Difference between revisions of "2004 AMC 10A Problems/Problem 16"
(New page: The answer is 19 or (D) since the number of ways of arranging squares 1x1 through 3x3 are squares( as in power of degree) of their sides. As for the 4x4 and 5x5, it's easy to find the few ...) |
(guys, DON'T WRITE SOLUTIONS IN THAT FORM!!!) |
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| − | The | + | ==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? | ||
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| + | [[Image:2004 AMC 10A problem 16.png]] | ||
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| + | <math> \mathrm{(A) \ } 12 \qquad \mathrm{(B) \ } 15 \qquad \mathrm{(C) \ } 17 \qquad \mathrm{(D) \ } 19\qquad \mathrm{(E) \ } 20 </math> | ||
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| + | ==Solution== | ||
| + | There is one 1-1 square containing the black square | ||
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| + | There are 4 2-2 squares containing the black square | ||
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| + | There are 9 3-3 squares containing the black square | ||
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| + | There are 4 4-4's. | ||
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| + | There is 1 5-5. | ||
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| + | <math>1+4+9+4+1=19\Rightarrow \boxed{\mathrm{(D) \ }}</math> | ||
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| + | ==See also== | ||
Revision as of 10:07, 15 April 2008
Problem
The 
grid shown contains a collection of squares with sizes from 
to . How many of these squares contain the black center square?
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.
