Enigma 339a: Christmas dice
1 April 2016
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From New Scientist #1487, 19th December 1985 [link]
During last Christmas’s intellectual activity — backgammon, ludo, and so on — Pam complained about the unfairness of using a pair of ordinary dice.
“With this pair,” she said, “you can only throw a total from 2 up to 12. But I should like to be able to throw any whole number from 2 up to much more than that. And with this pair I am much more likely to throw some totals that others — I get 7, for instance, six times as often as I get 12. What I want is a pair of dice which will throw every possible total with equal probability. And finally, there’s a 4 on each of these dice, and I object to square numbers. I don’t mind 1 — I don’t think of 1 as really square — but I don’t like 4 and I would equally object to 9 or 16 or 25 or 36.”
So, I have designed a special pair of dice for Pam’s Christmas present this year, which, I am glad to say, meets her wishes entirely. They are six-sided dice of the ordinary shape, with a positive whole number on each face, and they are equally likely to throw any total from 2 to 37 inclusive.
What are the numbers on the faces of each die, please?
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