2001 AMC 10 Problems/Problem 11
Problem
Consider the dark square in an array of unit squares, part of which is shown. The first ring of squares around this center square contains unit squares. The second ring contains unit squares. If we continue this process, the number of unit squares in the ring is
Solution
Solution 1
We can partition the ring into rectangles: two containing unit squares and two containing unit squares.
There are unit squares in the ring.
Thus, the ring has unit squares.
Solution 2
We can make the ring by removing a square of side length from a square of side length .
This ring contains unit squares.
Thus, the ring has unit squares.
See Also
2001 AMC 10 (Problems • Answer Key • Resources) | ||
Preceded by Problem 10 |
Followed by Problem 12 | |
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All AMC 10 Problems and Solutions |
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