Problem 13 · 2014 Math Kangaroo
Medium
Spatial & Visual Reasoning
tiling-tessellationspatial-reasoning
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Answer: B
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Hint 1 of 2
Each piece is a square with some sides pushed in (a dent) or pushed out (a bulge).
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Hint 2 of 2
When two pieces sit side by side, a bulge on one must drop into a matching dent on its neighbour; find the piece whose curves have no partner.
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Approach: match each piece's curved edges so bulges fill dents
- To build a square with straight outer sides, every outward bulge on one piece must fit a matching inward dent on a neighbour, so the curved edges have to pair up.
- Four of the pieces have curves that pair off neatly and tile a 2-by-2 square.
- Piece B's curves cannot be matched by the others, so it is the piece left over.
- The unused piece is B.
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