Difference between revisions of "2013 AMC 8 Problems/Problem 21"
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| − | We see that Samantha only has one way to go through in the city park, 6 ways to the city park to school, and 3 ways from her house to the city park. After this, we can see that there are 6X3=18 ways for Samantha to go to school ( | + | We see that Samantha only has one way to go through in the city park, 6 ways to the city park to school, and 3 ways from her house to the city park. After this, we can see that there are 6X3=18 ways for Samantha to go to school (E) |
==See Also== | ==See Also== | ||
{{AMC8 box|year=2013|num-b=20|num-a=22}} | {{AMC8 box|year=2013|num-b=20|num-a=22}} | ||
{{MAA Notice}} | {{MAA Notice}} | ||
Revision as of 17:52, 1 November 2017
Problem
Samantha lives 2 blocks west and 1 block south of the southwest corner of City Park. Her school is 2 blocks east and 2 blocks north of the northeast corner of City Park. On school days she bikes on streets to the southwest corner of City Park, then takes a diagonal path through the park to the northeast corner, and then bikes on streets to school. If her route is as short as possible, how many different routes can she take?
Solution
![[asy] unitsize(8mm); for(int i=0; i<=8; ++i) { draw((0,i)--(8,i)); draw((i,0)--(i,8)); } fill((2,1)--(6,1)--(6,6)--(2,6)--cycle); for(int j=0; j<= 38; ++j) { draw((0,0)--(2,0)--(2,1)--(0,1)--(0,0), black+linewidth(3)); draw((6,6)--(6,8)--(8,8)--(8,6)--(6,6), black+linewidth(3)); }[/asy]](http://latex.artofproblemsolving.com/c/4/c/c4c258dbd1d28f8138a2d43632bd2c86b1864e5e.png)
We see that Samantha only has one way to go through in the city park, 6 ways to the city park to school, and 3 ways from her house to the city park. After this, we can see that there are 6X3=18 ways for Samantha to go to school (E)
See Also
| 2013 AMC 8 (Problems • Answer Key • Resources) | ||
| Preceded by Problem 20 |
Followed by Problem 22 | |
| 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 | ||
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions. 
