Tile Puzzle 1

A large rectangle is divided into finitely many smaller rectangles. Each of the small rectangles has the property that at least one of its sides (height or width, or both) is an integer.

Show that: The large rectangle also has at least one side (height or width, or both) that is an integer.

Comment

There is a proof in Proofs from THE BOOK . A great explanation can also be found in this Ebima Lab’ YouTube video (in Japanese but English subtitles are available). I think that this Cirno in this video is too smart…