MathDB

We are given a supply of

a \times b

tiles with

a

and

b

distinct positive integers. The tiles are to be used to tile a

28 \times 48

rectangle. Find

a, b

such that the tile has the smallest possible area and there is only one possible tiling. (If there are two distinct tilings, one of which is a reflection of the other, then we treat that as more than one possible tiling. Similarly for other symmetries.) Find

a, b

such that the tile has the largest possible area and there is more than one possible tiling.

Problem Statement