Arrange the numbers from 1 to 15 in such an order that any two consecutive numbers in the sequence add up to a perfect square.
As some people have already mentioned(comments)
that 8 and 9 can not take other positions than
the ends, is good and agreed upon. 8 and 9 each
has only one partner(1, 7) to make perfect square.
When we fix them at the ends(for example,
position 1 for 8 and 15 for 9). Then obviously
position 2 should be UNIQUELY taken by 1 and
pos. 14 by 7.
If we start working from pos. 14, it is easy to
complete the series uniquely. As 7 can take only 2
and 2 can take only 14 and 14 can take only 11 etc.
so, the solution I gave long back is the unique
solution. Any how as the addition has commutative
property(a+b=b+a), inverting the above solution is
also a solution.
explanation for the arrangement of numbers 1 to 15
