# Calculate : 1

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What is the expression with the fewest number of operators inserted that evaluates to 1?

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The numbers need to be in the order that"s shown in the question.Only use the operators +,−,×,÷ and √ and ! (Implies that modulus "%", exponent "^", binomial coefficients, and other operators are not allowed).Parentheses will not be counted, so they can be used to change the order of operations.Rounding is not allowed, so it have to equal to 1.Verify your calculations in that calculator application that comes with your PC, if it ever did came with your PC.

This is my first time writing a puzzle here so obviously I should have thought this out a lot more instead of adding rules when situation comes.

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edited Apr 13, 2017 at 12:50

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asked Apr 15, 2015 at 20:35

John OdomJohn Odom

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## 12 Answers 12

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If √ can mean nth root:

$$\sqrt<1234567>{-8+9}$$

3 operators. Obviously...

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answered Apr 16, 2015 at 6:11

user23013user23013

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uses four. (I wrote a Python script.)

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answered Apr 15, 2015 at 20:52

LynnLynn

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How many significant digits matter here for rounding? Because if it"s anything less than $3,456,789$ zeroes, I can solve it in three ;)

$1+2/3456789! = ~1$

Many programming languages will evaluate it as "1". Even Wolfram Alpha can"t show me enough decimal digits to tell me I"m wrong ;P

**EDIT:**Yes, I know this is no longer valid as of the rule change that doesn"t include rounding. I didn"t expect it would be allowed anyways, just figured it would be worth submitting, since it comes so infinitesimally close to 1. Besides, kgull managed to get even closer using a similar method.

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edited May 1, 2018 at 4:25

SteamCode

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answered Apr 15, 2015 at 21:02

Mwr247Mwr247

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Assuming the binomial coefficient is not an operator itself and parentheses are allowed and not counted, this requires only 1 operator.

$$1+{2345\choose6789}=1$$

Check the Pochhammer symbol too:

$$1+(-2)_{3456789}$$

Some useful information on Wolfram Alpha.

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edited Jun 25, 2015 at 17:35

grg

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answered Apr 16, 2015 at 13:51

Francesco De LisiFrancesco De Lisi

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If parentheses will not be counted and if we could use it as multiply:

$12(34)-5(67)-8(9) = 1$

I used only 2 operators.

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edited May 1, 2018 at 3:49

JMP

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answered Apr 16, 2015 at 21:07

AlexAlex

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A simple expression that is exact, and only uses four operations without bending the rules (if exponentiation isn"t permitted, I assume that neither is using the numbers to create n-th roots) while using at least one non-basic operation, is$$((1+2-3)\times456789)!$$That"s one addition, one subtraction, one multiplication, and one factorial (actually, zero factorial, but you know what I mean). Another similar option is$$((12/3-4)\times56789)!$$A slightly more bendy solution using the fact that negative integer factorials can be considered to be infinite is$$1+2/(3-456789)!$$

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answered Apr 17, 2015 at 7:54

Glen OGlen O

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$$(1 + 23 + 45 + 6! - 789)! = 1$$

$$((1+2-3)\times456789)!=1$$

Everyone is trying with minimum operators.I guess, with

user23013"s solution, we can try with various possibilities :)

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edited Jun 17, 2020 at 8:22

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answered Apr 17, 2015 at 8:57

thepacethepace

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Three Operators

Similar idea to Mwr247"s solution, but even more significant figures:

$$\left(\frac1{23456789!}\right)! = 1$$

Wolfram Alpha seems to think it is exactly 1. Good enough for me >_>

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edited Jun 25, 2015 at 17:35

grg

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answered Apr 16, 2015 at 6:42

Kyle GKyle G

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$$1-23+45+67-89$$uses only 4 operators.

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edited Jun 25, 2015 at 17:36

grg

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answered Apr 15, 2015 at 21:08

My Life for AuirMy Life for Auir

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Edit: I realized Alex did it using 2 operations using this loophole so this is nothing special. I"d delete this normally but I think this solution is still kinda cool.

I got three operations without using an nth root:

$(12)(3)(4)(.5)(-6+7)/((8)(9))=1$Taking advantage of parentheses not counting. (Yes I know the rule wasn"t meant for them to be used this way but I spent a long time thinking of how to exploit this loophole so cut me some slack.)

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edited Jun 26, 2015 at 3:54

answered Jun 26, 2015 at 3:46

QuarkQuark

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In languages like C# and Java dividing two integers will always result in an integer (decimals will be omitted).Therefore only one operation is required to solve this problem:

12345/6789Which will result in 1.

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answered Apr 16, 2015 at 12:28

Mike.Mike.

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**One operator.**

Taking advantage of user23013 "s loop hole.

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If √ can mean nth root:

$$\sqrt<23456789>{1}$$

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answered Apr 16, 2015 at 10:42

user288447user288447

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