 855 3 (4 - .(sqrt(4)) / .4' % 3 (4 - sqrt(4%)) / .4`% 856 4 4! * (4! - .(sqrt(4))') / sqrt(.4') 4 (4 / .4`%) - 44 857 4 (4 - .(sqrt(4)) / .4' % ) + sqrt(4) 4 ((4 - sqrt(4%)) / .4`%) + sqrt(4) 858 4 (4! * 4! - 4) / sqrt(.4`) 859 4 (4 - .(sqrt(4))' + 4 % ) / .4' % 4 4 + ((4 - sqrt(4%)) / .4`%) 860 4 4! * 4! / sqrt(.4`) - 4 861 4 (4! * 4! - sqrt(4)) / sqrt(.4`) 862 4 4! * 4! / sqrt(.4`) - sqrt(4) 863 4 (4! * 4! - sqrt(.4`)) / sqrt(.4`) 864 3 4! * 4! / sqrt(.4`) 865 4 (4! * 4! + sqrt(.4`)) / sqrt(.4`) 866 4 4! * 4! / sqrt(.4`) + sqrt(4) 867 4 (4! * 4! + sqrt(4)) / sqrt(.4`) 868 4 4! * 4! / sqrt(.4`) + 4 869 4 (sqrt(4) - sqrt(.4' % ) - .(sqrt(4))' % ) / .(sqrt(4))' % 870 4 (4! * 4! + 4) / sqrt(.4`) 3 (sqrt(4) - sqrt(.4'%)) / .sqrt(4)'% 871 4 (sqrt(4) - sqrt(.4' % ) + .(sqrt(4))' % ) / .(sqrt(4))' % 872 4 (4 / .4' % ) - (4 + 4!) 873 4 (sqrt(4) - sqrt(.4' % ) + sqrt(.4') % ) / .(sqrt(4))' % 4 (4 - (4! / sqrt(4))%) / .4`% 874 4 ((4 - .(sqrt(4))') / .4' % ) + 4! 4 (4 / .4`%) - (sqrt(4) + 4!) 875 4 (4 - sqrt(.4' % ) - 4' % ) / .4' % 876 4 (4 - sqrt(.4' % ) - 4 % ) / .4' % 3 (4 / .4`%) - 4! 877 4 ((4 + .4' % ) / .4' %) - 4! 878 4 (4 / .4' % ) - (4! - sqrt(4)) 879 4 ((4 - .(sqrt(4))) / .4' % ) + 4! 4 ((4 - sqrt(4%)) / .4`%) + 4! 880 4 44 * (4! - 4) 3 (sqrt(4) - 4!%) / sqrt(4%)% 881 4 .(sqrt(4))^(-4) + (4 ^ 4) 4 4 ^ 4 + 4% ^ -sqrt(4) 882 4 (4 / .4' %) - (4 / .(sqrt(4))') 4 (4 - (4 + 4)%) / .4`% 3 (sqrt(4) - 4%) / .sqrt(4)'% 883 4 ((4 - sqrt(.4' %)) / .4' % ) - sqrt(4) 884 4 (4 - sqrt(.4' % ) - .4' % ) / .4' % 885 3 (4 - sqrt(.4' % )) / .4' % 886 4 ((4 + 4'%) / .4'%) - 4! 887 4 ((4 - sqrt(.4' % ) / .4' % ) + sqrt(4) 888 4 444 * sqrt(4) 889 4 ((4 - sqrt(.4' % )) / .4' % ) + 4 890 4 (4 - .4' % - 4 % ) / .4' % 3 (4 - 4'%) / .4'% 4 (4 - (4 + .4')%) / .sqrt(4)'% 891 4 ((4! / .(4!)') / .4') * 4 3 (4 - 4%) / .4`% 892 4 (4 - 4 % + .4' % ) / .4' % 893 4 ((4 - 4 % ) / .4' ) + sqrt(4) 894 4 ((4 - 4' % ) / .4' % ) + 4 895 4 ((4 - 4 % ) / .4' % ) + 4 896 4 4! * 4! * (sqrt(4) - .4`) 3 (4 / .4`%) - 4 897 4 ((4 - .4' % ) / .4' % ) - sqrt(4) 898 4 (4 - .4' % - .4' % ) / .4' % 3 (4 / .4`%) - sqrt(4) 899 4 root(.(sqrt(4)),4) - sqrt(sqrt(sqrt(.(sqrt(4)))))^(-4!) 3 (4 - .4`%) / .4`% 900 4 (4! + 4! / 4)^sqrt(4) 2 4 / .4' % 901 3 (4 + .4' % ) / .4' % 902 4 (4 + .4' % + .4' % ) / .4' % 3 (4 / .4`%) + sqrt(4) 903 4 ((4 + .4' % ) / .4' % ) + sqrt(4) 904 4 root(.(sqrt(4)),4) - (sqrt(4) / .4)! 3 4 + (4 / .4`%) 905 4 (4 / .4' %) + (sqrt(4) / .4) 906 4 (4 / .4' %) + (4! / 4) 907 4 ((4 + 4 %) / .4' % ) - sqrt(4) 908 4 (4 / .4' %) + 4 + 4 909 4 (4 / .4' %) + (4 / .4') 3 (4 + 4%) / .4`% 910 4 sqrt(4)^(4!) * .(sqrt(4)' - .(sqrt(4)' 4 (4 / .4) + (4 / .4`%) 3 (4 + 4'%) / .4'% 4 (4 + (4 + .4')%) / .4'% 911 4 ((4 + 4' %) + .4' %) / .4' % 912 4 4! * (4! / sqrt(.4`) + sqrt(4)) 913 4 ((4 + 4 % ) / .4' % ) + 4 914 4 ((4 + 4' %) / .4' %) + 4 915 3 (4 + sqrt(.4' %)) / .4' % 916 4 root(.(sqrt(4)),4) - (4! / .(sqrt(4))' 4 (4 * 4) + (4 / .4`%) 917 4 ((4 + sqrt(.4' % )) / .4' % ) + sqrt(4) 918 4 (4 / .4' % ) + (4 / .(sqrt(4))') 4 (4 + (4 + 4)%) / .4`% 3 (sqrt(4) + 4%) / (.sqrt(4)')% 919 4 ((4 + sqrt(.4' % )) / .4' % ) + 4 920 4 (4 / .4' %) + 4! - 4 921 4 (4 + .(sqrt(4)) / .4' %) - 4! 4 ((4 + sqrt(4%)) / .4`%) - 4! 922 4 (4 / .4' %) + 4! - sqrt(4) 923 4 ((4 - .4' % ) / .4' % ) + 4! 924 4 root(.(sqrt(4)),4) - (4! / .(4!)) 3 (4 / .4`%) + 4! 925 4 root(.(sqrt(4)),4) - (4! / .(4!)') 4 (4 + (.4` / 4)) / .4`% 926 4 (4 / .4' %) + 4! + sqrt(4) 927 4 (sqrt(4) + sqrt(.4' % ) - (sqrt(.4')) % / .(sqrt(4))' % 4 (4 + (4! / sqrt(4))%) / .4`% 928 4 4 * (4^4 - 4!) 929 4 (sqrt(4) + sqrt(.4' % ) - .(sqrt(4))' % ) / .(sqrt(4))' % 930 4 ((4 + .(4!)) / .4' %) - 4! 4 (4 - (4 + 4!)%) / .4% 3 (sqrt(4) + sqrt(.4'%)) / (.sqrt(4)')% 931 4 (sqrt(4) + sqrt(.4' % ) + .(sqrt(4))' % ) / .(sqrt(4))' % 932 4 (4 / .4' %) + root(.4,4) 933 4 ((4 + 4 % ) / .4' % ) + 4! 934 4 ((4 + 4' %) / .4' % ) + 4! 935 4 (4 + .(sqrt(4)) - 4' % ) / .4' % 4 (4 - (sqrt(4) + 4!)%) / .4% 936 4 (4! + sqrt(4)) * 4! / sqrt(.4`) 937 4 (sqrt(.4') - 4 % - .(sqrt(4)) % / sqrt(.4' % ) % 4 (sqrt(.4`) - (4 + sqrt(4%))%) / sqrt(.4`%)% 938 4 ((4 - .(4!)) / .4 % ) - sqrt(4) 4 ((4 - 4!%) / .4%) - sqrt(4) 939 4 (4 - .(4!) - .4 % ) / .4 % 4 (4 - (4! + .4)%) / .4% 940 4 (4 / .4%) - (4! / .4) 3 (4 - 4!%) / .4% 941 4 ((4 + 4'%) / .4'%) - 4! 942 4 (4 - .(4!)) / .4 % ) + sqrt(4) 4 ((4 - 4!%) / .4%) + sqrt(4) 943 4 ((4 + .(sqrt(4))) / .4' %) - sqrt(4) 4 ((4 + sqrt(4%)) / .4`%) - sqrt(4) 944 4 (4 / .4' %) + 44 945 4 (4 / .4' %) + (sqrt(4) / 4' %) 3 (4 + sqrt(4%)) / .4`% 946 4 (4 / .4 %) - (4! / .4') 947 4 (4 + .(sqrt(4)) / .4' %) + sqrt(4) 4 ((4 + sqrt(4%)) / .4`%) + sqrt(4) 948 4 (4 / .4' %) + 4! + 4! 949 4 (4 + .(sqrt(4)) / .4' %) + 4 4 4 + ((4 + sqrt(4%)) / .4`%) 950 3 (4 + .(sqrt(4))') / .4' % 3 (4 - sqrt(4%)) / .4% 951 4 ((4!) + (sqrt(sqrt(sqrt(.4))))^(-4!)) * (4!) 952 4 (4 / .4 %) - (4! + 4!) 953 4 (4 + .(4!) - .4' % ) / .4' % 4 (4 + (4! - .4`)%) / .4`% 954 3 (4 + .(4!)) / .4' % 3 (4 + 4!%) / .4`% 955 4 (4 / .4 %) - (sqrt(4)/ 4' %) 956 4 (4 / .4 %) - 44 957 4 ((4^4) - 4!) / .(4!)' 4 ((4! - sqrt(4%))% + .4) / sqrt(.4`%)% 958 4 ((4 + .(4!)) / .4' %) + 4 4 4 + ((4 + 4!%) / .4`%) 959 4 (sqrt(sqrt(sqrt(4 ^ 4!)))) - sqrt(.4' %)) / sqrt(.4' %) 960 4 (4 * 4!) * 4 / .4 3 4! / sqrt(.4 ^ -sqrt(4))% 961 4 (sqrt(sqrt(sqrt(4 ^ 4!)))) + sqrt(.4' %)) / sqrt(.4' %) 962 4 (sqrt(4) / .4' %) + root(.(sqrt(4))' ,4) 4 sqrt(4) + (4! / sqrt(.4 ^ -sqrt(4))%) 963 4 (sqrt(sqrt(sqrt(4 ^ 4!)))) + .(sqrt(4)) / sqrt(.4' %) 4 (4 + (4 + 4!)%) / .4`% 964 4 root(.(sqrt(4)),4) - 4! / .4 4 root(sqrt(4%), 4) - (4! / .4) 965 4 (4 + sqrt(.4' % ) + .(sqrt(4))') / .4' % 966 4 (4.4 / .4' %) - 4! 967 4 (sqrt(4) - sqrt(.4'%) + (sqrt(.4'%))%) / .(sqrt(4)%) 4 (sqrt(.4`) - (sqrt(4) + sqrt(4%))%) / sqrt(.4`%)% 968 4 44 * (4! - sqrt(4)) 969 4 ((4 + 4'%) / .4'%) - 4! 970 4 root(.(sqrt(4)),4) - 4! / .4' 3 (sqrt(.4`) - sqrt(4)%) / sqrt(.4`%)% 971 4 sqrt(sqrt(4^4!)) - (root(-(.(sqrt(4)),.(sqrt(4)) 4 ((4 - sqrt(4)%) / .4%) - 4! 972 4 4 * (root.4(4/.4')) 4 (4 / .4 %) - (4 + 4!) 973 4 ((sqrt(.4') - .(sqrt(4)) % ) / sqrt(.4' % ) % ) - 4! 4 ((sqrt(4%) - sqrt(4))% + sqrt(.4`)) / sqrt(.4`%)% 974 4 ((4 + .(sqrt(4))') / .4' % ) + 4! 4 (4 / .4%) - (sqrt(4) + 4!) 975 4 (4! + sqrt(4))! / sqrt(.4') * (4!)! 976 4 (4! / 4)! + 4 ^ 4 3 (4 / .4%) - 4! 977 4 ((4 + .4 % ) / .4 %) - 4! 978 4 (4 / .4 %) - (4! - sqrt(4)) 979 4 root(.(sqrt(4))' ,4) - (sqrt(4) / 4' % 4 root(sqrt(4%), 4) - (sqrt(4%) / .4`%) 980 4 root(.(sqrt(4)),4) - 44 3 (sqrt(4) - 4%) / sqrt(4%)% 981 4 (4.4 - 4 % ) / .4' % 982 4 (4 / .4 % ) - (4 / .(sqrt(4))') 4 (4 - (4 + sqrt(4))!%%) / .4% 983 4 (sqrt(4 ^ 4!) * .(4!)) - 4 % 984 4 sqrt(((4 + 4)! + 4!) * 4!) 985 4 (4 / .4 %) - (sqrt(.4') / 4' %) 986 4 (4.4 / .4' %) - 4 987 4 (4! - sqrt(4) - sqrt(.4' % )) / (sqrt(4) % )' 4 (sqrt(.4`) - (sqrt(4%) + sqrt(.4`))%) / sqrt(.4`%)% 988 4 root(.(sqrt(4)),4) - (4! / sqrt(.4')) 4 ((4 - 4%) / .4%) - sqrt(4) 989 4 (4.4 - .4' % ) / .4' % 990 4 44 / (.4` - .4) 2 4! / (4!)' %o 3 (4 - 4%) / .4% 991 4 (4 / .4 %) - (4 / .4') 992 4 root(.(sqrt(4)),4) - root(.4,4) 4 (4 / .4%) - (4 + 4) 993 4 (4! - sqrt(4) + sqrt(.4' % )) / sqrt(4) % )' 4 ((4 - sqrt(4)%) / .4%) - sqrt(4) 994 4 (4 / .4 %) - (4! / 4) 3 (sqrt(.4`) - .4%) / sqrt(.4`%)% 995 4 (4 / .4 %) - (sqrt(4) / .4) 3 (4 - sqrt(4)%) / .4% 996 4 sqrt(sqrt(sqrt((4 / .4)^4!))) - 4 3 (4 / .4%) - 4 997 4 (4 / .4 %) - sqrt(4 / .4') 3 (sqrt(.4`) - sqrt(4%)%) / sqrt(.4`%)% 998 4 sqrt(sqrt(sqrt((4 / .4)^4!))) - sqrt(4) 3 (4 / .4%) - sqrt(4) 999 4 444 / .4` 3 (4 - .4%) / .4% 2 4/(.4%)' `````` 1000 4 4 * 4^4 - 4! 3 sqrt(sqrt(sqrt((4 / .4)^4!))) 2 4 / .4 % 1001 4 4/.4 % + 4/4 3 (4 + .4%) / .4% 1002 3 4/.4 % + sqrt(4) 1003 4 4/.4 % + sqrt(4/.4') 3 (sqrt(4%)% + sqrt(.4`)) / sqrt(.4`%)% 1004 3 4/.4 % + 4 1005 4 4/.4 % + sqrt(4)/.4 3 (4 + sqrt(4)%) / .4% 1006 4 4/.4 % + sqrt(4) + 4 3 (.4% + sqrt(.4`)) / sqrt(.4`%)% 1007 4 (4 + 4! %o + .4 %) / .4 % 4 ((4 + 4)!% - .4) / .4 1008 4 4/.4 % + 4 + 4 3 ((4 + 4)! / .4)% 1009 4 4/.4 % + 4/.4' 1010 4 4/.4 % + 4/.4 3 (4 + 4%) / .4% 1011 4 ((sqrt(4)/.4' %) - sqrt(.4')) / .4' 1012 4 4/.4 % + 4!/sqrt(4) 1013 4 ((sqrt(4)/.4' %) + .(sqrt(4))' / .4' 4 ((4 + 4)!% + sqrt(4)) / .4 1014 3 (4!/(4!)' %o + 4! 4 4 + ((4 + 4%) / .4%) 1015 4 4/.4 % + sqrt(.4')/(4)' % 4 root(sqrt(4%), 4) - (4 / .4`) 1016 4 4/.4 % + (4 * 4) 1017 4 ((sqrt(4)/,4' %) + sqrt(4)) / .4' 1018 4 4/.4 % + 4/.(sqrt(4))' 4 (4 + (4 + 4)!%) / .4 4 (sqrt(sqrt(4^4!)) - 4!)/4 1019 4 root(.(sqrt(4)),4) - (sqrt(4)/.4) 4 root(sqrt(4%), 4) - (sqrt(4) / .4) 1020 4 4/.4 % + (4! - 4) 3 root(sqrt(4%), 4) - 4 1021 4 root(.(sqrt(4)),4) - sqrt(4/.4') 4 root(sqrt(4%), 4) - sqrt(4 / .4`) 1022 4 4/.4 % + (4! - sqrt(4)) 3 root(sqrt(4%), 4) - sqrt(4) 1023 4 root(.(sqrt(4)),4) - 4/4 4 root(sqrt(4%), 4) - (4 / 4) 4 (sqrt(sqrt(4^4!)) - 4)/4 3 4/(.4%)' + 4! 1024 2 root(.(sqrt(4)),4) 2 root(sqrt(4%), 4) 1025 4 root(.(sqrt(4)),4) + 4/4 4 (4 + (.4 / 4)) / .4% 4 (sqrt(sqrt(4^4!)) + 4)/4 1026 3 root(.(sqrt(4)),4) + sqrt(4) 3 sqrt(4) + root(sqrt(4%), 4) 1027 4 root(.(sqrt(4)),4) + sqrt(4/.4') 4 sqrt(4 / .4`) + root(sqrt(4%), 4) 1028 3 root(.(sqrt(4)),4) + 4 3 4 + root(sqrt(4%), 4) 1029 4 root(.(sqrt(4)),4) + sqrt(4)/.4 4 (sqrt(4) / .4) + root(sqrt(4%), 4) 1030 4 root(.(sqrt(4)),4) + sqrt(4) + 4 4 (sqrt(sqrt(4^4!)) + 4!)/4 3 (sqrt(4)% + sqrt(.4`)) / sqrt(.4`%)% 1031 4 (sqrt(.4') + sqrt(4) % + sqrt(.4' %)%) / sqrt(.4' %)% 1032 4 root(.(sqrt(4)),4) + 4 + 4 4 (4! * 44) - 4! 1033 4 root(.(sqrt(4)),4) + 4/.4' 4 (4 / .4`) + root(sqrt(4%), 4) 1034 4 root(.(sqrt(4)),4) + 4/.4 4 (4 / .4) + root(sqrt(4%), 4) 1035 4 (4!/sqrt(4) %) - (.4/.(4!)' %) 4 ((sqrt(4) / .4) - .4) / .4`% 1036 4 (4!/sqrt(4)' %) - 44 4 (4! / sqrt(4)) + root(sqrt(4%), 4) 1037 4 (sqrt(.4') + 4! %o + sqrt(.4' %) %) / (sqrt.4' %) %) 1038 4 (4!/(4!)' %o) + 4! + 4! 1039 4 root(.(sqrt(4)),4) + sqrt(.4')/4' % 4 root(-sqrt(4), .4`%) + root(sqrt(4%), 4) 1040 4 root(.(sqrt(4)),4) + (4 * 4) 4 4 * (4 + 4 ^ 4) 1041 4 ((.(sqrt(4) ^ -(sqrt(4)) / 4! %o) - sqrt(.4') 4 (4 - 4% + sqrt(.4`)) / .4`% 1042 4 root(.(sqrt(4)),4) + (4/.(sqrt(4))') 1043 5 ((4!/4)! - 4! - sqrt(.4')) / sqrt(.4') 4 44 + (sqrt(4) / (.(sqrt(4)) % )') 1044 4 (4/.4 %) + 44 1045 4 (4/.4 %) + (sqrt(4)/4' %) 1046 4 (4! - sqrt(4)) + root(.(sqrt(4)),4) 4 ((4 + sqrt(4%)) / .4%) - 4 1047 4 (4! - sqrt(.4') - sqrt(.4' %)) / sqrt(4)' % 1048 3 4! + root(.(sqrt(4)),4) 3 4! + root(sqrt(4%), 4) 1049 4 .(sqrt(4)) ^ -(sqrt(4)) + root(.(sqrt(4)),4) 4 (4 + sqrt(4%) - .4%) / .4% 1050 4 (4/.4 %) + sqrt(4) / 4 % 3 (4 + sqrt(4%)) / .4% 1051 4 (.4' - 4! %o - .4' % %) / 4 % % 4 (4 + sqrt(4%) + .4%) / .4% 1052 4 (4! * 44) - 4 1053 4 (.4' + 4! %o - 4 % %) / 4' % % 1054 4 (4/.4 %) + (4!/.4') 4 44*4! - sqrt(4) 1055 4 (4!/sqrt(4)' %) - (.(sqrt(4)) ^ -(sqrt(4)) 4 (4 - (sqrt(4) - 4!)%) / .4% 1056 4 (4!+4!)*(4! - sqrt(4)) 3 (4!/sqrt(4)' %) - 4! 3 4! * 44 1057 4 ((4 ^ 4) + .(4!)') / .(4!)' 4 ((4 - sqrt(4%))% + sqrt(.4`)) / sqrt(.4`%)% 1058 4 (4!/sqrt(4)' %) - (4! - sqrt(4)) 4 sqrt(4) + (4! * 44) 1059 4 (4! - .4 - (sqrt(.4' % )) / sqrt(4)' % 4 (4 + (4! - .4)%) / .4% 1060 4 (4! / sqrt(4)' %) - (4! - 4) 4 44*4! + 4 3 (4 + 4!%) / .4% 1061 4 (4! - (.4 + sqrt(4)' % )) / sqrt(4)' % 4 (4 + (4! + .4)%) / .4% 1062 4 (4! / sqrt(4)' %) - 4 / .(sqrt(4))' 4 ((4 + 4!%) / .4%) + sqrt(4) 3 (4! - .4) / (sqrt(4))'% 4 (4! - .4) / (sqrt(4) + sqrt(4%)')% 1063 4 (4! - .4 + sqrt(4)' % ) / sqrt(4)' % 4 ((4 + sqrt(4%))% + sqrt(.4`)) / sqrt(.4`%)% 1064 4 (4! / sqrt(4)' %) - (4 * 4) 4 4 + ((4 + 4!%) / .4%) 1065 4 (4! / sqrt(4)' %) - sqrt(.4') / 4' % 4 (4 ^ 4 - .4) / 4!% 1066 4 ((4 ^ 4) / .(4!)) - sqrt(.4') 4 (4 ^ 4 / 4!%) - sqrt(.4`) 1067 4 ((4! - .(sqrt(4)) / sqrt(4)' % ) - 4 1068 4 (4! / sqrt(4)' %) - 4!/sqrt(4) 4 root(sqrt(4%), 4) + 44 1069 4 ((4! - .(sqrt(4)) / sqrt(4)' % ) - sqrt(4) 4 root(sqrt(4%), 4) + (sqrt(4%) / .4`%) 1070 4 (4! / sqrt(4)' %) - 4/.4 4 (4 + (4 + 4!)%) / .4% 3 (4! - .sqrt(4)') / (sqrt(4))'% 4 (4! - .sqrt(4)') / (sqrt(4) + sqrt(4%)')% 1071 4 (4! / sqrt(4)' %) - 4/.4' 4 ((sqrt(4) / .4%) - 4!) / .4` 1072 4 (4! / sqrt(4)' %) - (4 + 4) 4 4! * (44 + sqrt(.4`)) 1073 4 (4! - .(sqrt(4)) + 4' % ) / sqrt(4)' % 1074 4 (4! / sqrt(4)' %) - (4 + sqrt(4)) 4 ((4 + sqrt(4))! - 4) / sqrt(.4`) 1075 4 (4! / sqrt(4)' %) - sqrt(4)/.4 4 (4 ^ 4 + sqrt(4)) / 4!% 1076 3 (4! / sqrt(4)' %) - 4 4 (44 / 4%) - 4! 1077 4 (4! / sqrt(4)' %) - sqrt(4/.4') 4 ((4 + sqrt(4))! - sqrt(4)) / sqrt(.4`) 3 (4! - sqrt(.4'%)) / (sqrt(4))'% 4 (4! - sqrt(.4'%)) / (sqrt(4) + sqrt(4%)')% 1078 3 (4! / sqrt(4)' %) - sqrt(4) 4 (4! / .4`) + root(sqrt(4%), 4) 1079 4 (4! / sqrt(4)' %) - 4/4 4 ((4 + sqrt(4))! - sqrt(.4`)) / sqrt(.4`) 1080 2 4! / sqrt(4)' % 3 (4 + sqrt(4))! / sqrt(.4`) 4 44*4! + 4! 1081 3 (4! + sqrt(4)' % ) / sqrt(4)' % 4 ((4 + sqrt(4))! + sqrt(.4`)) / sqrt(.4`) 1082 3 (4! / sqrt(4)' % ) + sqrt(4) 4 ((4 + sqrt(4))! / sqrt(.4`)) + sqrt(4) 1083 4 (4! / sqrt(4)' % ) + sqrt(4/.4') 4 ((4 + sqrt(4))! + sqrt(4)) / sqrt(.4`) 1084 3 (4! / sqrt(4)' % ) + 4 4 (4! / .4) + root(sqrt(4%), 4) 1085 4 (4! / sqrt(4)' % ) + sqrt(4)/.4 1086 4 (4! / sqrt(4)' % ) + sqrt(4) + 4 4 (4 + (4 + sqrt(4))!) / sqrt(.4`) 1087 4 ((.(4!) + 4! %o) / 4! % %o) - sqrt(4) 1088 4 (4! / sqrt(4)' % ) + 4 + 4 4 (4! - (sqrt(4) + 4!%)) / sqrt(4)% 1089 4 (4! / sqrt(4)' % ) + 4/.4' 4 ((4 / .4`) + 4!) ^ sqrt(4) 3 (4! + sqrt(4%)) / (sqrt(4))'% 4 (4! + sqrt(4%)) / (sqrt(4) + sqrt(4%)')% 1090 4 (4! / sqrt(4)' % ) + 4/.4 4 (44 - .4) / 4% 1091 3 ((.(4!) + 4! % %o) + sqrt(4) 4 (4! + sqrt(4%)%) / (sqrt(4) + sqrt(4%))% 1092 4 (4! / sqrt(4)' % ) + 4! / sqrt(4) 1093 4 ((.(4!) + 4! %o) / (4!)' % %o) + 4 1094 4 (44 - .(4!)) / 4 % 4 (44 - 4!%) / 4% 1095 4 (4! / sqrt(4)' % ) + (sqrt(.4') / 4' % ) 4 (44 - sqrt(4%)) / 4% 1096 4 (4! / sqrt(4)' % ) + (4 * 4) 4 (44 / 4%) - 4 1097 4 (4! + .4 - sqrt(4)' % ) / sqrt(4)' % 4 (sqrt(.4`) - sqrt(4%)% + sqrt(.4`%)) / sqrt(.4`%)% 1098 3 (4! + .4) / sqrt(4)' % 4 (44 / 4%) - sqrt(4) 1099 4 (4! + .4 + sqrt(4)' % ) / sqrt(4)' % 4 (44 - 4%) / 4% 1100 4 (4! / sqrt(4)' % ) + (4! - 4) 3 44 / 4% 1101 4 (4.4 + .4 % ) / .4 % 1102 4 (4! / sqrt(4)' % ) + (4! - sqrt(4)) 4 sqrt(4) + (44 / 4%) 1103 4 ((4! - sqrt(4)' %) / sqrt(4)' % ) + 4! 4 (sqrt(4%)% + sqrt(.4`) + sqrt(.4`%)) / sqrt(.4`%)% 1104 4 (4! / sqrt(4)' % ) + 4! 4 (44 + sqrt(4))*4! 4 4 + (44 / 4%) 3 4!/(sqrt(4))'% + 4! 4 4! / (sqrt(4) + sqrt(4%)')% + 4! 1105 4 (4! / sqrt(4)' % ) + .(sqrt(4)) ^ - (sqrt(4)) 4 (sqrt(4%) + 44) / 4% 1106 4 (4! / sqrt(4)' % ) + 4! + sqrt(4) 4 (4!% + 44) / 4% 1107 4 (4! + .4 + .(sqrt(4))) / (sqrt(4))' % 1108 4 (4! / sqrt(4)' % ) + 4! + 4 4 ((4 + 4)!%% + .4) / .4% 1109 4 (4! + .4' + .(sqrt(4)) / (sqrt(4))' % 1110 4 (4! / sqrt(4)' % ) + (sqrt(4) / sqrt(.4' % ) 4 444 / .4 3 (4! + sqrt(.4')) / (sqrt(4))'% 4 (4! + sqrt(.4')) / (sqrt(4) + sqrt(4%)')% 1111 4 (4! + sqrt(.4') + sqrt(4)' % ) / (sqrt(4))' % 2 .4' / (4%%)' 1112 4 (4! / sqrt(4)' % ) + root.4,(4) 4 (4! - sqrt(4) + 4!%) / sqrt(4)% 1113 4 (4! + sqrt(.4') + sqrt(.4' % )) / sqrt(4)' % 4 (sqrt((.4`% ^ -sqrt(4))%) - 4!%) / sqrt(4)% 3 .4'/(4%%)' + sqrt(4) 1114 4 ((4! + sqrt(.4')) / sqrt(4)' % ) + 4 4 root(sqrt(4%), 4) + (.4 / .4`%) 1115 4 ((.(sqrt(4)) ^ -(sqrt(4)) - (.(sqrt(4))) / (sqrt(4))' % 4 ((sqrt(4) / .4`%) - 4) / .4 3 .4'/(4%%)' + 4 1116 4 (4! / sqrt(4)' % ) + (4! / sqrt(.4')) 4 ((sqrt(4) / .4%) - 4) / .4` 1117 4 ((.4' + .(4!) % - .4' % % ) / 4 % % 1118 4 (sqrt(4) + (4! - .4)%) / sqrt(4%)% 1119 4 ((sqrt(4%) / .4`%) - 4!%) / 4% 1120 3 (sqrt(4) + 4!%) / sqrt(4%)% 1121 4 (sqrt(4) / (.4 * .4`)%) - 4 1122 4 (sqrt(4) + (4! + .4)%) / sqrt(4%)% 1123 4 (sqrt(4) / (.4 * .4`)%) - sqrt(4) 1124 4 4! + (44 / 4%) 1125 3 sqrt(4) / (.4 * .4`)% 1126 4 ((sqrt(4) / .4`%) + .4) / .4 1127 4 sqrt(4) + (sqrt(4) / (.4 * .4`)%) 1128 4 (sqrt(4) * 4! * 4!) - 4! 4 (4!+4!)*4! - 4! 1129 4 4 + (sqrt(4) / (.4 * .4`)%) 1130 4 (sqrt(4) + (sqrt(4) / .4`%)) / .4 1131 4 (4!% + (sqrt(4%) / .4`%)) / 4% 1132 4 (4! / .(sqrt(4))') + root(.(sqrt(4)), 4) 1133 4 (.(sqrt(4))' + .4' % - sqrt(.4') % % ) / sqrt(4) % % 1134 4 (4 + (sqrt(4) / .4%)) / .4` 1135 4 (4 + (sqrt(4) / .4`%)) / .4 3 .4'/(4%%)' + 4! 1136 4 ((sqrt(4) * 4!) - sqrt(.4`)) * 4! 1137 4 (4!% + sqrt((.4`% ^ -sqrt(4))%)) / sqrt(4)% 1138 4 (4 / .(4!)' % ) - root(.(sqrt(4))', 4) 1139 4 (4 + 4!) + (.(sqrt(4))' / sqrt(4) % % )' 1140 4 (4 + 4 - .4) / sqrt(.4`)% 1141 4 sqrt(4 / .4' % ) + (.(sqrt(4))' / sqrt(4) % % )' 1142 4 ((.4 ^ 4) - sqrt4)' % % ) / .(sqrt(4)) % % 1143 4 (root(.(sqrt(4))', 4)) - 4) / .4' 1144 4 (sqrt(4) + 4!) * 44 1145 4 (4 + sqrt(.4`% ^ -sqrt(4))) / sqrt(4%) 1146 4 (4! / sqrt(4)%) - (4! / .4`) 1147 4 (4! / sqrt(.4')) + (.(sqrt(4))' / sqrt(4) % % )' 1148 4 (sqrt(4) * 4! * 4!) - 4 4 (4!+4!)*4! - 4 1149 4 (sqrt(4) / (.4 * .4`)%) + 4! 1150 4 (sqrt(4) + 44) / 4% 4 4!*4! * sqrt(4) - sqrt(4) 1151 4 (root(.(sqrt(4))', 4) - .4') / .4' 1152 3 sqrt(4) * 4! * 4! 1153 4 root(.(sqrt(4))' 4) + .4') / .4' 1154 4 sqrt(4) + (sqrt(4) * 4! * 4!) 1155 4 (4! - (.4 / .4`)) / sqrt(4)% 3 (4! - sqrt(.4')) / (sqrt(4)%)' 1156 4 (4! / sqrt(4)%) - 44 4 4!*4! * sqrt(4) + 4 1157 4 ((4 + 4!) / (4!)' %o ) + sqrt(4) 1158 4 (4! / (sqrt(4) % )') - sqrt(4 / .4' % ) 1159 4 ((4 + 4!) / (4!)' %o ) + 4 1160 4 (4 + (4! * 4!)) * sqrt(4) 1161 4 ((4 ^ 4) + sqrt(4)) / .(sqrt(4))' 1162 4 (.(sqrt(4))' + ((4! / sqrt(.4')) %o ) / .(sqrt(4))' %o 1163 4 (4! / (sqrt(4) % )') - .(sqrt(4)) ^ -(sqrt(4)) 1164 4 (4 + 4 - 4!%) / sqrt(.4`)% 1165 4 (4 + sqrt(.4`) - sqrt(.4`)%) / .4% 1166 4 ((4 + sqrt(.4`)) / .4%) - sqrt(.4`) 3 (4! - .4') / (sqrt(4)%)' 1167 4 (4! - sqrt(.4`) + sqrt(.4`)%) / sqrt(4)% 1168 4 (4! / sqrt(4)%) - root(.4, 4) 1169 4 (sqrt(4) + 4! - sqrt(4)' % ) / sqrt(4)' % 1170 4 (4 + 4 - sqrt(4%)) / sqrt(.4`)% 3 (4! + sqrt(4)) / (sqrt(4))'% 4 (4! + sqrt(4)) / (sqrt(4) + sqrt(4%)')% 1171 4 (sqrt(4) + 4! + sqrt(4)' % ) / sqrt(4)' % 1172 4 (4! / sqrt(4)%) - (4 + 4!) 1173 4 (4! - (4! / .4`)%) / sqrt(4)% 1174 4 (4! / sqrt(4)%) - (sqrt(4) + 4!) 1175 4 (4! - (sqrt(4) / 4)) / sqrt(4)% 1176 3 (4! / sqrt(4)%) - 4! 4 4!*4! * sqrt(4) + 4! 1177 4 ((sqrt(4)% + 4!) / sqrt(4)%) - 4! 3 (4! - .(sqrt(4))') / (sqrt(4)%)' 1178 4 (4! - 44%) / sqrt(4)% 1179 4 ((sqrt(4) / .4%) + 4!) / .4` 1180 3 (4! - .4) / sqrt(4)% 1181 4 (sqrt(4)% + 4! - .4) / sqrt(4)% 1182 4 sqrt(4) + ((4! - .4) / sqrt(4)%) 1183 4 (4! / (sqrt(4) % )') - (sqrt(4) / .4) 1184 4 (4! / sqrt(4)%) - (4 * 4) 3 4!/(sqrt(4)%)' - 4 1185 4 ((sqrt(4) / .4`%) + 4!) / .4 1186 4 (4! - (4 + 4!)%) / sqrt(4)% 3 (4! - (4%)') / (sqrt(4)%)' 3 4!/(sqrt(4)%)' - sqrt(4) 1187 4 (4! - (sqrt(4) + 4!)%) / sqrt(4)% 3 (4! - (sqrt(4)%)') / (sqrt(4)%)' 1188 3 (4! - 4!%) / sqrt(4)% 3 4! / (.4!' - (.sqrt(4))') 1189 4 ((sqrt(4) - 4!)% + 4!) / sqrt(4)% 3 (4! + (sqrt(4)%)') / (sqrt(4)%)' 1190 4 4! /(.4!' - (.sqrt(4))' ) + sqrt(4) 3 (4! - sqrt(4%)) / sqrt(4)% 1191 4 (4! / sqrt(4)%) - (4 / .4`) 1192 4 sqrt(4) * ((4! / 4%) - 4) 3 4!/(sqrt(4)%)' + 4 1193 4 (4! / (sqrt(4) % )') + (sqrt(4) / .4) 1194 4 (4! / sqrt(4)%) - (4 + sqrt(4)) 1195 4 (4! - (.4 / 4)) / sqrt(4)% 1196 3 (4! / sqrt(4)%) - 4 1197 4 ((sqrt(4)% + 4!) / sqrt(4)%) - 4 1198 3 (4! / sqrt(4)%) - sqrt(4) 1199 4 (4! + (.sqrt(4))' )/(.4!' - (.sqrt(4))' ) 3 (4! - sqrt(4)%) / sqrt(4)% 1200 2 4! / sqrt(4) % 1201 3 (sqrt(4)% + 4!) / sqrt(4)% 1202 3 sqrt(4) + (4! / sqrt(4)%) 1203 4 4!/(sqrt(4))% + sqrt(4/.4') 1204 3 4 + (4! / sqrt(4)%) 1205 4 4!/(sqrt(4))% + sqrt(4)/.4 1206 4 4+sqrt(4)+(4!/sqrt(4)%) 1207 4 .4'/(4%%)' + (4! x 4) 1208 4 4!/(sqrt(4))% + (4 x sqrt(4)) 1209 4 4!/(sqrt(4))% + 4/.4' 1210 4 (4! + .4')/(.4!' - (.sqrt(4))' ) 3 (4! + sqrt(4%)) / sqrt(4)% 1211 4 .4'/(4%%)' + 4/4% 1212 4 4! /(.4!' - (.sqrt(4))' ) + 4! 3 (4! + 4!%) / sqrt(4)% 1215 4 4!/(.4' - .4) /.4' 1220 3 (4! + .4) / sqrt(4)% 1221 4 (4! + sqrt(.4'))/(.4!' - (.sqrt(4))' ) 1224 3 (4! / sqrt(4)%) + 4! 1225 4 sqrt((4! - sqrt(.4'))/sqrt(.4'))^4 1226 4 (.sqrt(4) ^ (- 4) )*sqrt(4) - 4! 1232 4 (4! + 4)*44 1242 4 (4!*4! - 4!)/.4' 1246 4 (.sqrt(4) ^ (- 4) )*sqrt(4) - 4 1248 4 (.sqrt(4) ^ (- 4) )*sqrt(4) - sqrt(4) 1250 3 sqrt(4) / 4 % / 4 % 1252 4 (.sqrt(4) ^ (- 4) )*sqrt(4) + sqrt(4) 1254 4 (.sqrt(4) ^ (- 4) )*sqrt(4) + 4 1256 4 4^4 /.sqrt(4) - 4! 1258 4 ((.sqrt(4) ^ (- 4) ) + 4) * sqrt(4) 1260 4 ((4!+4)/4)! /4 1270 4 (4^4 - sqrt(4))/.sqrt(4) 1272 4 4!*4!/.4' - 4! 1274 4 (.sqrt(4) ^ (- 4) )*sqrt(4) + 4! 1275 4 (root(.(sqrt(4))' , 4) - sqrt(4))/.4 1276 4 4^4 /.sqrt(4) - 4 1278 4 (4^4 - .4) /.sqrt(4) 1279 4 (root(.(sqrt(4))' , 4) - .4)/.4 1280 3 4 ^ 4 / sqrt(4%) 1281 4 (root(.(sqrt(4))' , 4) + .4)/.4 1282 4 (4^4 + .4) /.sqrt(4) 1284 4 4^4 /.sqrt(4) + 4 1285 4 (root(.(sqrt(4))' , 4) + sqrt(4))/.4 1287 4 (4!*4! - 4)/.4' 1290 4 (4^4 + sqrt(4))/.sqrt(4) 1292 4 4!*4!/.4' - 4 1294 4 4!*4!/.4' - sqrt(4) 1295 4 (4!*4! - .4')/.4' 1296 3 (4!/4)^4 1297 4 (4!*4! + .4')/.4' 1298 4 4!*4!/.4' + sqrt(4) 1300 4 4!*4!/.4' + 4 3 (sqrt(4) + 4!) / sqrt(4) % 1304 4 4^4 /.sqrt(4) + 4! 1305 4 (4!*4! + 4)/.4' 1308 4 (4! + .(sqrt(4))' )*4!/.4' 1311 4 sqrt(sqrt(sqrt(44/4)^4!)) 1312 4 (4!/.4' + sqrt(.4'))*4! 1320 4 4!*4!/.4' + 4! 1325 4 (4! - .4')/(.4! - (.sqrt(4))' ) 1326 4 4! /(.4! - (.sqrt(4))' ) - 4! 1331 4 sqrt(sqrt(sqrt(44/4)^4!)) 1332 4 (4! + sqrt(.4'))*4!/.4' 1340 4 (root(.(sqrt(4))' , 4) + 4!)/.4 1344 4 (4!/.4 - 4)*4! 1346 4 4! /(.4! - (.sqrt(4))' ) - 4 1348 4 4! /(.4! - (.sqrt(4))' ) - sqrt(4) 1350 4 (4!*4! + 4!)/.4' 3 (4 + sqrt(4)) / .4`% 3 4! / (.4! - (.sqrt(4))') 1352 4 4! /(.4! - (.sqrt(4))' ) + sqrt(4) 1354 4 4! /(.4! - (.sqrt(4))' ) + 4 1360 3 (4!% + sqrt(.4`)) / sqrt(.4`%)% 1369 4 sqrt((4! + sqrt(.4'))/sqrt(.4'))^4 1374 4 4! /(.4! - (.sqrt(4))' ) + 4! 1375 4 (4 - sqrt(.4') )/(.4!' - .4!) 1380 4 (4!*4! - 4!)/.4 1386 4 (4! + 4)/(.4!' - (.sqrt(4))' ) 1388 4 (root(-.sqrt(4), .sqrt(4)) - sqrt(4)) * .4' 1392 4 ((4!/4)! - 4!)*sqrt(4) 1400 4 (4! - sqrt(.4'))*4!/.4 3 (4 + 4!) / sqrt(4)% 1404 4 (4! + sqrt(4))*(4!/.4') 1408 4 (4! - sqrt(4))*sqrt(sqrt(sqrt(4^4!))) 1416 4 4!*4!/.4 - 4! 1424 4 (4!/.4 - sqrt(.4'))*4! 1428 4 (4! - .sqrt(4))*4!/.4 1430 4 (4!*4! - 4)/.4 1432 4 ((4!/4)! - 4)*sqrt(4) 1435 4 (4!*4! - sqrt(4))/.4 1436 4 4!*4!/.4 - 4 1438 4 4!*4!/.4 - sqrt(4) 1439 4 (4!*4! - .4)/.4 1440 3 (4!/4)! * sqrt(4) 1441 4 (4!*4! + .4)/.4 1442 4 4!*4!/.4 + sqrt(4) 1444 4 4!*4!/.4 + 4 1445 4 (4!*4! + sqrt(4))/.4 1448 4 ((4!/4)! + 4)*sqrt(4) 1450 4 (4!*4! + 4)/.4 1452 4 (4! + .sqrt(4))*4!/.4 1456 4 (4!/.4 + sqrt(.4'))*4! 1458 4 4*4/(sqrt(sqrt(sqrt( .(sqrt(4))' ^ 4!)))) 1464 4 4!*4!/.4 + 4! 1480 4 (4! + sqrt(.4'))*4!/.4 1485 4 (4 - .4)/(.4!' - .4!) 1488 4 (4!/.4 + sqrt(4))*4! 1500 4 sqrt(.4') / 4'% * 4 / 4% 4 (4!*4! + 4!)/.4 3 (4 + sqrt(4)) / .4% 2 sqrt(.4') / .4'% 1512 4 sqrt(sqrt(sqrt(4^4!)))*4! - 4! 1520 4 (sqrt(sqrt(sqrt(4^4!))) - sqrt(.4'))*4! 1521 4 (sqrt(4! + sqrt(4))^4)/.4' 1530 4 (root(.sqrt(4) , 4) - 4)/sqrt(.4') 1532 4 sqrt(sqrt(sqrt(4^4!)))*4! - 4 1533 4 (root(.sqrt(4) , 4) - sqrt(4))/sqrt(.4') 1534 4 sqrt(sqrt(sqrt(4^4!)))*4! - sqrt(4) 1535 4 (root(.sqrt(4) , 4) - sqrt(.4'))/sqrt(.4') 1536 3 root(sqrt(4%), 4) / sqrt(.4`) 1537 4 (root(.sqrt(4) , 4) + sqrt(.4'))/sqrt(.4') 1538 4 sqrt(sqrt(sqrt(4^4!)))*4! + sqrt(4) 1539 4 (root(.sqrt(4) , 4) - sqrt(4))/sqrt(.4') 1540 4 sqrt(sqrt(sqrt(4^4!)))*4! + 4 1542 4 (root(.sqrt(4) , 4) + 4)/sqrt(.4') 1550 4 (4 - .4!')/(.4!' - .4!) 1551 4 (4 - .4!)/(.4!' - .4!) 1552 4 (sqrt(sqrt(sqrt(4^4!))) + sqrt(.4'))*4! 1560 4 (4! + sqrt(4))/.4 * 4! 1562 4 ((.sqrt(4) ^ (- 4)) - .sqrt(4))/.4 1563 4 ((.sqrt(4) ^ (- 4)) + .sqrt(4))/.4 1566 4 ((4!/4)! - 4!)/.4' 1568 4 sqrt(4*(4! + 4)^4) 1572 4 (root(.sqrt(4) , 4) + 4!)/sqrt(.4') 1575 4 (4! + 4)/(.4! - (.sqrt(4))' ) 1577 4 (((4%)' - .(sqrt(4))') / .(4!)' % % ) + sqrt(4) 4 (4!‰)' /(.4!%%)' + 4!*4! 4 ((4%)'‰ + (sqrt(.4')% /.4!' )'% )/(.sqrt(4)‰)'‰ 1584 4 (root(.4 , 4))/(.4!' - (.sqrt(4))' ) 1596 4 (4!/4)! /.4' - 4! 1600 4 (4*4+4!)^sqrt(4) 3 ((4! - 4) ^ 4)% 1611 4 ((4!/4)! - 4)/.4' 1616 4 (4!/4)! /.4' - 4 1618 4 (4!/4)! /.4' - sqrt(4) 1619 4 ((4!/4)! - .4')/.4' 1620 3 (4 + sqrt(4))! / .4` 1621 4 ((4!/4)! + .4')/.4' 1622 4 (4!/4)! /.4' + sqrt(4) 1624 4 (4!/4)! /.4' + 4 1625 4 (4! + sqrt(4))!/(4!)! /.4 1626 4 4/(.4!' - .4!) - 4! 1629 4 ((4!/4)! + 4)/.4' 1632 4 (44 + 4!)*4! 1638 4 sqrt(sqrt(4^4!)) * .4 - .4 1640 4 (sqrt(sqrt(4^4!)) + 4) * .4 1644 4 (4!/4)! /.4' + 4! 1646 4 4/(.4!' - .4!) - 4 1648 4 (sqrt(sqrt(4^4!)) + 4!) * .4 4 4/(.4!' - .4!) - sqrt(4) 1650 2 4 / .(4!)' % 3 4/(.4!' - .4!) 1652 4 4/(.4!' - .4!) + sqrt(4) 1654 4 4/(.4!' - .4!) + 4 1656 4 (4+4)! /4! - 4! 1664 4 sqrt(sqrt(sqrt(4^4!))) * (4! + sqrt(4)) 1674 4 ((4!/4)! + 4!)/.4' 4 4/(.4!' - .4!) + 4! 1676 4 (4+4)! /4! - 4 1678 4 (4+4)! /4! - sqrt(4) 1679 4 ((4+4)! - 4!)/4! 1680 3 (4 + 4)! / 4! 1681 4 ((4+4)! + 4!)/4! 1682 4 (4+4)! /4! + sqrt(4) 1684 4 (4+4)! /4! + 4 1690 4 (sqrt(4! + sqrt(4))^4)/.4 1700 4 (root.4(4) + sqrt(4)) / sqrt(4) % 1704 4 (4+4)! /4! + 4! 1724 4 sqrt(sqrt(sqrt(4!/sqrt(4))^4!)) - 4 1726 4 sqrt(sqrt(sqrt(4!/sqrt(4))^4!)) - sqrt(4) 1728 4 4!*4!*sqrt(4/.4') 1730 4 sqrt(sqrt(sqrt(4!/sqrt(4))^4!)) + sqrt(4) 1732 4 sqrt(sqrt(sqrt(4!/sqrt(4))^4!)) + 4 1736 4 .4' + .4' + (4!%o ^ -sqrt(4)) 1740 4 ((4!/4)! - 4!)/.4 1749 4 (4 + .4!)/(.4!' - .4!) 1750 4 (4 + .4!')/(.4!' - .4!) 1752 4 sqrt(sqrt(sqrt(4!/sqrt(4))^4!)) + 4! 1764 4 sqrt(44 - sqrt(4))^4 1776 4 4 (444) 1782 4 (4!/sqrt(.4'))/(.4!' - (.sqrt(4))' ) 1790 4 ((4!/4)! - 4)/.4 1792 4 sqrt(sqrt(sqrt(4^4!))) * (4! + 4) 1795 4 ((4!/4)! - sqrt(4))/.4 1796 4 (4!/4)! /.4 - 4 1798 4 (4!/4)! /.4 - sqrt(4) 1799 4 ((4!/4)! - .4)/.4 1800 4 4 / .(sqrt(4))' * 4 / 4% 3 (4!/4)! /.4 2 4 / .(sqrt(4))' % 1801 4 ((4!/4)! + .4)/.4 1802 4 (4!/4)! /.4 + sqrt(4) 1804 4 (4!/4)! /.4 + 4 1805 4 ((4!/4)! + sqrt(4))/.4 1810 4 ((4!/4)! + 4)/.4 1815 4 (4 + .4)/(.4!' - .4!) 1820 4 sqrt(sqrt(4^4!)) * .4' - .4' 1824 4 (4!/4)! /.4 + 4! 1860 4 ((4!/4)! + 4!)/.4 1872 4 (4!/.4' + 4!)*4! 1875 4 (sqrt(4) /.4)! /(sqrt(sqrt(sqrt( .4^4! )))) 1880 3 (4 - 4!%) / sqrt(4%)% 1900 4 (4! / sqrt(.4') + sqrt(4)) / sqrt(4) % 3 (4 - sqrt(4%)) / sqrt(4%)% 1905 4 sqrt((4/.4)! + sqrt(.4'%) ^ (- sqrt(4))) 1912 4 sqrt(44^4) - 4! 1920 4 4!*4*(4! - 4) 1925 4 (4 + sqrt(.4') )/(.4!' - .4!) 1932 4 sqrt(44^4) - 4 1934 4 sqrt(44^4) - sqrt(4) 1936 4 (44) * (44) 3 44^sqrt(4) 1938 4 sqrt(44^4) + sqrt(4) 1940 4 sqrt(44^4) + 4 1944 4 4!/(.sqrt(4))' * 4/(.sqrt(4))' 1960 4 sqrt(44^4) + 4! 1976 3 (4 / sqrt(4%)%) - 4! 1980 4 (4!*4)/(.4!' * .sqrt(4)) 3 (4 - 4%) / sqrt(4%)% 1990 3 (4 - sqrt(4)%) / sqrt(4%)% 1996 3 (4 / sqrt(4%)%) - 4 1998 3 (4 / sqrt(4%)%) - sqrt(4) 1999 3 (4 - sqrt(4%)%) / sqrt(4%)% 2000 4 (4! - 4) * 4 / 4% 2 .4' / .(sqrt(4))' %o 2 4 / sqrt(4%)% 2001 3 (4 + sqrt(4%)%) / sqrt(4%)% 2002 3 (4 / sqrt(4%)%) + sqrt(4) 2004 3 4 + (4 / sqrt(4%)%) 2010 3 (4 + sqrt(4)%) / sqrt(4%)% 2013 4 (root(.(sqrt(4))' , 4) - 4!)/.4!' 2016 4 ((4!+4)/4)!*.4 3 ((4 + 4)! / sqrt(4%))% 2020 3 (4 + 4%) / sqrt(4%)% 2024 4 sqrt(sqrt(4^4!)) /sqrt(4) - 4! 3 (4 / sqrt(4%)%) + 4! 2025 3 (4 * .4`% ^ -sqrt(4))% 2036 4 (sqrt(sqrt(4^4!)) - 4!) /sqrt(4) 2044 4 sqrt(sqrt(4^4!)) /sqrt(4) - 4 2046 4 (sqrt(sqrt(4^4!)) - 4) /sqrt(4) 2047 4 (sqrt(sqrt(4^4!)) - sqrt(4)) /sqrt(4) 2048 3 sqrt(4) * root(sqrt(4%), 4) 2049 4 (sqrt(sqrt(4^4!)) + sqrt(4)) /sqrt(4) 2050 4 (sqrt(sqrt(4^4!)) + 4) /sqrt(4) 2052 4 sqrt(sqrt(4^4!)) /sqrt(4) + 4 2060 4 (sqrt(sqrt(4^4!)) + 4!) /sqrt(4) 2072 4 sqrt(sqrt(4^4!)) /sqrt(4) + 4! 2082 4 (root(-.sqrt(4), .sqrt(4)) - sqrt(4) )*sqrt(.4') 2084 4 (root(-.sqrt(4), .sqrt(4))*sqrt(.4') + sqrt(.4') 2086 4 (root(-.sqrt(4), .sqrt(4)) + 4)*sqrt(.4') 2088 4 (root(.(sqrt(4))' , 4))/.4!' - 4! 2091 4 (sqrt(sqrt(sqrt( .(sqrt(4))' ^ (- 4!) ))) - 4)*4! 2100 4 (44 - sqrt(4)) / sqrt(4) % 3 (4 + sqrt(4%)) / sqrt(4%)% 2108 4 (root(.(sqrt(4))' , 4))/.4!' - 4 2110 4 (root(.(sqrt(4))' , 4))/.4!' - sqrt(4) 2113 4 (root(.(sqrt(4))' , 4) + .4!')/.4!' 2114 4 (root(.(sqrt(4))' , 4))/.4!' + sqrt(4) 2116 4 (root(.(sqrt(4))' , 4))/.4!' + 4 2111 4 (root(.(sqrt(4))' , 4) - .4!')/.4!' 2112 3 (root(.(sqrt(4))' , 4))/.4!' 2120 3 (4 + 4!%) / sqrt(4%)% 2125 4 (root(.(sqrt(4))' , 4) - sqrt(4))/.4! 2134 4 (root(.(sqrt(4))' , 4))/.4! + sqrt(.4') 2136 4 (root(.(sqrt(4))' , 4))/.4!' + 4! 2139 4 (sqrt(sqrt(sqrt( .(sqrt(4))' ^ (- 4!) ))) - sqrt(4))*4! 2150 4 (root(.(sqrt(4))' , 4) + 4)/.4! 2160 4 4!*4/(.4' - .4) 3 4! * .4 / .4`% 2163 4 4!/(sqrt(sqrt(sqrt( .(sqrt(4))' ^ 4!)))) - 4! 2178 4 44 /(.4!' - (.sqrt(4))' ) 2183 4 4!/(sqrt(sqrt(sqrt( .(sqrt(4))' ^ 4!)))) - 4 2185 4 4!/(sqrt(sqrt(sqrt( .(sqrt(4))' ^ 4!)))) - sqrt(4) 2187 3 sqrt(sqrt(sqrt( .(sqrt(4))' ^ (- 4!) )))*4! 2189 4 4!/(sqrt(sqrt(sqrt( .(sqrt(4))' ^ 4!)))) + sqrt(4) 2191 4 4!/(sqrt(sqrt(sqrt( .(sqrt(4))' ^ 4!)))) + 4 2196 4 (root(.(sqrt(4))' , 4) - 4!)/.(sqrt(4))' 2197 4 sqrt(sqrt(sqrt( (4! + sqrt(4))/sqrt(4) )^4!)) 2200 4 (4! - sqrt(4)) * 4 / 4% 3 44 / sqrt(4)% 2208 4 4 * (4!)! / (4! - sqrt(4)) 2211 4 4!/(sqrt(sqrt(sqrt( .(sqrt(4))' ^ 4!)))) + 4! 2235 4 (sqrt(sqrt(sqrt( .(sqrt(4))' ^ (- 4!) ))) + sqrt(4))*4! 2240 4 ((4!+4)/4)!*.4' 2250 3 4 / (.4 * .4`)% 2256 4 (4!*4 - sqrt(4))*4! 2277 4 (4!*4! - 4!)/.4!' 2280 4 4!*4!*4 - 4! 2283 4 (sqrt(sqrt(sqrt( .(sqrt(4))' ^ (- 4!) ))) + 4)*4! 2286 4 (root(.(sqrt(4))' , 4) - 4)/.(sqrt(4))' 2288 4 (4!*4! - 4)*4 2295 4 (root(.sqrt(4) , 4) - 4)/.4' 2296 4 (4!*4! - sqrt(4))*4 2300 4 (44 + sqrt(4)) / sqrt(4) % 4 4!*4!*4 - 4 2301 4 (root(.(sqrt(4))' , 4) - sqrt(.4'))/.(sqrt(4))' 2302 4 4!*4!*4 - sqrt(4) 2303 4 (root(.sqrt(4) , 4) - .4' )/.4' 2304 4 (4!+4!) * sqrt(4) * 4! 3 4*4!^sqrt(4) 2305 4 (root(.sqrt(4) , 4) + .4' )/.4' 2306 4 4!*4!*4 + sqrt(4) 2307 4 (root(.(sqrt(4))' , 4) + sqrt(.4'))/.(sqrt(4))' 2308 4 4!*4!*4 + 4 2312 4 (4!*4! + sqrt(4))*4 2313 4 (root(.sqrt(4) , 4) + 4)/.4' 2320 4 (4!*4! + 4)*4 2322 4 (root(.(sqrt(4))' , 4) + 4)/.(sqrt(4))' 2328 4 4!*4!*4 + 4! 2332 4 (4! - .4')*4!/.4!' 2376 3 4!*4!/.4!' 2352 4 4!*4!/.4!' - 4! 2354 4 (4! - .(sqrt(4))')*4!/.4!' 2358 4 (root(.sqrt(4) , 4) + 4!)/.4' 2360 4 (4! - .4)*4!/.4! 2368 4 (4! + sqrt(.4'))*4!*4 2372 4 4!*4!/.4!' - 4 2374 4 4!*4!/.4!' - sqrt(4) 2375 4 (4!*4! - .4!')/.4!' 2376 4 44/.4' * 4! 2377 4 (4!*4! + .4!')/.4!' 2378 4 4!*4!/.4!' + sqrt(4) 2380 4 4!*4!/.4!' + 4 2396 4 4!*4!/.4! - 4 2398 4 (4! + .(sqrt(4))')*4!/.4!' 2399 4 (4!*4! - .4!)/.4! 2400 3 4!*4!/.4! 2401 4 ((4! + 4)/4)^4 2402 4 4!*4!/.4! + sqrt(4) 2404 4 ((.sqrt(4) ^ (- 4) ) - 4!) * 4 2412 4 (root(.(sqrt(4))' , 4) + 4!)/.(sqrt(4))' 2420 4 (4! + .sqrt(4))*4!/.4! 2424 4 (4! + .4!)*4!/.4! 2430 4 4!/(.4' - .4) /.(sqrt(4))' 2440 4 (4! + .4)*4!/.4! 2442 4 (4! + sqrt(.4'))*4!/.4!' 2448 4 (4!/.4! + sqrt(4))*4! 2472 4 (4!/.4!' + 4)*4! 2475 4 (4!*4! + 4!)/.4!' 2476 3 sqrt(4)% ^ -sqrt(4) - 4! 2484 4 ((.sqrt(4) ^ (- 4) ) - 4)*4 2492 4 ((.sqrt(4) ^ (- 4) ) - sqrt(4))*4 2496 4 (4!/.4! + 4)*4! 3 sqrt(4)% ^ -sqrt(4) - 4 2498 3 sqrt(4)% ^ -sqrt(4) - sqrt(4) 2500 4 qrt(sqrt(sqrt((4/.4)^4!)))/.4 2 sqrt(4)% ^ -sqrt(4) 2502 3 sqrt(4) + sqrt(4)% ^ -sqrt(4) 2504 3 4 + sqrt(4)% ^ -sqrt(4) 2508 4 ((.sqrt(4) ^ (- 4) ) + sqrt(4))*4 2516 4 ((.sqrt(4) ^ (- 4) ) + 4)*4 2517 4 (.4'% + (4!‰/(4%)')'‰)/(.sqrt(4)%)'‰ 2520 4 ((4!+4)/4)!)/sqrt(4) 2524 3 sqrt(4)% ^ -sqrt(4) + 4! 2536 4 (root(.(sqrt(4) , 4))/.4 - 4! 2540 4 (root(.(sqrt(4))' , 4) - 4)/.sqrt(4) 2544 4 (4!/(.sqrt(4))' - sqrt(4))*4! 2550 4 (root(.sqrt(4) , 4) - 4 )/.4 2555 4 (root(.sqrt(4) , 4) - sqrt(4) )/.4 2556 4 (root(.sqrt(4), 4))/.4 - 4 2556 4 (root(.sqrt(4), 4))/.4 - 4 2558 4 (root(.sqrt(4) , 4))/.4 - sqrt(4) 2559 4 (root(.sqrt(4) , 4) - .4)/.4 2560 4 4^4 * 4 / .4 3 root(sqrt(4%), 4) / .4 2561 4 (root(.sqrt(4) , 4) + .4)/.4 2562 4 (root(.sqrt(4) , 4))/.4 + sqrt(4) 2564 4 (root(.sqrt(4) , 4))/.4 + 4 2565 4 (root(.sqrt(4) , 4) + sqrt(4) )/.4 2568 4 4!*4!/(.sqrt(4))' - 4! 2570 4 (root(.sqrt(4) , 4) + 4)/.4 2574 4 (4!*4! - 4)/(.sqrt(4))' 2580 4 (root((.sqrt(4))' , 4) + 4)/.sqrt(4) 2583 4 (4!*4! - sqrt(4))/(.sqrt(4))' 2584 4 (root(.sqrt(4) , 4))/.4 + 4! 2588 4 4!*4!/(.sqrt(4))' - 4 2589 4 (4!*4! - sqrt(.4'))/(.sqrt(4))' 2590 4 4!*4!/(.sqrt(4))' - sqrt(4) 2591 4 (4!*4! - (.sqrt(4))' )/(.sqrt(4))' 2592 4 sqrt(4) * (4! / 4)^4 3 4!*4!/.(sqrt(4))' 2593 4 (4!*4! + (.sqrt(4))' )/(.sqrt(4))' 2594 4 4!*4!/(.sqrt(4))' + sqrt(4) 2595 4 (4!*4! + sqrt(.4'))/(.sqrt(4))' 2596 4 ((.sqrt(4) ^ (- 4) ) + 4!) * 4 2600 4 (4! + sqrt(4)) * 4 / 4% 2601 4 (4!*4! + sqrt(4))/(.sqrt(4))' 2610 4 (4!*4! + 4)/(.sqrt(4))' 2616 4 4!*4!/(.sqrt(4))' + 4! 2620 4 (root(.sqrt(4) , 4) + 4!)/.4 2640 4 (sqrt(4) /.4)! * (4! - sqrt(4)) 3 (sqrt(4) - 4!%) / sqrt(.4`%)% 2664 4 (4! + sqrt(.4'))*4! /.(sqrt(4))' 2673 4 (4!/.4')/(.4!' - (.sqrt(4))' ) 2680 4 (root(.(sqrt(4))' , 4) + 4!)/.sqrt(4) 2688 4 (4! + 4)*4!*4 3 (4 + 4)! * sqrt(.4`%) 2700 4 (sqrt(4) /.4)! /(.4' - .4) 3 4! / (sqrt(4) * .4`)% 2704 4 sqrt(4!+4!+4)^4 2728 4 (sqrt(sqrt(4^4!) - 4)*sqrt(.4') 2730 4 (sqrt(sqrt(4^4!))*sqrt(.4') - sqrt(.4') 2732 4 (sqrt(sqrt(4^4!) + sqrt(4))*sqrt(.4') 2744 4 sqrt(sqrt(sqrt(4! - 4/.4)^4!)) 2750 4 (sqrt(sqrt(sqrt(.sqrt(4) ^ (- 4!)))))*(4! - sqrt(4)) 2 sqrt(.4') / (4!) %o 2760 4 (sqrt(sqrt(sqrt(4!^4!))) - 4!) * .sqrt(4) 2763 4 (sqrt(sqrt(sqrt( (.sqrt(4))' ^ (- 4!) ))) + 4!)*4! 2764 4 (sqrt(sqrt(sqrt(4!^4!))) - 4)*.sqrt(4) 2765 4 sqrt(sqrt(sqrt(4!^4!))) * .sqrt(4) + .sqrt(4) 2784 4 ((sqrt(4) /.4)! - 4)*4! 2800 4 (4! + 4) * 4 / 4% 2808 4 4!/(.sqrt(4))' * (4! + sqrt(4)) 2809 4 sqrt((4! + .4')/.4')^4 2816 4 sqrt(sqrt(sqrt(4^4!)))*44 2832 4 ((sqrt(4) /.4)! - sqrt(4))*4! 2856 4 (sqrt(4) /.4)! *4! - 4! 2860 4 (4!*4! - 4)/.sqrt(4) 2864 4 ((4!/4)! - 4)*4 2870 4 (4!*4! - sqrt(4) )/.sqrt(4) 2871 4 ((4!/4)! - 4!)/.4!' 2872 4 ((4!/4)! - sqrt(4))*4 2876 4 (sqrt(4) /.4)! *4! - 4 2878 4 (sqrt(4) /.4)! *4! - sqrt(4) 2879 4 (4!*4! - .sqrt(4) )/.sqrt(4) 2880 4 (4!*4 + 4!)*4! 3 (sqrt(4) /4)! * 4! 2881 4 (4!*4! + .sqrt(4) )/.sqrt(4) 2882 4 (sqrt(4) /.4)! *4! + sqrt(4) 2884 4 (sqrt(4) /.4)! *4! + 4 2888 4 ((4!/4)! + sqrt(4))*4 2890 4 (4!*4! + sqrt(4))/.sqrt(4) 2892 4 sqrt(4!/.4')^4 - 4! 2896 4 ((4!/4)! + 4)*4 2900 4 ((4! / .4') + 4) / sqrt(4) % 3 (sqrt(4) - sqrt(.4`%)) / sqrt(.4`%)% 2904 4 (sqrt(4) /.4)! *4! + 4! 2912 4 sqrt(4!/.4')^4 - 4 2914 4 sqrt(4!/.4')^4 - sqrt(4) 2916 3 (4! / .4')^sqrt(4) 2918 4 sqrt(4!/.4')^4 + sqrt(4) 2920 4 sqrt(4!/.4')^4 + 4 2928 4 (4! + .4)*(sqrt(4) /.4)! 2940 3 (sqrt(4) - 4%) / sqrt(.4`%)% 2940 4 sqrt(4!/.4')^4 + 4! 2946 4 (4!/4)!/.4!' - 4! 2950 4 (4! - .4)*(sqrt(sqrt(sqrt( .sqrt(4) ^(- 4!))))) 2952 4 (4!/.4!' + 4!)*4! 2960 4 (4! + sqrt(.4'))*(sqrt(4) /.4)! 2966 4 (4!/4)!/.4!' - 4 2968 4 (4!/4)!/.4!' - sqrt(4) 2969 4 ((4!/4)! - .4!')/.4!' 2970 3 (sqrt(4) - sqrt(4)%) / sqrt(.4`%)% 3 (4!/4)! /.4!' 2971 4 ((4!/4)! + .4!')/.4!' 2972 4 (4!/4)!/.4!' + sqrt(4) 2974 4 (4!/4)!/.4!' + 4 2975 4 (4! - .sqrt(4))*(sqrt(sqrt(sqrt( (.sqrt(4))^( - 4!))))) 2976 4 ((sqrt(4) /.4)! + 4)*4! 3 (sqrt(4) / sqrt(.4`%)%) - 4! 2990 3 (sqrt(4) - sqrt(.4`)%) / sqrt(.4`%)% 2994 4 (4!/4)!/.4!' + 4! 3 (sqrt(4) - .4%) / sqrt(.4`%)% 2996 4 (4!/4)!/.4! - 4 3 (sqrt(4) / sqrt(.4`%)%) - 4 2997 3 (sqrt(4) - sqrt(4%)%) / sqrt(.4`%)% 2998 4 (4!/4)!/.4! - sqrt(4) 4 ((4!/4)! - .4!)/.4! 3 (sqrt(4) / sqrt(.4`%)%) - sqrt(4) 2999 3 (sqrt(4) - sqrt(.4`%)%) / sqrt(.4`%)% 3000 4 sqrt(sqrt(sqrt(sqrt(4) /.4)^4!)) * 4! 3 (4!/4)! /.4! 2 sqrt(.4') / .(sqrt(4))' %o 2 sqrt(4) / sqrt(.4`%)% 3001 4 ((4!/4)! + .4!)/.4! 3 (sqrt(4) + sqrt(.4`%)%) / sqrt(.4`%)% 3002 4 (4!/4)!/.4! + sqrt(4) 3 sqrt(4) + (sqrt(4) / sqrt(.4`%)%) 3003 3 (sqrt(4) + sqrt(4%)%) / sqrt(.4`%)% 3004 4 (4!/4)!/.4! + 4 3 4 + (sqrt(4) / sqrt(.4`%)%) 3005 4 ((.sqrt(4) ^ (- 4) ) - 4!)/.sqrt(4) 3006 3 (sqrt(4) + .4%) / sqrt(.4`%)% 3010 3 (sqrt(4) + sqrt(.4`)%) / sqrt(.4`%)% 3024 4 (4!/4)!/.4! + 4! 3 (sqrt(4) / sqrt(.4`%)%) + 4! 3025 4 sqrt((4! - sqrt(4))/.4)^4 3030 4 (4! + .4!)*(sqrt(sqrt(sqrt( (.sqrt(4))^( - 4!))))) 3 (sqrt(4) + sqrt(4)%) / sqrt(.4`%)% 3048 4 sqrt(sqrt(sqrt(4!^4!))) * (.sqrt(4))' - 4! 3050 4 (4! + .4)*(sqrt(sqrt(sqrt( .sqrt(4)^( - 4!))))) 3060 3 (sqrt(4) + 4%) / sqrt(.4`%)% 3068 4 sqrt(sqrt(sqrt(4!^4!))) * (.sqrt(4))' - 4 3069 4 ((4!/4)! + 4!)/.4!' 3070 4 sqrt(sqrt(sqrt(4!^4!))) * (.sqrt(4))' - sqrt(4) 3072 3 sqrt(sqrt(sqrt(4!^4!))) * (.sqrt(4))' 3074 4 sqrt(sqrt(sqrt(4!^4!))) * (.sqrt(4))' + sqrt(4) 3076 4 sqrt(sqrt(sqrt(4!^4!))) * (.sqrt(4))' + 4 3096 4 sqrt(sqrt(sqrt(4!^4!))) * (.sqrt(4))' + 4! 3100 4 ((4!/4)! + 4!)/.4! 3 (sqrt(4) + sqrt(.4`%)) / sqrt(.4`%)% 3101 4 (.sqrt(4) ^ (- 4) )/.sqrt(4) - 4! 3105 4 ((.sqrt(4) ^ (- 4) ) - 4)/.sqrt(4) 3115 4 ((.sqrt(4) ^ (- 4) ) - sqrt(4))/.sqrt(4) 3120 4 (sqrt(4) /.4)! * (4! + sqrt(4)) 3121 4 (.sqrt(4) ^ (- 4) )/.sqrt(4) - 4 3123 4 ((.sqrt(4) ^ (- 4) ) - .4)/.sqrt(4) 3124 4 ((.sqrt(4) ^ (- 4) ) - .sqrt(4))/.sqrt(4) 3125 2 root(-.(sqrt(4), .(sqrt(4)) 3 4% ^ -sqrt(4) / sqrt(4%) 3126 4 ((.sqrt(4) ^ (- 4) ) + .sqrt(4))/.sqrt(4) 3127 4 ((.sqrt(4) ^ (- 4) ) + .4)/.sqrt(4) 3129 4 (.sqrt(4) ^ (- 4) )/.sqrt(4) + 4 3132 4 ((4!/4)! - 4!)/(.sqrt(4))' 3135 4 ((.sqrt(4) ^ (- 4) ) + sqrt(4))/.sqrt(4) 3136 4 sqrt(4!/.4 - 4)^4 3145 4 ((.sqrt(4) ^ (- 4) ) + 4)/.sqrt(4) 3149 4 (.sqrt(4) ^ (- 4) )/.sqrt(4) + 4! 3168 4 (4!/(.sqrt(4))' + 4!)*4! 3200 3 sqrt(sqrt(sqrt(4 ^ (4!))) / sqrt(4) % 3216 4 (4!/4)! /(.sqrt(4))' - 4! 3222 4 ((4!/4)! - 4)/(.sqrt(4))' 3231 4 ((4!/4)! - sqrt(4))/(.sqrt(4))' 3236 4 (4!/4)! /(.sqrt(4))' - 4 3237 4 ((4!/4)! - sqrt(.4'))/(.sqrt(4))' 3238 4 (4!/4)! /(.sqrt(4))' - sqrt(4) 3239 4 ((4!/4)! - (.sqrt(4))' )/(.sqrt(4))' 3240 4 (4! / 4)^4 / .4 3 (4!/4)! /.(sqrt(4))' 3241 4 ((4!/4)! + (.sqrt(4))' )/(.sqrt(4))' 3242 4 (4!/4)! /(.sqrt(4))' + sqrt(4) 3243 4 ((4!/4)! + sqrt(.4'))/(.sqrt(4))' 3244 4 (4!/4)! /(.sqrt(4))' + 4 3245 4 ((.sqrt(4) ^ (- 4) ) + 4!)/.sqrt(4) 3249 4 ((4!/4)! + sqrt(4))/(.sqrt(4))' 3250 4 (sqrt(sqrt(sqrt(.sqrt(4) ^ (- 4!)))))*(4! + sqrt(4)) 3258 4 ((4!/4)! + 4)/(.sqrt(4))' 3264 4 (4!/4)! /(.sqrt(4))' + 4! 3300 4 (sqrt(sqrt(sqrt(4 ^ (4!))) + sqrt(4)) / sqrt(4) % 3 (4! - sqrt(4)) / sqrt(.4`)% 3312 4 (sqrt(sqrt(sqrt(4!^4!))) - 4!)*.4! 3318 3 (4!^4)% + .4! 3348 4 ((4!/4)! + 4!)/(.sqrt(4))' 3360 4 (sqrt(4) /.4)! * (4! + 4) 3 (sqrt(4) + 4!%) / sqrt(.4`%)% 3364 4 sqrt(4!/.4 - sqrt(4))^4 3375 4 sqrt(sqrt(sqrt((4 + sqrt(4))/.4)^4!)) 3 root(-sqrt(4), .4`%) / .4`% 3376 4 sqrt(sqrt(4^4!)) - (4!/4)! 3400 4 (sqrt(sqrt(sqrt(4 ^ (4!))) + 4) / sqrt(4) % 3432 4 sqrt(sqrt(sqrt(4!^4!)))/4 - 4! 3450 4 (sqrt(sqrt(sqrt(4!^4!))) - 4!)/4 3452 4 sqrt(sqrt(sqrt(4!^4!)))/4 - 4 3454 4 sqrt(sqrt(sqrt(4!^4!)))/4 - sqrt(4) 3455 4 (sqrt(sqrt(sqrt(4!^4!))) - 4)/4 3456 3 sqrt(sqrt(sqrt(4!^4!))) /4 3457 4 (sqrt(sqrt(sqrt(4!^4!))) + 4)/4 3458 4 sqrt(sqrt(sqrt(4!^4!)))/4 + sqrt(4) 3460 4 sqrt(sqrt(sqrt(4!^4!)))/4 + 4 3462 4 (sqrt(sqrt(sqrt(4!^4!))) + 4!)/4 3472 4 ((sqrt(sqrt(.(sqrt(4) ^ -4!) * .(sqrt(4))') - .(sqrt(4))' 3480 4 sqrt(sqrt(sqrt(4!^4!)))/4 + 4! 3481 4 sqrt((4! - .4)/.4)^4 3500 4 (4! / sqrt(.4') % ) - (4! / .(4!)) 3 (4! - sqrt(.4`)) / sqrt(.4`)% 3520 4 sqrt(sqrt(4^4!) - 4!*4! 3540 3 (4! - .4) / sqrt(.4`)% 3564 3 (4! - 4!%) / sqrt(.4`)% 3570 3 (4! - sqrt(4%)) / sqrt(.4`)% 3576 3 (4! / sqrt(.4`)%) - 4! 3580 4 ((4!/4)! - 4)/.sqrt(4) 3590 3 (4! - sqrt(.4`%)) / sqrt(.4`)% 3594 3 (4! - 4%) / sqrt(.4`)% 3596 3 (4! / sqrt(.4`)%) - 4 3597 3 (4! - sqrt(4)%) / sqrt(.4`)% 3598 3 (4! / sqrt(.4`)%) - sqrt(4) 3599 4 ((4!/4)! - .sqrt(4))/.sqrt(4) 3 (4! - sqrt(.4`)%) / sqrt(.4`)% 3600 3 (4! / .4)^sqrt(4) 2 4! / sqrt(.4') % 3601 4 ((4!/4)! + .sqrt(4))/.sqrt(4) 3 (4! + sqrt(.4`)%) / sqrt(.4`)% 3602 4 sqrt(4!/.4)^4 + sqrt(4) 3 sqrt(4) + (4! / sqrt(.4`)%) 3603 3 (sqrt(4)% + 4!) / sqrt(.4`)% 3604 4 sqrt(4!/.4)^4 + 4 3 4 + (4! / sqrt(.4`)%) 3606 3 (4! + 4%) / sqrt(.4`)% 3610 4 ((4!/4)! + sqrt(4))/.sqrt(4) 3 (4! + sqrt(.4`%)) / sqrt(.4`)% 3620 4 ((4!/4)! + 4)/.sqrt(4) 3624 4 sqrt(4!/.4)^4 + 4! 3 4! + (4! / sqrt(.4`)%) 3629 3 (4/.4')!% + .sqrt(4) 3630 3 (4! + sqrt(4%)) / sqrt(.4`)% 3636 3 (4! + 4!%) / sqrt(.4`)% 3645 4 (4!/4)! /(.4' * .4') 3660 3 (4! + .4) / sqrt(.4`)% 3700 4 (4! / .(4!)) + (4! / sqrt(.4') % ) 3 (4! + sqrt(.4`)) / sqrt(.4`)% 3720 4 ((4!/4)! + 4!)/.sqrt(4) 3750 3 root(-sqrt(4), .4`%) / .4% 3780 4 (4+4)! /4! /.4' 3800 4 (sqrt(.4') / (.4') % + sqrt(4)) / 4 % 3840 4 sqrt(sqrt(4^4!)) - 4^4 3 4 ^ 4 / sqrt(.4`%) 3844 4 sqrt(4!/.4 + sqrt(4))^4 3872 4 sqrt(44*4)^4 3888 4 sqrt(sqrt(sqrt(4!^4!)))/(4 - .4') 3900 4 ((4 * 4) - .4) / .4 % 3 (sqrt(4) + 4!) / sqrt(.4`)% 3969 4 sqrt((4! + 4)/.4')^4 3971 4 sqrt(sqrt(4^4!)) - sqrt(sqrt(sqrt(.sqrt(4) ^ (- 4!) ))) 3976 4 sqrt(sqrt(4^4!)) - (sqrt(4) /.4)! 3988 4 sqrt(sqrt(4^4!)) - 4!/(.sqrt(4))' 3996 4 sqrt(sqrt(4^4!)) - 4!/.4! 3997 4 sqrt(sqrt(4^4!)) - 4!/.4!' 4000 4 sqrt(sqrt(4^4!)) - 4!*4 3 4 * 4 / .4% 4032 4 (4+4)! /4 * .4 4036 4 sqrt(sqrt(4^4!)) - 4!/.4 4042 4 sqrt(sqrt(4^4!)) - 4!/.4' 4048 4 sqrt(sqrt(4^4!)) - 4! - 4! 4052 4 sqrt(sqrt(4^4!)) - 44 4060 4 sqrt(sqrt(4^4!)) - 4!/sqrt(.4') 4064 4 sqrt(sqrt(4^4!)) - root(.4 , 4) 4068 4 sqrt(sqrt(4^4!)) - 4! - 4 4070 4 sqrt(sqrt(4^4!)) - 4! - sqrt(4) 4071 4 sqrt(sqrt(4^4!)) - (.sqrt(4))^(- sqrt(4)) 4072 3 sqrt(sqrt(4^4!)) - 4! 4074 4 sqrt(sqrt(4^4!)) - 4! + sqrt(4) 4076 4 sqrt(sqrt(4^4!)) - 4! + 4 4078 4 sqrt(sqrt(4^4!)) - 4/(.sqrt(4))' 4080 4 sqrt(sqrt(4^4!)) - 4*4 4084 4 sqrt(sqrt(4^4!)) - 4!/sqrt(4) 4086 4 sqrt(sqrt(4^4!)) - 4/.4 4087 4 sqrt(sqrt(4^4!)) - 4/.4' 4088 4 sqrt(sqrt(4^4!)) - (4+4) 4090 4 sqrt(sqrt(4^4!)) - 4!/4 4091 4 sqrt(sqrt(4^4!)) - sqrt(4) /.4 4092 3 sqrt(sqrt(4^4!)) - 4 4093 4 sqrt(sqrt(4^4!)) - sqrt(4/.4') 4094 3 sqrt(sqrt(4^4!)) - sqrt(4) 4095 4 sqrt(sqrt(4^4!)) - 4/4 4096 3 (4 + 4)^4 2 sqrt(sqrt(4 ^ 4!)) 4097 4 sqrt(sqrt(4^4!)) + 4/4 4098 3 sqrt(sqrt(4^4!)) + sqrt(4) 4099 4 sqrt(sqrt(4^4!)) + sqrt(4/.4') 4100 3 sqrt(sqrt(4 ^ (4!)) + 4 4101 4 sqrt(sqrt(4^4!)) + sqrt(4) /.4 4102 4 sqrt(sqrt(4^4!)) + 4!/4 4104 4 sqrt(sqrt(4^4!)) + 4 + 4 4105 4 sqrt(sqrt(4^4!)) + 4/.4' 4106 4 sqrt(sqrt(4^4!)) + 4/.4 4108 4 sqrt(sqrt(4^4!)) + 4!/sqrt(4) 4112 4 sqrt(sqrt(4^4!)) + 4*4 4114 4 sqrt(sqrt(4^4!)) + 4/(.sqrt(4))' 4116 4 sqrt(sqrt(4^4!)) + 4! - 4 4118 4 sqrt(sqrt(4^4!)) + 4! - sqrt(4) 4120 3 sqrt(sqrt(4^4!)) + 4! 4200 4 (sqrt(4) / .4' %o ) - (sqrt(.4') / .(sqrt(4))' % ) 3 (4 + 4!) / sqrt(.4`)% 4121 4 sqrt(sqrt(4^4!)) + (.sqrt(4))^(- sqrt(4)) 4122 4 sqrt(sqrt(4^4!)) + 4! + sqrt(4) 4124 4 sqrt(sqrt(4^4!)) + 4! + 4 4125 4 sqrt(sqrt(sqrt((4/.4)^4!)))/.4!' 4128 4 sqrt(sqrt(4^4!)) + root(.4 , 4) 4132 4 sqrt(sqrt(4^4!)) + 4!/sqrt(.4') 4140 4 sqrt(sqrt(4^4!)) + 44 4144 4 sqrt(sqrt(4^4!)) + 4! + 4! 4150 4 sqrt(sqrt(4^4!)) + 4!/.4' 4156 4 sqrt(sqrt(4^4!)) + 4!/.4 4160 4 sqrt(sqrt(4^4!)) + sqrt(sqrt(sqrt(4^4!))) 4192 4 sqrt(sqrt(4^4!)) + 4! * 4 4195 4 sqrt(sqrt(4^4!)) + 4!/.4!' 4196 4 sqrt(sqrt(4^4!)) + 4!/.4! 4200 4 (4+4)! /(4! *.4) 4204 4 sqrt(sqrt(4^4!)) + 4!/(.sqrt(4))' 4216 4 sqrt(sqrt(4^4!)) + (sqrt(4) /.4)! 4220 4 (root(.sqrt(4) , 4))/.4!' - 4 4221 4 sqrt(sqrt(4^4!)) + sqrt(sqrt(sqrt(.sqrt(4) ^ (- 4!) ))) 4224 3 (root(.sqrt(4) , 4))/.4!' 4225 4 sqrt((sqrt(4) + 4!)/.4)^4 4228 4 (root(.sqrt(4) , 4))/.4!' + 4 4248 4 (root(.sqrt(4) , 4))/.4!' + 4! 4250 4 (root(.sqrt(4) , 4) - 4)/.4! 4266 4 (root(.sqrt(4) , 4))/.4! - sqrt(.4') 4275 4 (root(.sqrt(4) , 4) + sqrt(4))/.4! 4300 4 ((4 / (4)' % ) - 4) / sqrt(4) 4320 4 (4!/4)!*4!/4 4323 4 (root(.sqrt(4) , 4) + 4!)/.4!' 4336 4 ((4! / sqrt(4)'%) + 4) * 4 4352 4 sqrt(sqrt(4^4!)) + 4^4 4356 4 sqrt((sqrt(sqrt(sqrt(4^4!))) + sqrt(4) )^4 4374 4 sqrt(.4') * (4/.4')^4 4392 4 (4! + .4) / sqrt(4)'% * 4 4394 4 (sqrt(sqrt(sqrt(4! + sqrt(4))))^4! )/ 4 4400 4 44 * 4 / 4% 4444 4 4444 4500 2 sqrt(4) / .4' %o 3 (4! - 4) / .4`% 4600 4 (sqrt(4) / .4' %o ) + (4! / .(4!)) 4700 4 (sqrt(4) / .4' %o ) + (.4' / .(sqrt(4))' % ) 4800 4 (4! + 4!) * 4 / 4% 3 (4 / sqrt(4)%) * 4! 4900 4 (4! / 4' %o ) - (sqrt(4) / .4 %) 4950 3 (4! - sqrt(4)) / .4`% 5000 4 sqrt(4) / .4% * 4 / .4 3 (4! - 4) / .4% 5040 3 ((4 + 4!) / 4)! 5100 4 (4! / 4' %o ) - (sqrt(.4') / .(sqrt(4))' % ) 5120 3 root(sqrt(4%), 4) / sqrt(4%) 5184 4 4 * (4! / 4)^4 5200 4 (4! / 4' %o ) - (.4' / (sqrt(4))' % ) 5250 3 (4! - sqrt(.4`)) / .4`% 5300 4 (4! / 4' %o ) - (4! / .(4!)) 3 (4! - .4`) / .4`% 5310 3 (4! - .4) / .4`% 5346 3 (4! - 4!%) / .4`% 5355 3 (4! - sqrt(4%)) / .4`% 5376 3 (4! / .4`%) - 4! 5385 3 (4! - sqrt(.4`%)) / .4`% 5391 3 (4! - 4%) / .4`% 5396 3 (4! / .4`%) - 4 5398 3 (4! / .4`%) - sqrt(4) 5399 3 (4! - .4`%) / .4`% 5400 4 4! / 4'% * 4 / .4 2 4! / (4)' %o 2 4! / .4`% 5401 3 (4! + .4`%) / .4`% 5402 3 sqrt(4) + (4! / .4`%) 5404 3 4 + (4! / .4`%) 5409 3 (4! + 4%) / .4`% 5415 3 (4! + sqrt(.4`%)) / .4`% 5424 3 4! + (4! / .4`%) 5445 3 (4! + sqrt(4%)) / .4`% 5454 3 (4! + 4!%) / .4`% 5490 3 (4! + .4) / .4`% 5500 4 (4! / 4' %o ) + (4! / .(4!)) 3 (4! - sqrt(4)) / .4% 5550 3 (4! + sqrt(.4`)) / .4`% 5600 4 (4! / 4' %o ) + (.4' / .(sqrt(4))' % ) 5625 3 sqrt(4)% ^ -sqrt(4) / .4` 5640 3 (4 - 4!%) / sqrt(.4`%)% 5700 4 (4! / 4' %o ) + (sqrt(.4') / .(sqrt(4))' % ) 3 (4 - sqrt(4%)) / sqrt(.4`%)% 5760 3 (4!^sqrt(4)) * 4 5800 4 (4! / 4 %o ) - (.4' / .(sqrt(4))' % ) 5850 3 (sqrt(4) + 4!) / .4`% 5900 4 (4! / 4 %o ) - (4! / .(4!)) 3 (4! - .4) / .4% 5940 3 (4! - 4!%) / .4% 5950 3 (4! - sqrt(4%)) / .4% 5970 3 (4 - sqrt(4)%) / sqrt(.4`%)% 5976 3 (4! / .4%) - 4! 5990 3 (4! - 4%) / .4% 5994 3 (4 - .4%) / sqrt(.4`%)% 5995 3 (4! - sqrt(4)%) / .4% 5996 3 (4! / .4%) - 4 5997 3 (4 - sqrt(4%)%) / sqrt(.4`%)% 5998 3 (4! / .4%) - sqrt(4) 5999 3 (4! - .4%) / .4% 6000 4 4! / 4% * 4 / .4 2 4! / 4 %o 6001 3 (4! + .4%) / .4% 6002 3 sqrt(4) + (4! / .4%) 6003 3 (4 + sqrt(4%)%) / sqrt(.4`%)% 6004 3 4 + (4! / .4%) 6005 3 (sqrt(4)% + 4!) / .4% 6006 3 (4 + .4%) / sqrt(.4`%)% 6010 3 (4! + 4%) / .4% 6024 3 4! + (4! / .4%) 6030 3 (4 + sqrt(4)%) / sqrt(.4`%)% 6050 3 (4! + sqrt(4%)) / .4% 6060 3 (4! + 4!%) / .4% 6100 4 (4! / 4 %o ) + (4! / .(4!)) 3 (4! + .4) / .4% 6120 4 4^4*4!-4! 6144 3 4!*4^4 6200 4 (4! / 4 %o ) + (.4' / .(sqrt(4))' % ) 6250 3 sqrt(4)% ^ -sqrt(4) / .4 6300 4 (4! / 4 %o ) + (sqrt(.4') / .(sqrt(4))' % ) 3 (4 + 4!) / .4`% 6360 3 (4 + 4!%) / sqrt(.4`%)% 6400 4 sqrt(sqrt(sqrt(4^(4!)))) * 4 / 4% 3 4 ^ 4 / 4% 6500 4 (4! / 4 %o ) + (sqrt(4) / .4 % ) 3 (sqrt(4) + 4!) / .4% 6561 3 (4 / .4')^4 6600 4 ((4 * 4) + .(4!)') / .(4!)' % 3 44 / sqrt(.4`)% 6700 4 ((4 * 4) + .(4!)') / .(4!)' % 6750 3 sqrt(4 / .4`%) / .4`% 6800 4 (4 / .(sqrt(4))' % ) + (sqrt(4) / 4 % % ) 6900 4 (4! / 4 %o ) + (4 / .4' % ) 7000 4 (4! / 4 %o ) + (4 / .4 % ) 3 (4 + 4!) / .4% 7100 4 ((4 * 4) - .(sqrt(4))') / .(sqrt(4))' % 7200 4 (4! / 4 %o ) + (4! / sqrt(4) % ) 3 root(.4, 4) / .4`% 7300 4 ((4 * 4) + .(sqrt(4))') / .(sqrt(4))' % 7400 4 (.4' / .(sqrt(4))' %o ) + (4! / 4' %o ) 7500 4 (4! / 4 %o ) + (sqrt(.4') / .4' %o ) 3 sqrt(4 / .4`%) / .4% 7600 4 ((sqrt(4) / 4 % ) + sqrt(.4')) / sqrt(.4') % 7700 4 ((sqrt(.4') / 4' % ) + .4) / .(sqrt(4)) % 7776 3 root(-sqrt(4%), 4 / 4!) 7800 4 (4! / 4 %o ) + (4 / .(sqrt(4))' % ) 7744 4 44^sqrt(4) * 4 7800 4 (4! / 4 %o ) + (4 / .(sqrt(4))' % ) 7900 4 ((4 * 4) - .(sqrt(4))) / .(sqrt4)) % 8000 4 (4 + 4) * 4 / .4% 3 root(.4, 4) / .4% 8064 3 (4 + 4)! * sqrt(4%) 8100 3 (.4 / .4`%) ^ sqrt(4) 8192 4 sqrt(4) * (4 + 4)^4 3 root(sqrt(.4`%), sqrt(4)) / 4 8250 2 sqrt(4) / .(4!)' %o 8640 3 4! * 4! / sqrt(.4`%) 9000 4 4 / .4'% * 4 / .4 2 4 / .4' %o 3 4 / (.4` - .4)% 9216 3 (4*4!)^sqrt(4) 9375 3 4% ^ -sqrt(4) / sqrt(.4`%) 9600 4 4 * 4! * 4 / 4% 9900 2 4! / .(4!)' `````` 10000 3 (4/.4)^4 2 4 / 4 %% 10626 4 (4!)! / (4! - 4) / 4! 10800 2 4! / sqrt(4)' %o 11100 4 444 / 4% 12000 4 (sqrt(4) / .4)! * 4 / 4% 2 4! / sqrt(4) %o 12144 4 (4!)! / (4! - sqrt(4) / sqrt(.4`)) 12288 4 sqrt(4) * 4! * 4^4 13122 4 sqrt(4) * (4/.4')^4 13248 4 4! * (4!)! / (4! - sqrt(4)) 13824 3 4! * 4! * 4! 2 4! ^ sqrt(sqrt(sqrt(4!))) 14400 4 (4!^sqrt(4)) * 4 / .4% 14641 4 (44 / 4)^4 15000 4 sqrt(.4') / 4'% * 4 / .4% 2 sqrt(.4') / .4' %% 16000 4 4 * 4 * 4 / .4% 16384 4 ((4^4)^sqrt(4))/4 16500 2 4 / .(4!)' %o 18000 4 4 / .(sqrt(4))' * 4 / .4% 2 4 / .(sqrt(4))' %% 18432 4 (4*4!)^sqrt(4) * sqrt(4) 20000 4 (4! - 4) * 4 / .4% 2 .4' / .(sqrt(4))' %% 20736 3 (4! / sqrt(4))^4 21984 4 (4! / .4')^sqrt(4) * 4! 22000 4 (4! - sqrt(4)) * 4 / .4% 24000 3 4! * 4 / .4% 24576 4 4 * 4! * 4^4 25600 4 4^4 * 4 / 4% 26000 4 (4! + sqrt(4)) * 4 / .4% 26016 4 ((4! / sqrt(4)' % ) + 4) * 4! 26244 4 4 * (4/.4')^4 26352 4 (4! + .4) / sqrt(4)'% * 4! 27500 2 sqrt(.4') / (4!) %% 28000 4 (4! + 4) * 4 / .4% 30000 4 sqrt(4) / sqrt(.4'%) * 4 / .4% 2 sqrt(.4') / .(sqrt(4))' %% 31104 4 4! * (4! / 4)^4 32400 4 (4!/4)^4 / 4% 34560 3 (4!^sqrt(4)) * 4! 36000 4 4! / sqrt(.4`) * 4 / .4% 2 4! / sqrt(.4') %o 36864 4 (4*4!)^sqrt(4) * 4 40000 4 (4/.4)^4 * 4 40320 2 (4 + 4)! 41472 4 (4!)^4 / (4 * sqrt(4)) 44000 4 44 * 4 / .4% 45000 2 sqrt(4) / .4' %% 48000 4 (4! + 4!) * 4 / .4% 50000 4 sqrt(4) / .4% * 4 / 4% 54000 4 4! / 4'% * 4 / 4% 2 4! / (4)' %% 55296 4 4*4!^sqrt(4) * 4! 57600 4 4!^sqrt(4) * 4 / 4% 60000 4 4! / 4% * 4 / 4% 2 4! / 4 %% 64000 4 sqrt(sqrt(sqrt(4^(4!)))) * 4 / .4% 65536 3 (4 * 4)^4 63756 4 (4!)! / (4! - 4) / 4 69120 4 (4!^sqrt(4)) * 4! * sqrt(4) 72000 4 (4 + sqrt(4))! * 4 / 4% 82944 3 (4!)^4 / 4 85184 3 sqrt(sqrt(sqrt(44^4!))) 86400 4 (4! / .4)^sqrt(4) * 4! 90000 4 4 / .4'% * 4 / 4% 90720 4 (4 + sqrt(4)/.4)! / 4 95040 4 (4! / sqrt(4))! / (4 * sqrt(4)) 96000 4 4 * 4! * 4 / .4% 98304 4 (4 + 4)^4 * 4! `````` 100000 4 4! / .(4!) * 4 / .4% 111000 4 444 / .4% 120000 4 (sqrt(4) / .4)! * 4 / .4% 127512 4 (4!)! / (4! - 4) / sqrt(4) 131072 4 sqrt(4) 4^(4 * sqrt(4)) 138240 4 (4!^sqrt(4)) * 4! * 4 144000 4 (4!^sqrt(4)) * 4 / 4% 147456 4 4^(4 * sqrt(4)) / .4' 157464 4 (4 / .4')^4 * 4! 163840 4 4^(4 * sqrt(4)) / .4 165888 3 4!^4 / sqrt(4) 197136 4 444^sqrt(4) 221184 4 (4*4!)^sqrt(4) * 4! 234256 3 (4! - sqrt(4))^4 255024 3 (4!)! / (4! - 4) 256000 4 4^4 * 4 / .4% 262144 4 4 * 4^(4 * sqrt(4)) 324000 4 (4! / 4)^4 / .4% 331776 2 4!^4 362880 3 (4 + sqrt(4)/.4)! 2 (4 / .4')! 390625 4 (4! + 4/4)^4 409600 4 (4^4 / .4) ^ sqrt(4) 422500 4 ((4! + sqrt(4))! / (4!)!) ^ sqrt(4) 451584 4 (4! * (4! + 4)) ^ sqrt(4) 456976 3 (4! + sqrt(4))^4 483025 4 ((4 + sqrt(4))! - 4!) ^ sqrt(4) 500000 4 sqrt(4) / .4% * 4 / .4% 512656 4 ((4 + sqrt(4))! - 4) ^ sqrt(4) 515524 4 ((4 + sqrt(4))! - sqrt(4)) ^ sqrt(4) 518400 3 ((4 + sqrt(4))!) ^ sqrt(4) 521284 4 ((4 + sqrt(4))! + sqrt(4)) ^ sqrt(4) 524176 4 ((4 + sqrt(4))! + 4) ^ sqrt(4) 540000 4 4! / 4'% * 4 / .4% 553536 4 ((4 + sqrt(4))! + 4!) ^ sqrt(4) 576000 4 4!^sqrt(4) * 4 / .4% 600000 4 4! / 4% * 4 / .4% 614652 4 (((4!)+4)^4)-4 614656 3 (4! + 4)^4 614660 4 (4! + 4)^4 + 4 663552 3 sqrt(4) * 4!^4 720000 4 (4 + sqrt(4))! * 4 / .4% 731025 4 ((4 - .(sqrt(4)) / .4'%) ^ sqrt(4) 746496 4 (4! * 4! / sqrt(.4`)) ^ sqrt(4) 810000 3 (sqrt(4) / sqrt(.4'%))^4 811801 4 ((4 + .4' % ) / .4'%) ^ sqrt(4) 883225 4 ((4 - sqrt(.4' % )) / .4' %) ^ sqrt(4) 900000 4 4 / .4'% * 4 / .4% 907200 4 (4 + sqrt(4)/.4)! / .4 937024 4 44^4 / 4 990000 2 4! / .(4!)'%% ``````1000000 4 (4 / .4) ^ (4 + sqrt(4)) 1048576 4 sqrt(sqrt(4^44)) / 4 4 (4! + 4 + 4)^4 1098304 4 (4! + root(.(sqrt(4)),4)) ^ sqrt(4) 1106704 4 (sqrt(4)*4!^sqrt(4)) ^ sqrt(4) 1327104 3 4 * 4!^4 1440000 4 (4!^sqrt(4)) * 4 / .4% 1451520 4 4(4+(sqrt4)/.4)! 1572864 4 4! 4^(4 * sqrt(4)) 1600000 3 (4! - 4)^4 1679616 3 (4! / sqrt(.4`))^4 1874048 4 44^4 / sqrt(4) 2097152 4 sqrt(sqrt(4^44)) / sqrt(4) 2654208 4 4 * 4!^4 * sqrt(4) 2916000 4 (4! / 4)^4 / .4'% 3628800 2 (4 / .4)! 3748096 3 44^4 4194304 3 sqrt(sqrt(4^44)) 5308416 4 4 * 4!^4 * 4 7496192 4 sqrt(4) * 44^4 7962624 3 4!^(sqrt(4)/.4) 9370240 4 44^4 / .4 ``````Infinity 3 4 / (4-4) ```

### Contributors

The first contributors to the solutions I didn't find are listed below, note that in many cases the solution may have subsequently been replaced by simpler solutions.

 Matthew Cordone 1451520 Rizvan Dadaev 167, 187, 283, 340, 350, 415, 421, 427, 438, 447, 470, 553, 583, 588, 626, 683, 687, 701, 707, 713, 734, 737, 739, 743, 750, 754, 757, 763, 779, 793, 971, 1018, 1023, 1025, 1030, 1054, 1060, 1080, 1104, 1150, 1156, 1176, 1188, 1190, 1199, 1210, 1212, 1215, 1221, 1225, 1226, 1232, 1242, 1246, 1248, 1252, 1254, 1256, 1258, 1260, 1270, 1272, 1274, 1275, 1276, 1278, 1279, 1281, 1282, 1284, 1285, 1287, 1290, 1292, 1294, 1295, 1297, 1298, 1300, 1304, 1305, 1308, 1311, 1312, 1320, 1325, 1326, 1331, 1332, 1340, 1344, 1346, 1348, 1350, 1352, 1354, 1369, 1374, 1375, 1380, 1386, 1388, 1392, 1400, 1404, 1408, 1416, 1424, 1428, 1430, 1432, 1435, 1436, 1438, 1439, 1441, 1442, 1444, 1445, 1448, 1450, 1452, 1456, 1458, 1464, 1480, 1485, 1488, 1500, 1512, 1520, 1521, 1530, 1532, 1533, 1534, 1535, 1537, 1538, 1539, 1540, 1542, 1550, 1551, 1552, 1560, 1562, 1563, 1566, 1568, 1572, 1575, 1577, 1584, 1596, 1611, 1616, 1618, 1619, 1621, 1622, 1624, 1625, 1626, 1629, 1632, 1638, 1640, 1644, 1646, 1648, 1650, 1652, 1654, 1656, 1664, 1674, 1676, 1678, 1679, 1681, 1682, 1684, 1690, 1704, 1724, 1726, 1728, 1730, 1732, 1740, 1749, 1750, 1752, 1764, 1782, 1790, 1792, 1795, 1796, 1798, 1799, 1800, 1801, 1802, 1804, 1805, 1810, 1815, 1820, 1824, 1860, 1872, 1875, 1905, 1912, 1920, 1925, 1932, 1934, 1938, 1940, 1944, 1960, 1980, 2012, 2013, 2016, 2024, 2036, 2044, 2046, 2047, 2049, 2050, 2052, 2060, 2072, 2082, 2084, 2086, 2088, 2091, 2108, 2110, 2111, 2112, 2113, 2114, 2116, 2125, 2134, 2136, 2139, 2150, 2160, 2163, 2178, 2183, 2185, 2187, 2189, 2191, 2196, 2197, 2211, 2235, 2240, 2256, 2277, 2280, 2283, 2286, 2288, 2295, 2296, 2300, 2301, 2302, 2303, 2304, 2305, 2306, 2307, 2308, 2312, 2313, 2320, 2322, 2328, 2332, 2352, 2354, 2358, 2360, 2368, 2372, 2374, 2375, 2376, 2377, 2378, 2380, 2396, 2398, 2399, 2400, 2401, 2402, 2404, 2412, 2420, 2424, 2430, 2440, 2442, 2448, 2472, 2475, 2484, 2492, 2496, 2500, 2508, 2516, 2520, 2536, 2540, 2544, 2550, 2555, 2556, 2558, 2559, 2561, 2562, 2564, 2565, 2568, 2570, 2574, 2580, 2583, 2584, 2588, 2589, 2590, 2591, 2592, 2593, 2594, 2595, 2596, 2601, 2610, 2616, 2620, 2640, 2664, 2673, 2680, 2688, 2700, 2704, 2728, 2730, 2732, 2744, 2750, 2760, 2763, 2764, 2765, 2784, 2808, 2809, 2816, 2832, 2856, 2860, 2864, 2870, 2871, 2872, 2876, 2878, 2879, 2880, 2881, 2882, 2884, 2888, 2890, 2892, 2896, 2904, 2912, 2914, 2918, 2920, 2928, 2940, 2946, 2950, 2952, 2960, 2966, 2968, 2969, 2970, 2971, 2972, 2974, 2975, 2976, 2994, 2996, 2998, 2999, 3000, 3001, 3002, 3004, 3005, 3024, 3025, 3030, 3048, 3050, 3068, 3069, 3070, 3072, 3074, 3076, 3096, 3100, 3101, 3105, 3115, 3120, 3121, 3123, 3124, 3126, 3127, 3129, 3132, 3135, 3136, 3145, 3149, 3168, 3216, 3222, 3231, 3236, 3237, 3238, 3239, 3240, 3241, 3242, 3243, 3244, 3245, 3249, 3250, 3258, 3264, 3312, 3318, 3348, 3360, 3364, 3375, 3376, 3432, 3450, 3452, 3454, 3455, 3456, 3457, 3458, 3460, 3462, 3480, 3481, 3520, 3580, 3599, 3601, 3602, 3604, 3610, 3620, 3624, 3629, 3645, 3720, 3780, 3840, 3844, 3872, 3888, 3969, 3971, 3976, 3988, 3996, 3997, 4000, 4032, 4036, 4042, 4048, 4052, 4060, 4064, 4068, 4070, 4071, 4072, 4074, 4076, 4078, 4080, 4084, 4086, 4087, 4088, 4090, 4091, 4092, 4093, 4094, 4095, 4097, 4098, 4099, 4100, 4101, 4102, 4104, 4105, 4106, 4108, 4112, 4114, 4116, 4118, 4120, 4121, 4122, 4124, 4125, 4128, 4132, 4140, 4144, 4150, 4156, 4160, 4192, 4195, 4196, 4200, 4204, 4216, 4220, 4221, 4224, 4225, 4228, 4248, 4250, 4266, 4275, 4320, 4323, 4352, 4356, 4374 4394 . Contributed the following solutions using just two "4"s. π and e were also contributed, although the solution for e requires 5 fours. Ewart Shaw 219, 267, 351, 371, 373, 377, 379, 705, 727, 731, 733, 753, 972, 975 Richard Schorn First to uncover a solution for 113 but it uses rather "non-standard" combination of decimal place (.) and repeated digit (`), see 2/9. Ewald R. de Wit 103, 121, 125, 142, 146 Martin Olivella 181, 186, 188, 190, 194, 286, 290, 292, 362, 380, 384, 386, 388, 408, 488, 514, 536, 832, 900, 976, 1000 Heiner Marxen 154, 164, 169, 179, 182, 184, 204, 238, 242, 251, 275, 287, 289, 295, 296, 298, 299, 301, 302, 305, 310, 316,325,338, 348, 356, 358, 359, 361, 364, 372, 375, 426, 450, 472, 476, 478, 482, 496, 510, 520, 524, 526, 530, 601, 621, 622, 623, 626, 627, 628, 629, 635, 636, 638, 639, 641, 642, 644, 645, 646, 649, 654, 660, 664, 660, 670, 750, 841 Scott Forschler The solutions for 90, 100, 113, 165 using "%" Wayne Goode 202, 214, 218, and a simpler solution to 66 Jörg Wiegels 165, 177, 183, 195, 269, 270, 271, 274, 279, 294, 318, 322, 344, 378, 381, 383, 385, 387, 390, 405, 441, 495, 522, 525, 531, 538, 542, 544, 549, 555, 608, 612, 656, 666, 675, 684, 688, 768, 774, 810, 828, 848, 856, 860, 861, 862, 863, 865, 867, 868, 870, 896, 990, 1008, 1014, 1016 Simpler solutions for 13, 39, 41, 47, 57, 58, 78, 90, 116, 118, 120, 122, 124, 180, 288, 300, 320, 360, 484, 640, 540, 560, 567, 585, 592, 864 Charles Dillingham Pointed out that there are simpler solutions for some numbers than those listed above. For example "4 * 4 * 4" for 64 instead of "sqrt(sqrt(sqrt(4^(4!))))". The definition of the simplest was determined by the number of 4's needed, consideration of the operator complexity was only used when there was the same number of 4's. This has been partially resolved by giving double solutions for some numbers where the solution with the minimum number of 4's is particularly clumsy. Peter Karsanow Donated some solutions which have five 4's, (See the comment above regarding the use of 2 instead of sqrt(4)) for example, 157, 167, 193, 197, 203, 223, 231, 281, 337, 406, 551, 657 836, 856, and 881. Also some three 4 solutions for numbers over 1000, namely 1440, 1936, 2304, 2916, 3600, 4096, 6144, 6561, 9216, 10000, >3824, and 16384. Some simpler solutions for 81, 567, and 650. Brad McInnes Provided solution for 984, 996, 998, and a three 4's solution for 1000. Frank Mrazik 73, 167, 171, 173, 185, 187, 191, 193, 197, 198, 199, 201, 203, 205, 206, 209, 211, 213, 217, 221, 223, 226, 227, 229, 231, 233, 237, 249, 263, 273, 277, 283, 285, 291, 293, 297, 303, 306 - 309, 311, 313, 314, 315, 317, 319, 321, 323, 326 - 335, 337, 339 - 342, 345, 346, 347, 349, 353, 354, 355, 357, 363, 365 - 370, 374, 391, 393 - 397, 399, 401, 403, 406, 407, 409, 411, 412, 413, 415, 417, 419, 421, 423, 425, 429, 435, 437, 439, 414, 418, 428, 422, 430, 431, 432, 433, 434, 436, 438, 443, 445, 447, 449, 451 - 455, 457 - 461, 463, 465, 466, 467, 469, 470, 471, 473, 474, 475, 477, 479, 481, 483, 485, 487, 489 - 495, 497, 498, 499, 501, 502, 503, 505, 506, 507, 509, 511, 513, 515, 517, 518, 519, 521, 523, 527, 533, 534, 535, 537, 539, 541, 543, 545, 547, 553, 557, 559, 561, 563, 565, 583, 587, 589, 593 - 597, 599, 603, 606, 607, 609 - 611, 613 - 615, 617, 619, 630 - 634, 637, 643, 647, 651, 653, 655, 657 - 659, 661 - 663, 665, 667, 669, 671, 673, 677, 679, 681, 682, 683, 685 - 687, 689 - 691, 693, 695, 697, 699, 701, 702, 703, 706, 709, 713, 734, 735, 737, 738, 739, 741, 743, 745, 747, 749, 751, 752, 754, 755, 757 - 759, 761, 762, 765, 767, 771, 773, 775 - 779, 781, 783, 785, 787, 789 - 791, 793 - 799, 801 - 807, 809, 811 - 815, 817 - 827, 829 - 831, 834 - 839, 842 - 847, 849 - 857, 859, 869, 871 - 879, 881 - 887, 889 - 895, 897, 898, 899, 901 - 911, 913 - 927, 929 - 935, 937 - 952, 954 - 959, 961 - 967, 969, 970, 971, 973, 974, 977 - 983, 985 - 989, 991 - 995, 997, 1001 - 1117, 1132, 1133, 1138, 1139, 1141, 1142, 1143, 1147, 1151, 1153, 1157 - 1163, 1169, 1171, 1183, 1193, 1250, 1577, 2517. Rick Hevener Provided solution for 18, 157 and 163 using the very imaginative 24/99. Contributed more elegant solutions for 31, 49, 76, 89, 125, 146, 159 and interesting alternatives for 17, 21, 36, 100, 102, 107, 109, 126, 140, 141, 162, 279. David Bevan Provided lots of solutions based upon a computer search, this includes lots of more elegant solutions. In particular he pointed out a third solution for 17 and noted the following cleaner notations, .(4!) is the same as 4!% and .(sqrt(4)) is the same as sqrt(4%). Vijay Kailas Came up with 1206. Guido Roach An alternative 4 four solution for 113, namely ( sqrt(4) / .4' + sqrt(4)% ) / 4% Joe Martin An improved solution for 533 = (4! * .4' - sqrt(.4)%) / sqrt(4)% Toufic Batouli Toufic proposed the use of degrees, minutes, and seconds as standard notation. Using these symbols provides some additional solutions to numbers using only two 4s. Since each degree is 60 minutes, or 3600 seconds, we have ```[(4!) Deg / 4 Sec] = 21,600 [(4!) Deg / 4 Sec]% = 216 [(4!) Deg / 2 Sec] = 43,200 [(4!) Deg / 2 Sec]% = 432 ``` We also have additional results for both 0 and 1 using only one 4 because 24! is an integer (N) multiple of 360: ```Sin((4!)! Deg) = Sin(N * 360 Deg) = 0 Cos((4!)! Deg) = Cos(N * 360 Deg) = 1 ``` Also, since one degree is equal to pi/180 radians we can get many additional numbers using only two 4s. The additional solutions come from the relationship arccos(x) = 90 Deg - x. So only two 4's are needed for: ```Arccos(Sin(4 Deg))/(Sqrt(4) Deg) = 86 Deg / 2 Deg = 43 ``` Further examples are given here. And of course the well known problem of 113 without using the double factorial: ```129 - 16 = [Arccos(Sin(4 Deg))/(4! Sec)]% - 4*4 = 113 ``` Nikkol Bauer New or alternative answers for the following: 729, 777, 792, 821, 823, 824, 825, 826, 827, 829, 834, 835, 849, 850, 870, 882, 890, 910, 918, 930, 999, 1023, 1062, 1062, 1070, 1070, 1077, 1089, 1089, 1104, 1104, 1110, 1111, 1113, 1115, 1135, 1155, 1166, 1170, 1177, 1184, 1186, 1187, 1189, 1192, 1203, 1205, 1207, 1208, 1209, 1211 largely based upon the following relationships and observations. ```.(4!)'% = .002424242424... .sqrt(4)'% = .002222222... .4'% = .0044444.... 4'% = .04444444.... (this is really stretching it because four repeating divided by 100 is infinity) (4 + .4')% = same as above with two fours (sqrt(4))'% = .022222222 ... (also pushing it) (4%%)' = 0.000400040004 ... (sqrt(4) + sqrt(4%)')% = same as above with two fours ```