Two sides of a cube are painted red, two sides are painted white, and the remaining two sides are painted blue. The cube is cut up into a number of smaller cubes of the same size using slices parallel to the orignal faces. The number of small cubes that have at least one red face and at least one white face is different than the number that have at least one red face and at least one blue face, but no white face, but these two numbers are two-digit numbers that are the reverse of each other (e.g. 13 and 31). How many of the small cubes have at least one white face, but no red or blue faces?

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Source: Susan Denham
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