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by Brian Gladman on October 13, 2019

New Scientist Back Page Puzzle 23 – Circling the Squares

by Rob Eastaway

From New Scientist #3249, 28th September 2019

Darts player Juan Andred has noticed that on a standard dartboard, there are some neighbouring pairs of numbers that add up to a square number. For example, 20 and 5 make 25, while 6 and 10 add up to 16. He has been wondering if he can come up with a new arrangement of the numbers 1 to 20 so that all neighbouring pairs add up to a square number. And he has nearly succeeded.

He has 20 at the top of the board, and every pair of neighbours adds to a square — with one exception. On his new board, 18 doesn’t form a square with its clockwise neighbour, which is 15, or with its anticlockwise neighbour.

What does Juan’s “square” dartboard look like?

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