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MAX Club’s Problem of the month Mathematics and Computer Science Club |
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Resources
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September 09: The following ``chessboard” 9 by 9 (below) is covered with L-shaped tiles. · What are all the rectangular type boards, m by n, which can be L-tiled? · What about other regions of the plane? (For instance, a board of size 2^n by 2^n with a square removed can be L-tiled too.)
October 09: (Penny problem) We consider the operation P on collections of groups of pennies. P applied to a collection C of groups of pennies is a new collection obtained by taking a penny from each group of C and form a new group that is added to C. For instance, If the collection is C=[{2},{3}] then P(C)=[{1},{2},{2}]. For n a positive integer, determine the collections C which are invariant in n steps, i.e. P^n(C)=C. Example: If we continue with the above example, P^2(C)=[{1},{1},{3}], P^3(C)=[{2},{3}]=C. So, C is invariant in 3 steps. November 09: (AMM, October 2009, Problem 11455) Determine the triangle T of maximal area in the Cartesian plane with the property that for all nonzero integer pairs (m,n) the interior of T and T+(m,n) are disjoint. See figure below:
Last Updated: 10th November 2009 visits
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