Long out of math, an AI programmer cracks a pure math problem

Re:Long out of math, an AI programmer cracks a pure math pro... by SideQuark on Tuesday January 03, 2023 @06:26PM (#34239620)

It's not out of the box when I apply error correcting codes to a massive range of problems ;)

If you like cool problems, here is one I have not found a simple solution for, but I once saw it in a place where a simple solution should exist.

You have an odd number >=3 of items with the property that any time you remove one, there is a way to split the remaining items into two piles of equal weight. Show all items have the same weight.

It's easy for 3 items, A,B,C. Remove C, A balances B, then do A,C, now all equal.

It's easy to check by hand for a few small cases.

I proved it using more advanced stuff from lin alg. But I've never found a simple solution yet.

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Re:Long out of math, an AI programmer cracks a pure math pro... by Fetiorin on Tuesday January 03, 2023 @06:53PM (#34239859)

I'm not sure I get the problem.

For number 5, I can use items of weights 3 1 1 1 1 and they are not equal. If you remove 3, you get 1+1=1+1 and in case you remove only of 1s, you can split 3 = 1+1+1.

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Re:Long out of math, an AI programmer cracks a pure math pro... by SideQuark on Tuesday January 03, 2023 @07:32PM (#34240195)

Ah, problem is in memory. Probably also needs two piles of equal number of items :)

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Re:Long out of math, an AI programmer cracks a pure math pro... by danbruc on Tuesday January 03, 2023 @07:17PM (#34240059)

And this generalizes - if n = 2k + 1, 2k times x and once (2k - 1)x can be split into twice kx after removing the single (2k - 1)x or twice (2k - 1)x after removing one x. For k = 1, i.e. n = 3, (2k - 1)x = x. So there is an infinite family of counter examples for all odd n > 3.

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Re:Long out of math, an AI programmer cracks a pure math pro... by zem on Tuesday January 03, 2023 @07:00PM (#34239919)

I remember that problem from my college linear algebra course! I found a nice simple proof for integers (which was very satisfying!) but afaik you do need heavy linear algebra machinery to generalise it to the reals.

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Re:Long out of math, an AI programmer cracks a pure math pro... by thaumasiotes on Tuesday January 03, 2023 @07:13PM (#34240021)

> I found a nice simple proof for integers (which was very satisfying!)

But no such proof can exist because the claim is not true. When you posted your comment, Fetiorin had already given a counterexample.

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Re:Long out of math, an AI programmer cracks a pure math pro... by SideQuark on Tuesday January 03, 2023 @07:33PM (#34240200)

I was pulling the problem from memory. Add the requirement boths sides are same number of items.

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Re:Long out of math, an AI programmer cracks a pure math pro... by hgsgm on Wednesday January 04, 2023 @08:31AM (#34245307)

Why doesn't the integer proof work on reals?

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Re:Long out of math, an AI programmer cracks a pure math pro... by zem on Wednesday January 04, 2023 @04:29PM (#34251997)

it relied on modular arithmetic

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