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covering board with L-shaped pieces and at most one unit

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April 23, 2009
modular arithmeticgeometryrectanglerotation

Problem Statement

For which of the following n n, n×n n\times n chessboard cannot be covered using at most one unit square piece and many L-shaped pieces (an L-shaped piece is a 2x2 piece with one square removed)?
<spanclass=′latex−bold′>(A)</span> 96<spanclass=′latex−bold′>(B)</span> 97<spanclass=′latex−bold′>(C)</span> 98<spanclass=′latex−bold′>(D)</span> 99<spanclass=′latex−bold′>(E)</span> 100<span class='latex-bold'>(A)</span>\ 96 \qquad<span class='latex-bold'>(B)</span>\ 97 \qquad<span class='latex-bold'>(C)</span>\ 98 \qquad<span class='latex-bold'>(D)</span>\ 99 \qquad<span class='latex-bold'>(E)</span>\ 100
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