AMC 8 2025 Problem 11
AMC8 2025 年第 11 题
四边形与多边形★★★☆☆
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?
一个四格拼板由四个正方形沿边相连组成。下图展示了五种可能的四格拼板形状：I、O、L、T和S，这些形状可以旋转或翻转。用三个四格拼板可以完全覆盖一个3×4的矩形，其中至少有一个是S形拼板。请问另外两个拼板的形状是什么？
- A. and
- B. and
- C. and
- D. and
- E. and
正确答案 · Correct Answer
C
解析 · Solution
Solution 1
The 3×4 rectangle allows for 7 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 and \ L.
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