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==Problem==
The <math>5\times 5</math> grid shown contains a collection of squares with sizes from <math>1\times 1</math> to <math>5\times 5</math>. How many of these squares contain the black center square?

[[Image:2004 AMC 10A problem 16.png]]

<math> \mathrm{(A) \ } 12 \qquad \mathrm{(B) \ } 15 \qquad \mathrm{(C) \ } 17 \qquad \mathrm{(D) \ }  19\qquad \mathrm{(E) \ } 20  </math>

==Solution==
There are:
*<math>1</math> of the <math>1\times 1</math> squares containing the black square,
*<math>4</math> of the <math>2\times 2</math> squares containing the black square,
*<math>9</math> of the <math>3\times 3</math> squares containing the black square,
*<math>4</math> of the <math>4\times 4</math> squares containing the black square,
*<math>1</math> of the <math>5\times 5</math> squares containing the black square.

Thus, the answer is <math>1+4+9+4+1=19\Rightarrow \boxed{\mathrm{(D)}}</math>.

==See also==
{{AMC10 box|year=2004|ab=A|num-b=15|num-a=17}}

[[Category:Introductory Combinatorics Problems]]