Suppose you have a rectangle with which is tiled with finitely many smaller rectangles, not necessarily congruent to each other, such that each smaller rectangle has at least one side of integer length. Then show that the original rectangle also has at least one side of integer length.

Hint: Look at the hashtags.

Okay, hint: Integrate a cleverly chosen function in two variables.

The social network of the future: No ads, no corporate surveillance, ethical design, and decentralization! Own your data with Mastodon!