Maths Olympiad Prep

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, 2001

Combinatorics Difficulty 3.0 AMC 10/12 Find the answer Canada

Sixty-four white 1×1×11\times 1\times 1 cubes are used to form a 4×4×44\times 4\times 4 cube, which is then painted red on each of its six faces. This large cube is then broken up into its 64 unit cubes. Each unit cube is given a score as follows: Exact number of faces painted red: 3, Score: 3; Exact number of faces painted red: 2, Score: 2; Exact number of faces painted red: 1, Score: 1; Exact number of faces painted red: 0, Score: 7-7. The total score for the 4×4×44\times 4\times 4 cube is

(A) 4040 (B) 4141 (C) 4242 (D) 4343 (E) 4444

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