2015 UNCO Math Contest II Problems/Problem 9
Problem
![[asy] pair A=dir(90),B=dir(210),C=dir(330),O=(0,0); draw(circle(O,1),black); draw(O--A--B--O--B--C--O--C--A,dot); [/asy]](http://latex.artofproblemsolving.com/e/8/3/e83f523d4c2a6a2715d1879d2d1cba2c04fa6d2d.png)
Starting at the node in the center of the diagram, an orb spider moves along its web. It is permissible for the spider to backtrack as often as it likes, in either direction, on segments it has previously traveled. On each move, the spider moves along one of the segments (curved or straight) to some adjacent node that is different from the node that it currently occupies.
(a) How many different five-move paths start at the center node and end at the center node?
(b) How many different seven-move paths start at the center node and end at the center node?
Solution
(a) 
(b) 
See also
| 2015 UNCO Math Contest II (Problems • Answer Key • Resources) | ||
| Preceded by Problem 8 |
Followed by Problem 10 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 | ||
| All UNCO Math Contest Problems and Solutions | ||
