Solution to: Men on the Moon

The moon's diameter is not needed to solve this problem! Let the moon's radius be r meters. Then the length of the cable is 2 × π × r - 1 meters. Let the depth of the groove be x meters. 2 × π × (r - x) must be equal to 2 × π × r - 1. Solving the equation 2 × π × (r - x) = 2 × π × r - 1 gives x = 1/(2 × π) meters (about 0.159 meters).

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