When the spaceship Bagel returned from its mission to Titan (see puzzle 23), it went first to the U.S. moon base for repair. Two weeks later it was on its way to the moon.
Ronald Couth, who headed the Bagel’s computer science crew, was playing a game of go with VOZ, the ship’s computer, when his daughter Tanya, now twelve, entered the computer shack. “I just noticed something unusual,” the computers shack. “I looked at the earth through a front window. Then I went to the back of the ship and looked at the moon. They look exactly the same size!”
Colonel Couth smiled, “of course you know there’s just one spot along the way where that happens, and locating the spot on a chart is a good exercise in geometry. To simplify the problem, let’s round off all the relevant dimension. Assume the distance from the moon’s center to the earth’s center is 240,000 miles; the earth’s diameter is 8,000 miles; and the moon’s diameter is 2,000 miles. Do you think you can figure out how far we are now from the moon’s center?”
Tanya, who loved geometry problems, had no trouble with this one.