Difference between revisions of "2012 AMC 10A Problems/Problem 14"
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| + | == Problem == | ||
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Chubby makes nonstandard checkerboards that have <math>31</math> 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? | Chubby makes nonstandard checkerboards that have <math>31</math> 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? | ||
| − | <math> \textbf{(A)}\ 480 | + | <math> \textbf{(A)}\ 480 \qquad\textbf{(B)}\ 481 \qquad\textbf{(C)}\ 482 \qquad\textbf{(D)}\ 483 \qquad\textbf{(E)}\ 484</math> |
| − | \qquad\textbf{(B)}\ 481 | + | |
| − | \qquad\textbf{(C)}\ 482 | + | == Solution == |
| − | \qquad\textbf{(D)}\ 483 | + | |
| − | \qquad\textbf{(E)}\ 484 | + | 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> |
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| − | + | == See Also == | |
| − | + | {{AMC10 box|year=2012|ab=A|num-b=13|num-a=15}} | |
Revision as of 23:37, 8 February 2012
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
There are 15 rows with 15 black tiles, and 16 rows with 16 black tiles, so the answer is 
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 | ||
