2025 AMC 8 Problem 11

Attempt Problem 11 of the 2025 AMC 8 below, then check your answer against the video solution and professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2025 AMC 8 solutions, or check the answer key.

All problems are used with official legal permission of the Mathematical Association of America (MAA).

11.

A tetromino consists of four squares connected along their edges. There are five possible tetromino shapes, I\mathrm{I}, O\mathrm{O}, L\mathrm{L}, T\mathrm{T}, and S\mathrm{S}, shown below, which can be rotated or flipped over. Three tetrominoes are used to completely cover a 3×43 \times 4 rectangle. At least one of the tiles is an S\mathrm{S} tile. What are the other two tiles?
I\mathrm{I} and L\mathrm{L}
I\mathrm{I} and T\mathrm{T}
L\mathrm{L} and L\mathrm{L}
L\mathrm{L} and S\mathrm{S}
O\mathrm{O} and T\mathrm{T}
Answer: C
Concepts:tilingcasework
Small hint:
Try placing the S\mathrm{S} tile so the leftover region separates cleanly
Big hint:
After one S\mathrm{S} tile is placed, check which pair can tile the rest
Video solution:
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Written solution:
A little trial-and-error suggests placing the S\mathrm{S} tetromino in a way that does not block too much, like this:
It is then easy to see that the remainder can be partitioned into two L\mathrm{L} tetrominoes, and so the answer is C.
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