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Consider a random walk on the 2-d integer lattice starting at (0,0). From a lattice point (i,j) the walk moves to one of the four points (i-1, j), (i+1, j), (i, j-1) or (i, j+1) with equal probability. The walk continues until four different points (including (0,0)) have been visited. These four points will form one of the five free tetrominoes ("free" means considering rotations and mirror images to be the same). For each tetromino find the probability that it will be the one formed in this way.
Source: IBM Ponder This, December 2008
Polyominoes enumerates and classifies polyominoes by their bilateral and rotational symmetries, and the size of the smallest rectangle that encloses them.
Tetris enumerates the ways to tile an n-by-n square by one-sided n-polyominoes
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