2004 AMC 10A Problems/Problem 16
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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.
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 | |
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All AMC 10 Problems and Solutions |
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