Combinatorics · Covering · Tilings · Tetromino · Extremal argument
We want to cover a \(4 \times 4\) board with tiles of the shape shown below, rotations and reflections being allowed. The tiles are permitted to overlap one another and to stick out beyond the edge of the board. Every cell of the board must end up covered by at least one tile.
What is the smallest number of tiles that is enough?
Sign in to check answers, open hints, read the full solution, and track your progress. Statements are always free.
Slovenian High School Mathematics Competition for Vega Awards (MaSSA), drzavno (national) round 2013, 1. letnik, category A, problem 4. Organized by DMFA Slovenije (Society of Mathematicians, Physicists and Astronomers of Slovenia). Source