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Forum: Puzzles

2021-11-15, 15:12

Replies: 31

The Square-Sum problem

Views: 18,304

Posted By R. Gerbicz

Thanks for the idea, then I'll try the AMM first,...

Thanks for the idea, then I'll try the AMM first, need to write down the solution.
It is a somewhat recreational Maths problem, but worth a paper.

Forum: Puzzles

2021-11-02, 10:51

Replies: 31

The Square-Sum problem

Views: 18,304

Posted By R. Gerbicz

There was a request to explain this more, took me...

There was a request to explain this more, took me some time to understand some tricks.

First why parity is so important here. It is trivial: for each c=-24..24 we choose T(c,0) or T(c,1), exactly...

Forum: Puzzles

2018-03-17, 09:05

Replies: 31

The Square-Sum problem

Views: 18,304

Posted By R. Gerbicz

Thanks for your interest! I"ve constructed all...

Thanks for your interest!
I"ve constructed all basic sequences that holds this, and then by induction we still maintain this. Note that all integers in [1,24] is free, because T(c,0) and T(c,1)...

Forum: Puzzles

2018-01-23, 21:59

Replies: 31

The Square-Sum problem

Views: 18,304

Posted By R. Gerbicz

I've thought the same in the recent days, maybe...

I've thought the same in the recent days, maybe I'll come up with a paper.

Forum: Puzzles

2018-01-21, 17:09

Replies: 31

The Square-Sum problem

Views: 18,304

Posted By R. Gerbicz

There is a solution for every n>=25 ! Giving a...

There is a solution for every n>=25 !
Giving a Hamiltonian cycle for all n>=32, see my linked code:
https://drive.google.com/file/d/1XpYRdJR00CldIfssjDW1clkh-HdPA708/view
somewhat large file ( 5.7...

Forum: Puzzles

2018-01-17, 22:26

Replies: 31

The Square-Sum problem

Views: 18,304

Posted By R. Gerbicz

Correct, but the goal was to prove that n>=25 is...

Correct, but the goal was to prove that n>=25 is in the sequence. Since it wasn't reached I've posted the above weaker result.

Yes, you need odd square, otherwise c=k^2/2 gives the same...

Forum: Puzzles

2018-01-17, 21:15

Replies: 31

The Square-Sum problem

Views: 18,304

Posted By R. Gerbicz

Returning to the original square-sum problem, a...

Returning to the original square-sum problem,
a non trivial result: the sequence is infinite, for n=(71*25^k-1)/2 there is a solution for every k>=0 integer.

For given "a" sequence that is a...

Forum: Puzzles

2018-01-12, 23:58

Replies: 31

The Square-Sum problem

Views: 18,304

Posted By R. Gerbicz

Nice problem, easily outperformed that in one day...

Nice problem, easily outperformed that in one day of work.

There exists a solution for n=15,16,17,23 and for all 25<=n<=1048576. (the last checked is n=2^20).
To prove more we give a Hamiltonian...

Showing results 1 to 8 of 8

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