Glue 27 standard dice to form a big 3×3×3 cube, sort of like a Rubik’s cube. Both faces in each pair of faces that are glued together have the same number of pips. How many pips are showing on the outside of the big cube?
Each die consists of 3 pairs of opposite faces each of which sum to 7.
Therefore each column (or column equivalent even if horizontal) looks something like:
cube 1 cube 2 cube 3
1 6 6 1 1 6 or, say
5 2 2 5 5 2
So the surface pip sets, at the extreme left and right of the above, come in pairs that each add up to 7. There are 6 * 9 pip sets (die faces) on the surface; that's 54, so there are 28 pairs. And 28 * 7 = 196.
There would be 196 pips on the surface of the large cube.
|
|
Posted by Charlie
on 2025-01-15 10:19:34 |
solution
