SOLUTION: A bug lives on a corner of a cube and is allowed to travel only on the edges of the cube. In how many ways can the bug visit each of the other seven corners once and only once, ret

Algebra ->  Points-lines-and-rays -> SOLUTION: A bug lives on a corner of a cube and is allowed to travel only on the edges of the cube. In how many ways can the bug visit each of the other seven corners once and only once, ret      Log On


   

Question 1206483: A bug lives on a corner of a cube and is allowed to travel only on the edges of the cube. In how many ways can the bug visit each of the other seven corners once and only once, returning to its home corner only at the end of the trip?
Found 2 solutions by ikleyn, KMST:
Answer by ikleyn(54018) About Me  (Show Source):
You can put this solution on YOUR website!
.

See the solution 2 under this link

https://artofproblemsolving.com/wiki/index.php/2006_AMC_12A_Problems/Problem_20


They say that if you are able to understand it, then you are officially good in Math.



Answer by KMST(5434) About Me  (Show Source):
You can put this solution on YOUR website!
This is my translucent cube with the bug's home marked, and the corners numbered.
The green edges would not be visible if I had not made it translucent.

The bug has to visit each corner once and only once, and then return home.
No one said the bug has to travel along each and every edge.
That would be exhausting, and it would end up visiting corners twice.
He just goes from each corner to the next number corner, in order.
At the end of the trip, from corner 8 it goes back home.
I will add red arrows to show the bug's path, just in case my explanation is not clear.