Problem
2004 AMC 10A Problem 16
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?
![[asy] unitsize(6mm); defaultpen(linewidth(.8pt)); for(int i=0; i<=5; ++i) { draw((0,i)--(5,i)); draw((i,0)--(i,5)); } fill((2,2)--(2,3)--(3,3)--(3,2)--cycle); [/asy]](/static/aops/2454b625e7480a14ad4a2ed8b0e49aa43f01ae24.png)
\mathrm{(A) \ } 12 \qquad \mathrm{(B) \ } 15 \qquad \mathrm{(C) \ } 17 \qquad \mathrm{(D) \ } 19\qquad \mathrm{(E) \ } 20
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