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

Gregory Marsh

Mathematics

25 November, 12:19

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.

+3

Answers (2)

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Tyshawn Ochoa · Answer 1

Perfect squares are

1,4,9,16,25,36

obviously cannot add to 1 or 36

4,9,16,25 are the sums to add up 2

ok so

8,1,15,10,6,3,13,12,4,5,11,14,2,7,9

after lots of trial and error

Adrianna Valenzuela · Answer 2

The perfect squares 1, 4, 9, 16, and 25 are possible in this problem since the biggest numbers which are 14 and 15 add up to 29 only.

A possible sequence would be,

9 - 7 - 2 - 14 - 11 - 5 - 4 - 12 - 13 - 3 - 6 - 10 - 15 - 1 - 8

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.

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.