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Sequence of Numbers . Can a given set of integers be ordered such that the sum of any two consecutive numbers in the sequence is
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.
- 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)
- 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 .
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