MathDB

8

Part of 1990 Austrian-Polish Competition

Problems(1)

tiling a 28 x48 rectangle with axb tiles

Source: Austrian - Polish 1990 APMC

5/7/2020
We are given a supply of a×ba \times b tiles with aa and bb distinct positive integers. The tiles are to be used to tile a 28×4828 \times 48 rectangle. Find a,ba, 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,ba, b such that the tile has the largest possible area and there is more than one possible tiling.
rectangletilesTilingcombinatoricscombinatorial geometry