# Solving the 24 Game for 5, 5, 5 and 1 [closed]

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

• Define $x,y,z,w\mapsto 24$, then $5,5,5,1\mapsto 24$. – YoTengoUnLCD Aug 15 '16 at 21:47
• 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 - stop hurting Monica Aug 15 '16 at 21:48
• @Henrik Spoil-sport – ÍgjøgnumMeg Aug 15 '16 at 21:55
• @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
• Can this just be moved to the mathematics puzzle section? – Olive Stemforn Aug 17 '16 at 18:22

Here's a solution using just the $+$, $-$, $\times$, $/$ operations, and parentheses: $$5 \times (5 - (1/5))$$
$$\phi(5 \cdot 5) + \phi(5 \cdot 1)$$
$$-1^5 + 5*5$$
• Where does the $2$'s come from? And what does $(5)$ mean? – Henrik - stop hurting Monica Aug 15 '16 at 21:45
• You should add $$around the expression. – Matt Watkins Aug 15 '16 at 21:58 One possible answer is$$5 \cdot 5 - \lceil \frac{1}{5} \rceil$$One easy way:$$(5-1)!\cdot\frac{5}5$$Or$$\sqrt{5\cdot 5} \cdot5 - 1$$1\times\frac{5}{5}\Gamma(5){}{}{}{}{}{}{}{} • Care to elaborate a bit? – Namaste Aug 15 '16 at 22:26 • Gamma function \Gamma(n) = (n-1)! – John Aug 15 '16 at 22:30 • Was a bit of a silly answer, although it's true. @John for n \in \Bbb Z^+ – ÍgjøgnumMeg Aug 15 '16 at 23:13 One possible way:$$(5-5)+(5-1)!=24$$With derangements:$$!5 - 5(5 - 1)