Squares and Graphs

Recently I came across this intriguing little puzzle… Take the integers 1..n and, if possible, arrange them in a list in such a way that consecutive numbers in the list add up to a square number. Use each number 1..n once only. In exploring this puzzle I started writing down the numbers and forming a graph where two numbers are connected if they add up to a square. Drawing such graphs is fun but slightly tedious for, for example, [1..300]… Here’s such a graph for numbers 1..15. Starting at 8 then 1 etc. and following the path gives the solution Read More

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