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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?
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