UKMT - Junior Kangaroo - 2023 - 24 | Exact Science

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 × 2 × 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

Answer

C. 68

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 × (6 + 5 + 4 + 2) = 68.

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