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The 24 Game is an arithmetical card game in which the objective is to find a way to manipulate four integers so that the end result is 24.

How do you get $24$ using $5, 5, 5,$ and $1?$

Solution: $\displaystyle5\times\left[5-\left(\frac{1}{5}\right)\right].$

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clache547
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    Define $x,y,z,w\mapsto 24$, then $5,5,5,1\mapsto 24$. – YoTengoUnLCD Aug 15 '16 at 21:47
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    In the "24 game" I have on my phone, only $+$, $-$, $\cdot$, $/$ and parentheses are allowed - you should clarify if that is also what you intended with this question (it would invalidate all the current answers). – Henrik supports the community Aug 15 '16 at 21:48
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    @Henrik Spoil-sport – Edward Evans Aug 15 '16 at 21:55
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    @YoTengoUnLCD I loved that comment, especially since I used this game when teaching pre-algebra students about order of operations. I think the mapping concept would have been too much though (well maybe not...looking back, I am quite annoyed I was not introduced to the concept of a mapping until far later than I should have been). Fwiw, this site gives 10 easy solutions right away. – Daniel W. Farlow Aug 15 '16 at 22:26
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    Can this just be moved to the mathematics puzzle section? – Olive Stemforn Aug 17 '16 at 18:22

9 Answers9

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Here's a solution using just the $+$, $-$, $\times$, $/$ operations, and parentheses: $$ 5 \times (5 - (1/5)) $$

grand_chat
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5

With Euler's Totient function:

$$\phi(5 \cdot 5) + \phi(5 \cdot 1)$$

John
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Here is one for you guys

$$ -1^5 + 5*5 $$

Erock Brox
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3

One possible answer is $$5 \cdot 5 - \lceil \frac{1}{5} \rceil$$

benguin
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3

One easy way:

$$(5-1)!\cdot\frac{5}5$$

Brian M. Scott
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Or $$\sqrt{5\cdot 5} \cdot5 - 1$$

thanasissdr
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$1\times\frac{5}{5}\Gamma(5){}{}{}{}{}{}{}{}$

Edward Evans
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1

One possible way:

$$(5-5)+(5-1)!=24$$

Siong Thye Goh
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1

With derangements:

$$!5 - 5(5 - 1)$$

John
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