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2004 AMC 10A Problems/Problem 16

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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?

Image:2004 AMC 10A problem 16.png

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

Solution

There are:

  • 1 of the 1\times 1 squares containing the black square,
  • 4 of the 2\times 2 squares containing the black square,
  • 9 of the 3\times 3 squares containing the black square,
  • 4 of the 4\times 4 squares containing the black square,
  • 1 of the 5\times 5 squares containing the black square.

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

See also

2004 AMC 10A (ProblemsResources)
Preceded by
Problem 15
Followed by
Problem 17
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
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