Enigma 1768: Die hard
25 September 2013
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From New Scientist #2936, 28th September 2013 [link]
I wanted a cube-shaped dice with each of three of its faces having a perfect square number of spots and each of the remaining faces having a prime number of spots. To follow convention I wanted each face to have a different number of spots and I also wanted opposite pairs of faces to add up to the same total.
To make this dice I took eight identical standard dice and stuck them together to form a cube of double the size. On closer investigation I found that none of the faces of four spots from the eight original dice was visible on the exterior of my new dice.
How many faces of one spot and how many faces of two spots from the original dice were visible on the exterior of my new dice?
Historically the singular of “dice” is “die”, but “dice” is now accepted as both a plural and a singular.