Problem

Source: 2023 Paraguayan Mathematical Olympiad L3 p5 - OMAPA

Tags: combinatorics



In a $2\times 2$ Domino game, each tile is square and divided into four spaces, as shown in the figure. In each box there is a number of points that varies from $0$ points (empty) to $6$ points. Two $2\times 2$ Domino tiles are equal if it is possible to rotate one of the two tiles until the other is obtained. In a $2\times 2$ Domino pack, what is the maximum number of different tiles that can be such that on each tile at least two squares have the same number of points?