2025 AMC 8 Problems/Problem 11
Contents
[hide]Problem
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?
and
and
and
and
and
Solution 1
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
.
~bubby617
Video Solution (A Clever Explanation You’ll Get Instantly)
https://youtu.be/VP7g-s8akMY?si=mhn50YKL4_Yo1PH6&t=965 ~hsnacademy
Video Solution 1 by Thinking Feet
See Also
2025 AMC 8 (Problems • Answer Key • Resources) | ||
Preceded by Problem 10 |
Followed by Problem 12 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
All AJHSME/AMC 8 Problems and Solutions |
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