Difference between revisions of "2012 AMC 10A Problems/Problem 14"
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== Solution 1== | == Solution 1== | ||
| − | There are 15 rows with 15 | + | There are 15 rows with 15 black tiles, and 16 rows with 16 black tiles, so the answer is <math>15^2+16^2 =225+256= \boxed{\textbf{(B)}\ 481}</math> |
Note: On getting <math>16^2</math>+<math>15^2</math> you only need to calculate the units digit | Note: On getting <math>16^2</math>+<math>15^2</math> you only need to calculate the units digit | ||
Revision as of 21:52, 21 November 2020
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: On getting 
+
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 | |
| 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 | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
