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Prime Square Dice (Posted on 2011-09-10) Difficulty: 3 of 5
I have in front of me five standard dice, touching in a row, left to right.

Treating each face as a base-10 digit with the value of its number of pips, the five dice, on their faces that are toward me, form a 5-digit prime. The tops of the dice, also taken in order, form a 5-digit perfect square.

If I were looking at these five dice from the opposite direction, I'd see a different prime number formed by the digits on the vertical faces in order, and I'd see a different perfect square formed by the tops, again taken in order, as seen. In fact, that perfect square would be larger than the one I'm seeing from the side I'm actually on.

And one more thing: the five digits of each prime are different, but of course any given digit might or might not be on both primes.

1. Identify the primes and squares involved.

2. If duplicate digits (any multiples of the same digit within a number) were allowed, what could the front and back primes be, and the resulting squares on top, other than the ones found in part 1, using the same other rules as part 1?

See The Solution Submitted by Charlie    
Rating: 4.0000 (1 votes)

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  Subject Author Date
SolutionsolutionDej Mar2011-09-10 13:48:40
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