24 Puzzle

[1vRz3TCk]

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Please DO NOT post the answer to this thread.
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It took me a while to solve this so I thought I would post it here. It would be nice if you don't post the answer.

How do you make 24 from 1, 3, 4, and 6 using all numbers and only addition, subtraction, multiplication and/or division?

PS please post other puzzles if you have any.

I'm also wondering if there is an elegant generics algorithm for solving the above type of puzzle.

[1yR4jE8b]

can you use a number more then once?

[1vRz3TCk]

No, each number has to be used once and only once.

For an example, with the numbers 4,7,8,8, a possible solution is the following:
( 7 - ( 8 / 8 ) ) * 4 = 24.

[quirkyusername]

I presume we're allowed fractional results and aren't restricted to integer division? If I'm wrong them I'm really baffled as to what the solution could be but I've got it otherwise

[1vRz3TCk]

I presume we're allowed fractional results

obviously the end result has to be 24 but yes intermediate results can be fractional.


The aim of this type of puzzle is to do it in you head, so it is simple maths.

[strongdrink]

got it.

EDIT:
Did you get this puzzle from "Hacking - The Art of Exploitation" ?

[1vRz3TCk]

Did you get this puzzle from "Hacking - The Art of Exploitation" ?

No, a friend posed it. (I don't know where he got it from though). I quite like this type of puzzle (using four number to make 24), I have in the past used four ten sided dice to give me random numbers and then try to make 24 without knowing if it is possible.

[R0mai]

Are there only one solution to this? I think I bruteforced all possible combinations, I'm just not sure.
I would be interested in clever algorithms too, but I don't think it exists. Anyway, my bruteforce 'algorithm' has to check 5184 combinations, which is not too much.

[zwA4jE8b]

Fun one, I remember seeing this a while back.

[strongdrink]

A program to solve/create these type of problems would be pretty cool :P

[1vRz3TCk]

Are there only one solution to this?

I don't know how many solutions there are, I stooped at one. ;0)

[Disch]

Well I'm baffled. Mainly because of quirkyusername's hint

I presume we're allowed fractional results and aren't restricted to integer division?

I'm failing to see how division could be used in a solution, other than to throw out the 1.

I mean both 6*4/3 and 6*3/4 put you well under 24.

Even if you add 1 to the numerator to push it up as high as possible, dividing still leaves you way short of the goal:

6*(4+1)/3 = 10
6*(3+1)/4 = 6

The way I see it, 6 has to be somehow involved in a multiplication (either before or after you add to it). There's no way to get up to 24 otherwise. But I can't seem to figure it out. Closest I can get is 25.

[quirkyusername]

@Disch

here's an even bigger hint, if you want to solve it yourself don't read below...











remember that dividing by a fraction is equivalent to multiplication

[Disch]

Well yeah -- but that doesn't really make sense. There's still division involved.

I mean x/(y/z) is the same as (x*z)/y. So either way you have a division by y. So unless y is 1 and you're just dividing by it to throw it out, that division seems to make it impossible to get up to 24. Even if you multiply every other number.

I'm not doubting you. I mean I'm sure there's a solution. I'm just not seeing it.

EDIT: I should also mention I'm bad at these kinds of puzzles. =P

[1vRz3TCk]

Would you like me to PM the answer?

[Disch]

yes plz =P

EDIT: pft, of course now that I see the solution I get it XD. But yeah I probably never would have gotten it.

[quirkyusername]

I probably wouldn't have gotten it if I hadn't been practicing this sort of thing so much recently, I've had several job interviews for programming positions and problem solving puzzles crop up a lot.

EDIT - I might make a post full them actually

[ne555]

I found 2 more solutions (by now, but I will not expand it)
Hint: 6*9 = 42

[quirkyusername]

what? 6*9 = 54, and I can't see how that would get us any closer to 24

[ascii]

Haha, I had one of these in a math class where the solution was just to add up all of the numbers, and it took most people a good 15 minutes :)

Back to work anyhow, I'm assuming its not (6*4) + 1/3 and letting python truncate the decimal :/