1986 AJHSME Problems/Problem 9
Problem
Using only the paths and the directions shown, how many different routes are there from to ?
Solution
There is 1 way to get from C to N. There is only one way to get from D to N, which is DCN.
Since A can only go to C or D, which each only have 1 way to get to N each, there are ways to get from A to N.
Since B can only go to A, C or N, and A only has 2 ways to get to N, C only has 1 way and to get from B to N is only 1 way, there are ways to get from B to N.
M can only go to either B or A, A has 2 ways and B has 4 ways, so M has ways to get to N.
6 is .
A diagram labeled with the number of ways to get to from each point might look like
See Also
1986 AJHSME (Problems • Answer Key • Resources) | ||
Preceded by Problem 8 |
Followed by Problem 10 | |
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.