Math Gold Medalist

Lor

2024 AMC 8 

Problem 7

A $3$x$7$ rectangle is covered without overlap by 3 shapes of tiles: $2$x$2$, $1$x$4$, and $1$x$1$, shown below. What is the minimum possible number of $1$x$1$ tiles used?

2024-AMC8-q7.png

$\textbf{(A) } 1\qquad\textbf{(B)} 2\qquad\textbf{(C) } 3\qquad\textbf{(D) } 4\qquad\textbf{(E) } 5$

Considering Range

First prove that answer>=5 by finding a good example.

Prove that answer = 1 or 5

Reject 1 by considering rows

So the answer will be 5

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   Solution