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It’s a mechanical solution which doesn’t use recursion. Try it out using 3 or 4 coins of different sizes.

Arrange the three rods to form a triangle. Starting position (where X, Y and Z are different size coins): empty rod Z YYY XXXXX starting rod destination rod Finished position: empty rod Z YYY XXXXX starting rod destination rod Move the smallest disk on every other turn — always in the same direction.

On the remaining turns make the only valid move that does not involve the smallest disk. The following rule will make sure that the tower of disks end up on the third rod: If the number of disks in the puzzle is an odd number then always move the smallest disk counter-clockwise around the triangle; if the number of disks in the puzzle is an even number then always move the smallest disk clockwise around the triangle. With this solution the even numbered disks move around the triangle in one direction while the odd numbered disks move around the triangle in the opposite direction.