The Dice Sum


by Henry E. Dudeney

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Suppose you have a set of four dice, not marked with spots in the ordinary way, but with the digits as shown in the illustration. Each die has the digits 1 to 6 on its respective faces.

When put together the four dice form plenty of different four-figure numbers. One of them - 1246 - is shown in the illustration.

The question is if one makes all the different four-figure numbers that are possible with these dice (never putting the same figure more than once in any number), what will they all add up to? It is allowed to turn the 6 upside down, so as to represent a 9.

Seems, it should take a lot of work to go and write out the full list of numbers and then add them up. Instead, there should be at least some other way to get at the answer. Can you find it?

Last Updated: January 21, 2008  |  Posted: July 8, 2007
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