Barring Rectangles from the Plane
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Abstract The problem of what proportion of squares of an infinite checkerboard must be barred so as to bar all a × b rectangles from the board is considered. If a ⩽ b is assumed, a complete answer is obtained except when the fractional part of b a is ϵ( 1 3 , 1 2 ) and b a > 2 .
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[2] James B. Shearer. Barring Hexominoes from the Infinite Checkerboard , 1982 .