Difference between revisions of "2004 AMC 10A Problems/Problem 16"
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Revision as of 10:27, 4 July 2013
Contents
Problem
The 
grid shown contains a collection of squares with sizes from 
to . How many of these squares contain the black center square?
Solution 1
There are:
of the 
squares containing the black square,
of the 
squares containing the black square,
of the 
squares containing the black square,- of the
squares containing the black square, - of the
squares containing the black square.
of the 
of the 
squares containing the black square,
of the 
squares containing the black square,
squares containing the black square,Thus, the answer is 
.
Solution 2
We use complementary counting.
There are only 2x2 and 1x1 squares that do not contain the black square.
Counting, there are 
2x2, and 
1x1 squares that do not contain the black square.
That gives 
squares that don't contain it.
There are a total of 
squares possible, therefore there are 
squares that do not contain the black square, which is 
. .
See also
| 2004 AMC 10A (Problems • Answer Key • Resources) | ||
| 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 | ||
| All AMC 10 Problems and Solutions | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
