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jmc

counting and probability junior

Problem

The large cube shown is made up of identical sized smaller cubes. For each face of the large cube, the opposite face is shaded the same way. The total number of smaller cubes that must have at least one face shaded is
problem
(A)
(B)
(C)
(D)
Solution
Clearly, no unit cube has more than one face painted, so the number of unit cubes with at least one face painted is equal to the number of painted unit squares. There are painted unit squares on the half of the cube shown, so there are unit cubes with at least one face painted, thus our answer is .
Final answer
C