How must one place the integers from 1 to 15 in each of the spaces below in such a way that no number is repeated and the sum of the numbers in ANY TWO consecutive spaces is a perfect square?
Note: the sum can repeat,like u can have the sum as 9 as many times as u want.

Question

How must one place the integers from 1 to 15 in each of the spaces below in such a way that no number is repeated and the sum of the numbers in ANY TWO consecutive spaces is a perfect square?
Note: the sum can repeat,like u can have the sum as 9 as many times as u want.

debbieg · Answer

Is it just a row of 15 spaces?

debbieg · Answer

Using 1 to 15 without repeats, the largest possible sum is 29. The only perfect squares, the, that are possible candidates for each some are 4, 9, 16 and 25.

It's not too hard to list all the possible pairs for each of those. That is, list all the pairs of integers from 1 to 15 that make a sum of 4 (without repeating a number); all that sum to 9, to 16 and to 25. That gives you every possible combination of sum pairs.

Then you just need to figure out how to arrange those in the spaces. If the spaces are a single row of spaces, I think it will be a matter of just playing around with the order.

debbieg · Answer

For example, if you place 3,13 (sum of 16) then the next number has to be 12, because 13 pairs only with 3 and with 12 to make a perfect square. That's just one example, but that's the general idea.

Neat little "puzzle" problem! :)