# Coppers - Make 24 [closed]

The make-24 puzzle is an oldie, but a very fun one at that.

Given four different numbers, produceâ€”through a sequence of operations upon only those four numbersâ€”the number twenty-four.

For example, given $2,2,3,8$ you can make $24$ by: $2\times 3\times\frac82$.

Note that each of the given numbers must be used exactly one time each in the solution, and no other digits may appear anywhere.

Here cops can submit puzzles for the robbers to solve!

As a cop, your job is to create a specific make-24 problem. You must specify:

• The four numbers a robber is allowed to use to solve your problem
• and the operations they are allowed to use (note that it's implied by default an answer should use a finite number of operations.)

For example, a good cop post may look like:

I remember being set this kind of challenge in school, one of them was quite tricky. I'll just give you the same problem our teacher gave us:

Make $24$ using $2,2,2$ and $1$ and any of the operations: multiplication, addition, subtraction, unary negation, division, factorial, square rooting, and modulus.

I managed to solve it with three of those operations, maybe you can beat me!

For the example, is the goal is to get 24 out of 2, 2, 2, 1 using 3 operations tops? An answer with 4 operations is not valid.

Actually, the cop is not allowed to limit the number of operations. However, unless the cop states otherwise, you should assume that the number of operations you use must be finite.

• @theonlygusti I have a feeling that its moving in a direction of semi-interactive-puzzle – Techidiot Mar 22 '17 at 16:21
• The more normal procedure would be for any given make-24 problem to be submitted as a question, and answers to those problems to be submitted as answers to the corresponding questions. It's not clear to me what advantage the more indirect approach here has. I suppose it clutters up the most-recent-questions less. – Gareth McCaughan Mar 22 '17 at 16:29
• @Deusovi I feel that that's a false premise upon which to close a question on this site, I can think of many (well-received) questions here which have infinitely-many correct solutions. I feel too that judging this significantly different type of question by the criteria used to judge the regular questions here won't work. But you're much more experienced than me on this site, so I'll pretend to take your word for it. – theonlygusti Mar 22 '17 at 16:40
• I feel like this may be a discussion for the meta. – F1Krazy Mar 22 '17 at 16:57
• Yeah. Personally, I don't think this is a bad style of question. I think it would have been extremely fun to allow the community to challenge each other with similarly narrowly-scoped problems. Some people are allergic to fun. – theonlygusti Mar 22 '17 at 18:18

[I hope I'm understanding the intended procedure correctly: an answer here is meant to be a question, to be answered by an answer to the "robbers" question. Right?]

My personal favourite 24-puzzle sounds very simple but is surprisingly tricky: make 24 from the numbers 3,3,8,8, using only arithmetic operations.

• Yeah, you understood the task perfectly! And that looks like a very interesting problem... – theonlygusti Mar 22 '17 at 16:11
• Jolly good. You suggested an edit that removes my initial comment in square brackets; I'm afraid I'm going to reject that edit because I think it's helpful to be more explicit about what's going on here. The "cops and robbers" format is a bit unusual. – Gareth McCaughan Mar 22 '17 at 16:14
• If this proves popular then once there are a few separate "cops" posts I will remove the bracketed comment. – Gareth McCaughan Mar 22 '17 at 16:14
• Ok, sure :) I know that the cops and robbers format is quite popular on other SE sites, but there's only a couple posts here. – theonlygusti Mar 22 '17 at 16:15
• @theonlygusti Am I suppose to put the solution to this here ? – Techidiot Mar 22 '17 at 16:16

Ok, the only solution I know for this one is extremely surprising as it really forces you to think outside of the box.

Use $1,3,4,6$ and any of the arithmetic operators to make $24$. Trust me, the solution I've seen is really beautiful :)