Andrei Sakharov (1921-1989) was a Soviet physicist. He is well known (among other things) for his work on the origin of baryon asymmetry in the Universe, his contributions to the Soviet hydrogen bomb program, and his political activism.
Here is one of his math problems.
A pizza his cut by straight lines into small pieces. The number of lines is very large and the cuts are drawn completely randomly. Most of the pizza pieces are then polygons with straight edges, with varying number of vertices.
Question 1: What is the average number of vertices of a pizza piece?
Question 2: Let S be the average area and p be the average perimeter of a pizza piece. What is the value of S/p2?
(In the original version, the pizza is replaced by a slice of cabbage. It is said that Sakharov made up this problem while he was cutting cabbage to help his wife with pirogi making.)
Source: Сахаровский сборник, изд. Хроника, Нью-Йорк, 1981, с. 140.