Problem: The Letter Block Puzzle


Here is a little reminiscence of our old friend the Fifteen Block Puzzle. Eight wooden blocks are lettered and are placed in a box, as shown in the illustration. It will be seen that you can only move one block at a time to the place vacant for the time being, as no block may be lifted out of the box. The puzzle is to shift them about until you get them in the order —

\[\begin{array}{ccc} A&B&C\\ D&E&F\\ G&H \end{array}\]

This you will find by no means difficult if you are allowed as many moves as you like. But the puzzle is to do it in the fewest possible moves. I will not say what this smallest number of moves is, because the reader may like to discover it for himself. In writing down your moves you will find it necessary to record no more than the letters in the order that they are shifted. Thus, your first five moves might be $C, H, G, E, F;$ and this notation can have no possible ambiguity. In practice, you only need eight counters and a simple diagram on a sheet of paper.

Solutions: 1

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Project Gutenberg

  1. Dudeney, H. E.: "Amusements in Mathematics", The Authors' Club, 1917

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