Question

Dicey math. You can see three faces of each of two dice. The total number of pips on these faces is 27. How many pips can you see on each die?

Answer 1

1. total of all faces on a die is 21
2. the minimum total of three faces is 1+2+3=6
3. the maximum total of three faces is 4+5+6=15

since the total pips is 27, the dice can only be in these arrangements:\[
\begin{align}
\text{dice 1:}\quad&6\quad&7\quad&8\quad&9\quad&10\quad&11\quad&12\quad&13\quad&14\quad&15\\
\text{dice 2:}\quad&-\quad&-\quad&-\quad&-\quad&-\quad&-\quad&15\quad&14\quad&13\quad&12\\
\text{total:}\quad&-\quad&-\quad&-\quad&-\quad&-\quad&-\quad&27\quad&27\quad&27\quad&27\\
\end{align}\]The only unique combinations here are: (12, 15) and (13, 14)

There must be some other property about dice that can be used to eliminate one of these pairs and just leave the solution.

Answer 2

I believe you cannot get three faces that total 13.
so solution must be 12 and 15.