Difference between revisions of "2009 AMC 8 Problems/Problem 10"
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==Solution 2== | ==Solution 2== | ||
− | The squares that don't touch the border are in a 6 by 6 square. Therefore, the number of squares that don't touch the border is <math>6*6=36</math>. There are 64 choices total. Therefore, the answer is <math>36/64</math>, which simplifies to <math>\framebox{(D) 9/16}</math>. | + | The squares that don't touch the border are in a 6 by 6 square. Therefore, the number of squares that don't touch the border is <math>6*6=36</math>. There are 64 choices total. Therefore, the answer is <math>36/64</math>, which simplifies to <math>\framebox{(D) </math>9/16<math>}</math>. |
==See Also== | ==See Also== | ||
{{AMC8 box|year=2009|num-b=9|num-a=11}} | {{AMC8 box|year=2009|num-b=9|num-a=11}} | ||
{{MAA Notice}} | {{MAA Notice}} |
Revision as of 22:04, 3 September 2019
Contents
Problem
On a checkerboard composed of 64 unit squares, what is the probability that a randomly chosen unit square does not touch the outer edge of the board?
Solution
There are total squares. There are unit squares on the perimeter and therefore NOT on the perimeter. The probability of choosing one of those squares is .
Solution 2
The squares that don't touch the border are in a 6 by 6 square. Therefore, the number of squares that don't touch the border is . There are 64 choices total. Therefore, the answer is , which simplifies to $\framebox{(D)$ (Error compiling LaTeX. ! File ended while scanning use of \fbox .)9/16$}$ (Error compiling LaTeX. ! Extra }, or forgotten $.).
See Also
2009 AMC 8 (Problems • Answer Key • Resources) | ||
Preceded by Problem 9 |
Followed by Problem 11 | |
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 AJHSME/AMC 8 Problems and Solutions |
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