Difference between revisions of "2004 AMC 10A Problems/Problem 16"

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

Revision as of 11:08, 15 April 2008

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?

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 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.

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

See also

2004 AMC 10A (ProblemsAnswer KeyResources)
Preceded by
Problem 15
Followed by
Problem 17
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All AMC 10 Problems and Solutions