AUSTRIAN-POLISH 2006 Problem 9
We have an 8x8 chessboard with 64 squares. Then we have 3x1 dominoes which cover exactly 3 squares. Such dominoes can only be moved parallel to the borders of the chessboard and also only if the passing squares are free. If no dominoes can be moved, then the position is called stable. a. Find the smalles number of covered squares neccessary for a stable position. b. Prove: There exist a stable position with only one square uncovered. c. Find all Squares which are uncoverd in at least one position of b).
Dataset text AI-MO AoPS. Quoted with source.
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