The Magic Hexagon: One Honeycomb, Every Line Equal
Arrange the numbers 1 through 19 into a honeycomb of nineteen small hexagons — rows of 3, 4, 5, 4 and 3 — so that all fifteen straight lines, in every one of the three directions, add up to the exact same total. It sounds like there should be many ways to do it. There's exactly one, up to rotation and reflection.
Reveal the answer
The magic total is 38. The unique arrangement was found by Clifford W. Adams, a retired railway clerk, who worked the problem in his spare time from 1910 until 1957, when he finally wrote to Martin Gardner with his solution. Gardner featured it in his Scientific American 'Mathematical Games' column — and it turns out no magic hexagon of any other size (order 4, 5, and up) can ever exist.