Sequence of Numbers. Can a given set of integers be ordered such that the sum of any two consecutive numbers in the sequence is a square. For example, in the sequence (3,6,10), 3+6=9 and 6+10=16.

1. Provide an algorithm that can find out whether such an arrangement is possible in a feasible time. Explain your algorithm in detail along with pictures to explain the steps. (15)
2. Show that such a sequence is possible for (i) the set of integers from 1 to16; (ii) the set of integers from 1 to 17 .