Solving the Normal Magic Hexagon of Order Three: A “Smart Odometer” Treatment

Abstract

This article develops an efficient algorithm to solve the normal magic hexagon with side length three as a demonstration of a smart odometer model. Each odometer corresponds to a possible distribution of the puzzle tiles, and in principle they could all be considered in turn. But various tests on one distribution allow us to skip over billions, even trillions of consecutive cases without fear of discarding a valid solution, thus providing an amazing acceleration in comparison to the simple approach of trying all options, even if done using parallel processing. We highlight trade-offs of additional testing versus fewer tested prospects. After the unique solution is found, we show how to apply the algorithm to abnormal magic hexagons, including the magic zero puzzle.