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Assume that we wish to cover an a×b rectangle with square tiles exactly, where a is the larger of the two numbers. We first attempt to tile the rectangle using b×b square tiles; however, this leaves an r 0 ×b residual rectangle untiled, where r 0 < b. We then attempt to tile the residual rectangle with r 0 ×r 0 square tiles.
There is no known formula for the exact number of solutions for placing n queens on an n × n board i.e. the number of independent sets of size n in an n × n queen's graph. The 27×27 board is the highest-order board that has been completely enumerated. [ 5 ]
More generally, an a-by-b rectangle can be covered with square tiles of side length c only if c is a common divisor of a and b. For example, a 24-by-60 rectangular area can be divided into a grid of: 1-by-1 squares, 2-by-2 squares, 3-by-3 squares, 4-by-4 squares, 6-by-6 squares or 12-by-12 squares.
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B&Q Limited (short for Block & Quayle after the company's two founders) is a British multinational DIY, home improvement and garden centre retailing company, with headquarters in Eastleigh, England. It is a wholly owned subsidiary of Kingfisher plc .
The study of polyomino tilings largely concerns two classes of problems: to tile a rectangle with congruent tiles, and to pack one of each n-omino into a rectangle. A classic puzzle of the second kind is to arrange all twelve pentominoes into rectangles sized 3×20, 4×15, 5×12 or 6×10.
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