MathDB

same no of tiles of 2x2 and 3x1 tile completely a floor nxn

Source: Caucasus 2015 8.3

April 26, 2019

Tilingtilescombinatoricscombinatorial geometry

Problem Statement

The workers laid a floor of size

n \times n

with tiles of two types:

2 \times 2

and

3 \times 1

. It turned out that they were able to completely lay the floor in such a way that the same number of tiles of each type was used. Under what conditions could this happen? (You can’t cut tiles and also put them on top of each other.)

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