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Can you place the numbers 1 through 9 in the honeycomb so that the sum of the numbers in the adjacent hexagons is a multiple of the number in the hexagons? This must be true in all hexagons.

The top green hexagon is a 3.

puzzle

I've made several attempts but can't figure it out myself. What is the method to solve such puzzles?

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    $\begingroup$ Welcome to Puzzling, take our tour! Could you please provide proper attribution for this question? $\endgroup$
    – bobble
    May 27, 2022 at 13:56

1 Answer 1

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One possible solution I found:

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This works because:

4 + 7 + 6 + 9 = 26 = 0 mod 1
9 + 6 + 8 + 5 = 28 = 0 mod 2
7 + 6 + 8 = 21 = 0 mod 3
7 + 1 = 8 = 0 mod 4
8 + 2 = 10 = 0 mod 5
7 + 3 + 8 + 1 + 9 + 2 = 30 = 0 mod 6
4 + 1 + 6 + 3 = 14 = 0 mod 7
3 + 6 + 2 + 5 = 16 = 0 mod 8
1 + 6 + 2 = 9 = 0 mod 9

I suppose you could flip it horizontally which would still keep the 3 at the top and produce a valid solution as well. And if there was no requirement for the 3 to be at top, you could flip it vertically as well.

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    $\begingroup$ I verified via enumeration of all possibilities that this solution and its horizontal reflection are the only 2 solutions $\endgroup$
    – JLee
    May 27, 2022 at 18:19
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    $\begingroup$ How did you come up with that solution? Or is it just try and try again? $\endgroup$
    – Antoon Verroken
    May 28, 2022 at 5:53

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