- #1
Canada_Whiz
- 14
- 0
Suppose an ant is on a vertex of a cube. On one of the three vertices neighboring the ant, there is a black hole. On each move, the ant travels to one of it's neighboring vertices, being careful not to pass through the black hole. The ant makes N moves in total. How many different paths lead the ant back to his original vertex after these N moves?
NOTE: The answer is in terms of N. Also, the ant may cross an edge he has already crossed, so long as he does NOT go through the black hole.
My Data:
For N=0, there is 1 way
For N=2, there are 2 ways
For N=4, there are 8 ways
For N=2z+1, there are 0 ways
Help is much appreciated!
NOTE: The answer is in terms of N. Also, the ant may cross an edge he has already crossed, so long as he does NOT go through the black hole.
My Data:
For N=0, there is 1 way
For N=2, there are 2 ways
For N=4, there are 8 ways
For N=2z+1, there are 0 ways
Help is much appreciated!