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Dominos on field

Source: Moscow Olympiad 2018, Grade 11, P8

April 7, 2018
combinatorics

Problem Statement

2018×20182018\times 2018 field is covered with 1×21 \times 2 dominos, such that every 2×22 \times 2 or 1×4,4×11 \times 4,4 \times 1 figure is not covered by only two dominos. Can be covered more than 99%99\% of field ?
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