Minimum n for Squares from Pairs
Number Theory
Level
2
What is the smallest integer n > 1 such that the first n integers can be arranged into a sequence where the sum of any two adjacent numbers is a perfect square?
The answer is 15.
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1 solution
The flowchart below shows all possible pairs for the first 15 integers, as well as a workable sequence from 8 to 9 shown in red. Removing numbers, starting at 15 and working down, shows that no complete paths through all numbers obtainable until only 1 remains.