1. Claudette has eight dice, each with one of the letters $\mathrm{P}, \mathrm{Q}, \mathrm{R}$ and $\mathrm{S}$ written on all six faces. She builds the block shown in the diagram so that dice with faces which touch have different letters written on them.
What letter is written on the faces of the one dice which is not shown on the picture?
A P
B Q
C R
D S
E It is impossible to say
Solution
B

The dice above the hidden one has $\mathrm{R}$ marked on it, while the dice on the bottom level that touch the hidden dice have $\mathrm{P}$ and $\mathrm{S}$ marked on them. Hence the missing dice can have none of these letters on it. Therefore the missing dice has $\mathrm{Q}$ marked on its faces.