24. Emily makes four identical numbered cubes using the net shown. She then glues them together so that only faces with the same number on are glued together to form the $2 \times 2 \times 1$ block shown.
What is the largest possible total of all the numbers on the faces of the block that Emily could achieve?

A 72
B 70
C 68
D 66
E 64
SolUTION
Each cube in the block has two adjacent faces that do not form part of the faces of the block. Since the numbers 1 and 2 are on opposite faces, it is not possible for both of these numbers to be hidden. However, the numbers 1 and 3 are on adjacent faces. Therefore, to obtain the largest possible total on the faces of the block, each cube will have numbers 1 and 3 hidden. Hence the largest possible total of the numbers on the faces on the block is $4 \times(6+5+4+2)=68$.