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Covering a 15x36 checkerboard

Source: Finnish Mathematics Competition 1998, Final Round, Problem 5

November 14, 2011
combinatorics unsolvedcombinatoricsTiling

Problem Statement

15\times 36-checkerboard is covered with square tiles. There are two kinds of tiles, with side 77 or 5.5. Tiles are supposed to cover whole squares of the board and be non-overlapping. What is the maximum number of squares to be covered?