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Magic Zero Hexagons

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The numbers to 9 can be arranged in a hexagon so that all lines of hexes have a sum of zero. There seem to be 19 distinct ways to do this. By comparison, the numbers 1 to 19 can be arranged for a magic sum of 38 in a unique way; select arrangement 20 to see it.

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The triangular numbers are . This Demonstration shows that to make magic zero hexagons. Can to make a magic hexagon for all ?

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Contributed by: Ed Pegg Jr (January 2021)
Open content licensed under CC BY-NC-SA

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[1] Wikipedia. "Magic Hexagon." (Dec 4, 2020) en.wikipedia.org/wiki/Magic_hexagon.

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