On the cube below, note that there are three directions in which we can travel:
ID: 3076514 • Letter: O
Question
On the cube below, note that there are three directions in which we can travel: left/right, front/back, up/down. Also notice that if we start at any vertex, we can travel in each of the three listed directions. Start at the vertex v. Now, read your solution to the 3-disk puzzle and create a path using the following rules. Each time you encounter a 0, move left or right. Each time you encounter a 1, move forwards or backwards. Each time you encounter a 2, (you guessed it) move up or down.
What kind of path is the resulting path? Explain in your own words why the solution to this problem gives this kind of path.
Explanation / Answer
It is a Hamiltonian path because each vertex is visited only once. The reason that this is a Hamiltonian path is that we have 8 vertices to move between in this graph. Also, there are only 7 numbers in the solution but 8 vertices on the graph and each vertex directs the path such that there is no backtracking.
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