12 and 15
Dice are made so that the number of pips on opposite sides add up to seven; that is, the pairs of opposite faces on any die are 1 and 6, 2 and 5, and 3 and 4.
If you can see three sides of the die, then you see only one of each of these faces. There are 2³=8 possible ways to pick one of three pairs of numbers; namely:
1 2 3 = 6
1 2 4 = 7
1 5 3 = 8
1 5 4 = 10
6 2 3 = 11
6 2 4 = 12
6 5 3 = 14
6 5 4 = 15
The sum of three sides on each of two dice can't be less than 12 or greater than 30; obviously, the cube in question must be 27.
From these numbers, there is only way to make a sum of 27, from 12 and 15. More specifically, you can see the 2, 4, and 6 on one die, and the 4, 5, and 6 on the other. |
