B-24 Liberator Job Sheet Manual - Airplane, Engine Mechanic

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Extra info for B-24 Liberator Job Sheet Manual - Airplane, Engine Mechanic Course [Pt 4]

Sample text

Give them a try. 1 Tile an 8 x 8 checkerboard with twenty-one straight trominoes and one monamino. 2 Can you tile an 8x 8 checkerboard with twenty-one L-trominoes and one monomioo? POlYOMINOES ProblEm 33 Can you tile a 5 x 5 square with eight £-trominoes and one monomino. no matter where the the monomino is placed? 4 Can you tile a 7 x 7 square with sixteen £-trominoes and one monomino, no matter where the the monomino is placed? ProblEm3S Can you tile a 9 x 9 square with twenty-seven L-trominoes?

Let x be the number of T-tetrominoes that cover three black squares and one white square. Let y be the number of T -tetrominoes that cover one black square and three white squares. This time we have 3x+y+ 2 = x+3y+2 and x + y = 15, which is impossible since x and yare integers. 3 by the Z-tetromino or by the straight tetromino also leads to an impossibility by the same reasoning. Under the alternate coloring of the columns with two colors. the L-tetromino covers three of one color and one of the other while the sq uare telromino covers two of each color.

19 I-- POlYOMINOES some of the L-trominoes in the tiling appears almost haphazard, rather Ihan being detennined by the strict rule of replicating the reptile on an increasingly larger scale. Rotating copies of the tiled quadrant about the origin produces a tiling of the plane. 8 Show thai a polyomino that tiles a rectangle is a reptile. iles. 20 indicates a simple, fa ult~free til ing of the plane with 2 x 3 rectangles. 21 onto the rectangle, you may produce an infinite number of simple, fault-free tilings of thc plane with L-trominocs.

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