Thinking Cap

Problem of the Month

Winners of the academic year 2022/23 are Matthew Hudson and Jacob Norris.

March 2024

Integer grids

Suppose that we place real numbers from [0,1] on points in the Euclidean plane with integer coordinates in such a way that the number we put at any given point is the average of its four immediate neighbors (above, below, to the left, and to the right). What are all possible ways we can do this?