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1x2 tiles in 1995x1005 board minus BBW

Source: I Soros Olympiad 1994-95 Ukraine R2 10.3 https://artofproblemsolving.com/community/c2416727_soros_olympiad_in_mathematics

June 6, 2024
combinatoricstiles

Problem Statement

Given a square board with dimensions 1995×19951 995 \times 1 995. These cells are painted with black and white paints in checkerboard order like this. that the corner cells are black. Two black and one white cells were randomly cut out of the board. Prove that the rest of the board can be divided into rectangles of size 1×21 \times 2 .