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MathNet 2011 Question 76

Math Olympiad Vault · MathNet 2011

Question 76

A $4 \times 4$ board is divided into 16 squares. Onto this board we place several tiles like the one in the picture
Question illustration
(the tiles can be rotated),
each tile covering two squares. At least how many tiles do we need to place onto the board, so that every uncovered square will be adjacent to at least one covered square? (Two squares are adjacent if they share a common side.)