MathDB

same no of tiles of 2x2 and 5x1 tile completely a floor nxn , 10<n<20

Source: Caucasus 2015 11.3

April 26, 2019

combinatoricscombinatorial geometrytilesTiling

Problem Statement

The workers laid a floor of size

n\times n

(

10 <n <20

) with two types of tiles:

2 \times 2

and

5\times 1

. It turned out that they were able to completely lay the floor so that the same number of tiles of each type was used. For which

n

could this happen? (You can’t cut tiles and also put them on top of each other.)