user
An ant starts at one corner of a cube and wants to get to the diagonally opposite corner. It can only walk along the edges of the cube. How many different paths can the ant take if it never travels along the same edge more than once? Detail your thinking.
assistant
Let's reason through this:

1. From the starting point, the ant has 3 options for the first move (it can go along any of the three edges connected to the corner it's currently at).

2. After the first move, no matter which path was chosen, the ant has 2 options for the second move (since it can't travel back along the edge it just used).

3. For the third and final move, the ant again has 3 options (the remaining edges leading to the destination corner).

4. Therefore, the total number of paths is the product of the number of options at each step: 3 (for the first move) * 2 (for the second move) * 3 (for the third move) = 18 paths.

So, there are 18 different paths the ant can take to get to the diagonally opposite corner of the cube without traveling along the same edge more than once.