Solutions from 0 to 116, not including 113 i beg your pardon is more than likely not findable through the rule given.You are watching: 4 4s answers 1-100

This puzzle is most generally formulated as follows:

"Given no more than 4 instances that the number "4", stand for all integers making use of a finite number of mathematical symbols and also operators in usual use."

Notes top top the Rules:

You can not use depictions for other numbers, eg: usage of π in sin(π / 2) = 1Cannot use ... To stand for an infinite variety of operations eg: sqrt(sqrt(sqrt(...4))) = 1 Obviously an adverse integers have the right to be stood for if a optimistic number can. It can be proved that no all integers deserve to be represented.

Subset of agree symbols and operators:+,-addition subtraction*,/multiplication, divisionsqrt,^square root, power!factorial, eg: n! = n * (n-1) * (n-2) * ... * 2 * 1.decimal point, eg: .4′repeating decimal, eg: .4′ = .444444444...

With various other rules, various other answers room possible. Some variations enable you to use any number of 4s as much as 4.Others allow more obscure mathematical operator (gamma functions, for example). It have the right to be easily demonstrated that,even by the conservative ruleset the I explain above, part numbers deserve to be created an infinite number of different ways.The existence of unary operators method that there are an infinite variety of different fads to search for the answer to these problems,which makes computer solutions an exciting problem, which will certainly never have actually a perfect solution.

For your convenience, I present a table of useful 1- and also 2-4 combinations.

 0 " hspace="45" width="77" height="15" align="absmiddle"> 59 " hspace="45" width="59" height="30" align="absmiddle"> 1 " hspace="45" width="29" height="30" align="absmiddle"> 60 " hspace="45" width="62" height="15" align="absmiddle"> 2 " hspace="45" width="51" height="30" align="absmiddle"> 61 " hspace="45" width="59" height="30" align="absmiddle"> 3 " hspace="45" width="78" height="30" align="absmiddle"> 62 " hspace="45" width="104" height="32" align="absmiddle"> 4 " hspace="45" width="98" height="15" align="absmiddle"> 63 " hspace="45" width="104" height="35" align="absmiddle"> 5 " hspace="45" width="78" height="30" align="absmiddle"> 64 " hspace="45" width="37" height="23" align="absmiddle"> 6 " hspace="45" width="78" height="30" align="absmiddle"> 65 " hspace="45" width="75" height="35" align="absmiddle"> 7 " hspace="45" width="64" height="30" align="absmiddle"> 66 " hspace="45" width="68" height="30" align="absmiddle"> 8 " hspace="45" width="76" height="30" align="absmiddle"> 67 " hspace="45" width="104" height="35" align="absmiddle"> 9 " hspace="45" width="64" height="30" align="absmiddle"> 68 " hspace="45" width="49" height="33" align="absmiddle"> 10 " hspace="45" width="50" height="30" align="absmiddle"> 69 " hspace="45" width="88" height="35" align="absmiddle"> 11 " hspace="45" width="59" height="30" align="absmiddle"> 70 " hspace="45" width="122" height="19" align="absmiddle"> 12 " hspace="45" width="99" height="15" align="absmiddle"> 71 " hspace="45" width="67" height="30" align="absmiddle"> 13 " hspace="45" width="78" height="35" align="absmiddle"> 72 " hspace="45" width="58" height="35" align="absmiddle"> 14 " hspace="45" width="104" height="30" align="absmiddle"> 73 " hspace="45" width="127" height="50" align="absmiddle"> 15 " hspace="45" width="62" height="30" align="absmiddle"> 74 " hspace="45" width="122" height="19" align="absmiddle"> 16 " hspace="45" width="77" height="15" align="absmiddle"> 75 " hspace="45" width="88" height="35" align="absmiddle"> 17 " hspace="45" width="79" height="30" align="absmiddle"> 76 " hspace="45" width="85" height="30" align="absmiddle"> 18 " hspace="45" width="92" height="15" align="absmiddle"> 77 " hspace="45" width="86" height="41" align="absmiddle"> 19 " hspace="45" width="72" height="30" align="absmiddle"> 78 " hspace="45" width="104" height="30" align="absmiddle"> 20 " hspace="45" width="67" height="30" align="absmiddle"> 79 " hspace="45" width="102" height="41" align="absmiddle"> 21 " hspace="45" width="72" height="30" align="absmiddle"> 80 " hspace="45" width="84" height="30" align="absmiddle"> 22 " hspace="45" width="88" height="35" align="absmiddle"> 81 " hspace="45" width="63" height="31" align="absmiddle"> 23 " hspace="45" width="88" height="30" align="absmiddle"> 82 " hspace="45" width="97" height="30" align="absmiddle"> 24 " hspace="45" width="76" height="35" align="absmiddle"> 83 " hspace="45" width="102" height="41" align="absmiddle"> 25 " hspace="45" width="88" height="30" align="absmiddle"> 84 " hspace="45" width="69" height="19" align="absmiddle"> 26 " hspace="45" width="84" height="30" align="absmiddle"> 85 " hspace="45" width="63" height="38" align="absmiddle"> 27 " hspace="45" width="126" height="60" align="absmiddle"> 86 " hspace="45" width="85" height="19" align="absmiddle"> 28 " hspace="45" width="80" height="15" align="absmiddle"> 87 " hspace="45" width="79" height="32" align="absmiddle"> 29 " hspace="45" width="72" height="30" align="absmiddle"> 88 " hspace="45" width="50" height="15" align="absmiddle"> 30 " hspace="45" width="101" height="19" align="absmiddle"> 89 " hspace="42" width="91" height="45" align="absmiddle"> 31 " hspace="45" width="104" height="35" align="absmiddle"> 90 " hspace="45" width="85" height="19" align="absmiddle"> 32 " hspace="45" width="42" height="33" align="absmiddle"> 91 " hspace="45" width="87" height="35" align="absmiddle"> 33 " hspace="45" width="88" height="35" align="absmiddle"> 92 " hspace="45" width="69" height="19" align="absmiddle"> 34 " hspace="45" width="101" height="19" align="absmiddle"> 93 " hspace="45" width="104" height="46" align="absmiddle"> 35 " hspace="45" width="97" height="40" align="absmiddle"> 94 " hspace="45" width="127" height="39" align="absmiddle"> 36 " hspace="45" width="85" height="15" align="absmiddle"> 95 " hspace="45" width="83" height="35" align="absmiddle"> 37 " hspace="45" width="97" height="40" align="absmiddle"> 96 38 " hspace="45" width="114" height="19" align="absmiddle"> 97 39 " hspace="45" width="66" height="35" align="absmiddle"> 98 40 " hspace="45" width="128" height="21" align="absmiddle"> 99 41 " hspace="45" width="97" height="35" align="absmiddle"> 100 42 " hspace="45" width="66" height="35" align="absmiddle"> 101 43 " hspace="45" width="50" height="30" align="absmiddle"> 102 44 " hspace="45" width="49" height="30" align="absmiddle"> 103 45 " hspace="45" width="50" height="30" align="absmiddle"> 104 46 " hspace="45" width="110" height="19" align="absmiddle"> 105 47 " hspace="45" width="87" height="30" align="absmiddle"> 106 48 " hspace="45" width="84" height="30" align="absmiddle"> 107 49 " hspace="45" width="95" height="30" align="absmiddle"> 108 50 " hspace="45" width="57" height="30" align="absmiddle"> 109 51 " hspace="45" width="88" height="35" align="absmiddle"> 110 52 " hspace="45" width="63" height="15" align="absmiddle"> 111 53 " hspace="45" width="97" height="35" align="absmiddle"> 112 54 " hspace="45" width="110" height="19" align="absmiddle"> 113 55 " hspace="45" width="75" height="35" align="absmiddle"> 114 56 " hspace="45" width="94" height="15" align="absmiddle"> 115 57 " hspace="45" width="104" height="35" align="absmiddle"> 116 58 " hspace="45" width="111" height="35" align="absmiddle">

A note to mathematics teachers: i have obtained abusive e-mails from math teachers that feel that this page is essentially a cheat sheet, offering away the answers to a puzzle they would like to provide as homework. Frankly, this is a widely known puzzle that I first heard in the Reagan management and the wasn"t new then. Not only are remedies widely known, however software that permits the automated generation of remedies has likewise been released into the publicly domain (not the I have actually used any such software application above). What I"m trying to say is it’s time to find new assignments.

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Assigning the four fours difficulty in a math class is in ~ this suggest like asking student to predict the finish of the vietnam battle in existing events class — it might have to be a great question in 1970 however it doesn’t test what you want it to anymore.