2025 AMC 8
Complete problem set with solutions and individual problem pages
A consists of four squares connected along their edges. There
are five possible tetromino shapes, , , , , and , shown below, which can be rotated or flipped over. Three tetrominoes are used to completely cover a rectangle. At least one of the tiles is an tile. What are the other two tiles?
- A.
and
- B.
and
- C.
and
- D.
and
- E.
and
The rectangle allows for possible places to put the S piece, with each possible placement having an inverted version. One of the cases looks like this:
As you can see, there is a hole in the top left corner of the board, which would be impossible to fill using the tetrominos. There are three cases in which a hole isn't created; the S lies flat in the bottom left corner, it lies flat in the top right corner, or it stands upright in the center. All three tilings are shown below.
For each of the inverted cases, the L pieces can be inverted along with the S piece. Because the only cases that fill the rectangle after the S is placed are the ones that use two L pieces, the answer must be .
