You can see three sides of each of two dice, and notice that the total number of pips showing is a perfect cube.
What are the numbers of pips on each face that you see?
The largest numbers shown on three sides of any die would be 4, 5 and 6 giving a maximum number of 15 or 30 for the 2 dice.
Perfect cubes less than or equal to 30 are 1, 8 and 27. Since it's impossible to have 3 faces of two dice adding up to less than 12, the perfect cube has to be 27.
If we're assuming these are normal dice, then no two faces will be the same, and opposite faces will add up to 7 (again we're assuming that we're in an ordinary universe and we no 2 of visible faces are opposites).
27 is only 3 less than the maximum, so we get to take away 3 pips somewhere. The only way this can work is if we set one die to show 6, 5 and 4 and the other to show 6, 4 and 2.
There are a number of solutions already posted for this question. Why isn't it marked as solved??
Solution
