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?

Question

anonymous · Answer

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anonymous · Answer

i think we dont have so many perfect squares that come from single digits
4,9,16,25...

anonymous · Answer

that are less than 15

hartnn · Answer

u can start with 8 or 9
lets start with 9,
which number u can place next so that sum is perfect square ?

anonymous · Answer

7

hartnn · Answer

correct :) 
now u have  2 choices with 7,
7+2=9 
and 7+9 = 16 
but 9 is already there!
so next number is obviously 2.
did u get this ???

anonymous · Answer

ya i get it now i can do it myself now thanks!

hartnn · Answer

welcome :)
let me know the final answer though, so we both can verify ...

anonymous · Answer

yeah. i got:
9, 7, 2, 14, 11, 5, 4, 12, 13, 3, 1, 15, 10, 6, and then 8 should be next but 8 doesn't fit for some reason

hartnn · Answer

try, 13,3,6,10,15,1,8....

anonymous · Answer

oh wow thanks!

hartnn · Answer

welcome, just trial and error for this part....