Problem

Source: Czech-Polish-Slovak Junior Match 2014, Individual p3 CPSJ

Tags: tiles, Tiling, combinatorics



We have $10$ identical tiles as shown. The tiles can be rotated, but not flipper over. A $7 \times 7$ board should be covered with these tiles so that exactly one unit square is covered by two tiles and all other fields by one tile. Designate all unit sqaures that can be covered with two tiles.