Magic Hexagon Quiz Puzzle Answer

We quite like puzzles that are easy to state but difficult to solve, and we have an example of that right here. It should while away many an hour of Self Isolation or Lockdown.

All you have to do (all you have to do) is put the numbers 1 through to 19 into an order 3 hexagon so that every row of three, four or five hexagons, in all three directions, adds up to the same number. Just like a Magic Square.

What is an order 3 hexagon? Well, the easiest way to see one is look at the image that accompanies this puzzle in our blog. Or it is a hexagon built of three hexagons along the bottom, four on the next row, five across the middle, four on top of that, and topped off with another row of three hexagons.

There is only one solution, with rotations and mirror images.

3, 17 and 18 in the top row,

19, 7, 1 and 11 in the next

16, 2, 5, 6 and 9 across the middle,

12, 4, 8 and 14 in the next row,

and 10, 13 and 15 in the bottom row.

Apart from the trivial example with a single hexagon (an order 1 hexagon) there are no solutions for magic hexagons of any other order, using consecutive integers.


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