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 8 Dice II (Posted on 2013-12-03)
Eight standard dice are arranged to form one larger die with twice the linear size.

Just as in ordinary dice, the opposite faces of the larger die add up to some constant value, though of course larger than the standard 7.

Three of the faces of the large die each have a perfect square number of pips and three have a prime number of pips each. No two faces of the large die have the same number of pips.

There are several ways of accomplishing the above, but only one uses no 4's from the original smaller dice. What is the arrangement of the smaller dice that keeps all their 4-pip faces hidden while forming a larger die that meets the criteria of the first three paragraphs?

From Enigma No. 1768, "Die hard", by Susan Denham, New Scientist, 28 September 2013, page 32.

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