Problem 16 · 2016 Math Kangaroo
Medium
Spatial & Visual Reasoning
tiling-tessellation
What is the maximum number of pieces of the shape shown (a piece made of four unit squares) that can be cut from a 5×5 square?
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Answer: D — 6
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Hint 1 of 3
Count the little cells in the board and the little cells in one piece.
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Hint 2 of 3
Pieces cannot overlap, so the cells they cover must fit inside the 25 cells of the board.
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Hint 3 of 3
After finding the largest number that could fit, draw that many to make sure they really do.
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Approach: first a counting limit, then show a real packing
- The \(5 \times 5\) board has 25 little cells, and each piece covers 4 cells.
- Since \(6 \times 4 = 24 \le 25\) but \(7 \times 4 = 28 > 25\), at most 6 pieces can fit.
- You can actually place 6 pieces (covering 24 cells, leaving 1 cell empty), so the maximum is 6, choice (D).
Mark:
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