Not sure I've understood this question. If you want to index n-disc 3-pin legal positions, you can obvously pack each irredundantly into a base-3 n-digit number --- digit i equals the pin occupied by disc i. Then via change of basis pack this into base-2 with [1.5850 n] digits. Was this what you meant by "Godel numbering"? If you just want to index positions along the classical shortest path solution, you can do better and compress the base-3 into base-2 with only n digits. There is an algorithm to to do this efficiently, buried somewhere in my (paper) files --- I can disinter it if required. Fred Lunnon On 2/9/08, Guy Haworth <g.haworth@reading.ac.uk> wrote:

The recent question about a fallible agent taking on the 'Towers of Hanoi' leads me to look for a way of compactly indexing the 'States of Hanoi', i.e. the different states of the 1-person game.

Godel-numbering the states is too 'spacious' but might be a element of the algorithm to achieve compact indexing.

All ideas welcome: thank you - Guy

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