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×pi×r-1 meters. Let the depth of the groove be x meters. 2×pi×(r-x) must be equal to 2×pi×r-1. Solving the equation 2×pi×(r-x)=2×pi×r-1 gives x = 1/(2×pi) meters (about 0.159 meters).