3-inch cube

Question:

A 3-inch cube is painted on all sides with red paint. The cube is then cut into small cubes of dimension 1 inch. All the cubes so cut are collected and thrown on a flat surface. What is the probability that all the top-facing surfaces have red paint on them?

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A

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A

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N

I

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R

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W

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Solution: The key to solving this problem is to visualize a cube cut into three sections. The core of the 3-inch cube when cut is a cube with all internal faces and as such has none of its faces painted red. Hence, one cube with no painted face always occurs, making the probability of having all red faces zero.

Solution: The probability is zero.

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