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Dumb Kopf...

Joe Riel 9575
August 03 2005
1
I hadn't carefully read the puzzle conditions of the Kopf und Kopf puzzle mentioned by Thomas Richard, I didn't realize that the digits had to be unique. He asked for a hint on how to handle that with my recursive method. The idea is simple, add a parameter (to the recursive procedure) that supplies the available digits. I've attached the code that does this. This would have been a response, rather than a separate blog entry, however, there does not appear to be a way to add attachments to a response. Is there a maximum base beyond which there is no solution for this puzzle (i.e. not all digits used)? I've attached a second file that briefly explores this. The largest base I've found that has a solution is 14, however, I've only checked up to base 20 (the test gets increasingly slower, naturally). So far, the only bases with solutions are even---is there a simple proof of that?

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