2025 AMC 8 Problems/Problem 11

Problem 11

A $\textit{tetromino}$ consists of four squares connected along their edges. There are five possible tetromino shapes, $I$ , $O$ , $L$ , $T$ , and $S$ , shown below, which can be rotated or flipped over. Three tetrominoes are used to completely cover a $3\times4$ rectangle. At least one of the tiles is an $S$ tile. What are the other two tiles?

$\textbf{(A)}I$ and $L\qquad \textbf{(B)} I$ and $T\qquad \textbf{(C)} L$ and $L\qquad \textbf{(D)}L$ and $S\qquad \textbf{(E)}O$ and $T$

Solution 1

The $3\times4$ rectangle allows for 4 possible places to put the S piece, with each possible placement having an inverted version.


path x = (0,0)--(0,2)--(1,2)--(1,3)--(2,3)--(2,1)--(1,1)--(1,0)--cycle;
add(grid(4,3));
fill(x; gray(1));
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2025 AMC 8 Problems/Problem 11

Problem 11

Solution 1