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.
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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