Problem 11 · 2007 AMC 8
Medium
Logic & Word Problems
matching-puzzle
Tiles I, II, III and IV are translated so one tile coincides with each of the rectangles A, B, C and D. In the final arrangement, the two numbers on any side common to two adjacent tiles must be the same. Which of the tiles is translated to Rectangle C?
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Answer: D — Tile IV.
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Hint 1 of 2
A number that appears on only one tile-edge has no partner to match against — so that edge can't be an interior seam. It must face outward, which pins the tile to the boundary.
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Hint 2 of 2
Solve constraint puzzles from the unique pieces in: anchor the forced tile first, then propagate by matching the shared-edge numbers to its neighbors, one link at a time.
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Approach: anchor on outside-only numbers, then propagate matches
- Some edge numbers appear on only one tile (no other tile carries that number), so those edges must lie on the outer boundary of the 2 × 2 arrangement. Pinning those tiles into their forced corners removes most of the freedom.
- From the anchored tile, walk to its neighbors by matching the shared edge number. The chain forces tile IV into rectangle C.
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