2004 AMC 10A Problems/Problem 16
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 
and 
squares that do not contain the black square. Counting, there are 
, and 
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 contains 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 | ||
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