Problem 11 · 2025 AMC 8
Medium
Geometry & Measurement
spatial-reasoningarea-decomposition
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Answer: C — L and L.
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Hint 1 of 2
You're told one tile is an S, the trickiest, kinkiest shape. Lock it down first — commit to placing it, then see what hole is left for the other two.
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Hint 2 of 2
Slide the S along an edge so it leaves a tidy hole. The remaining 8 squares fall into an L-shape — what two tetrominoes fill that?
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Approach: place the most constrained piece first, then read off the leftover
- The 3 × 4 rectangle is 12 squares = three tetrominoes. Start with the given S piece, because it's the most awkward — pinning the hardest constraint first leaves you the least to juggle.
- Tuck the S against an edge so it doesn't fracture the rest. The 8 squares left over form one connected L-shaped region.
- That region splits neatly down the middle into two L tetrominoes — so the other two tiles are L and L.
- Why this transfers: in any tiling or fitting puzzle, place the piece with the fewest legal positions first. It collapses the casework, instead of building up a mess of options you later have to undo.
Another way — eliminate by what can't reach a corner:
- Once the S sits in place, look at the leftover region's corners: each is a square that only an L (or I) can reach into without poking outside.
- An O or T can't fill those notched corners, and a single I plus the S won't close the gap — so the pair must be two L's, choice L and L.
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