Combinatorics · Domination on a grid · Tiles and boards · Extremal arguments · Case analysis
A \(4 \times 4\) table is divided into \(16\) unit cells. On this table we place tiles of the shape drawn alongside: two unit squares that meet at a single corner. A tile may be rotated, and each tile covers exactly two cells of the table.
What is the smallest number of tiles that must be placed on the table so that every uncovered cell has at least one covered neighbour? (Two cells are neighbours when they share a side.)
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Slovenian High School Mathematics Competition for Vega Awards (MaSSA), drzavno (national) round 2011, 1. letnik, category A, problem 4. Organized by DMFA Slovenije (Society of Mathematicians, Physicists and Astronomers of Slovenia). Source