Difference between revisions of "2024 AMC 8 Problems/Problem 7"
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A <math>3x7</math> rectangle is covered without overlap by 3 shapes of tiles: <math>2x2</math>, <math>1x4</math>, and <math>1x1</math>, shown below. What is the minimum possible number of <math>1x1 tiles used? | A <math>3x7</math> rectangle is covered without overlap by 3 shapes of tiles: <math>2x2</math>, <math>1x4</math>, and <math>1x1</math>, shown below. What is the minimum possible number of <math>1x1 tiles used? | ||
| − | </math>\textbf{(A) } 1\qquad\textbf{(B) } 2\qquad\textbf{(C) } 3\qquad\textbf{(D) } 4\qquad\textbf{(E) } 5 | + | </math>\textbf{(A) } 1\qquad\textbf{(B) } 2\qquad\textbf{(C) } 3\qquad\textbf{(D) } 4\qquad\textbf{(E) } 5 |
==Solution 1== | ==Solution 1== | ||
| − | We can eliminate B, C, and D, because they are not < | + | We can eliminate B, C, and D, because they are not <math>21-</math> any multiple of <math>4</math>. Finally, we see that there is no way to have A, so the solution is <math>(E) \boxed{5}</math>. |
==Solution 1== | ==Solution 1== | ||
Revision as of 17:08, 25 January 2024
Problem
A 
rectangle is covered without overlap by 3 shapes of tiles: 
, 
, and 
, shown below. What is the minimum possible number of 
\textbf{(A) } 1\qquad\textbf{(B) } 2\qquad\textbf{(C) } 3\qquad\textbf{(D) } 4\qquad\textbf{(E) } 5
Solution 1
We can eliminate B, C, and D, because they are not 
any multiple of 
. Finally, we see that there is no way to have A, so the solution is 
.
