2004 AMC 10A Problems/Problem 16

Problem

The $5\times 5$ grid shown contains a collection of squares with sizes from $1\times 1$ to $5\times 5$ . How many of these squares contain the black center square?

$\mathrm{(A) \ } 12 \qquad \mathrm{(B) \ } 15 \qquad \mathrm{(C) \ } 17 \qquad \mathrm{(D) \ } 19\qquad \mathrm{(E) \ } 20$

Solution

There is one 1-1 square containing the black square

There are 4 2-2 squares containing the black square

There are 9 3-3 squares containing the black square

There are 4 4-4's.

There is 1 5-5.

$1+4+9+4+1=19\Rightarrow \boxed{\mathrm{(D) \ }}$

Page

Toolbox

Search

2004 AMC 10A Problems/Problem 16

Problem

Solution

See also