2012 AMC 10A Problems/Problem 14
Contents
Problem
Chubby makes nonstandard checkerboards that have squares on each side. The checkerboards have a black square in every corner and alternate red and black squares along every row and column. How many black squares are there on such a checkerboard?
Solution 1
There are 15 rows with 15 black tiles, and 16 rows with 16 black tiles, so the answer is
Note: When solving +
, you only need to calculate the units digit.
Solution 2
We build the checkerboard starting with a board of
that is exactly half black. There are
black tiles in this region.
Add to this checkerboard a
strip on the bottom that has
black tiles.
Add to this checkerboard a
strip on the right that has
black tiles.
In total, there are tiles, giving an answer of
See Also
2012 AMC 10A (Problems • Answer Key • Resources) | ||
Preceded by Problem 13 |
Followed by Problem 15 | |
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All AMC 10 Problems and Solutions |
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