## Renumbering levels

Often, when constructing a maze with students calling out the next number to use, the maze ends up with fewer than the planned number of levels. For example, suppose we are trying to build a 10-level maze and we get to
```
0   9   4   7   8   1   2   3          10.
___ ___ ___ ___ ___ ___ ___ ___ ___ ___ ___

```
Levels 5 and 6 are inaccessible. There are two things that can be done. One is to analyze the process to see where the 5 and 6 levels got cut off, and to change the construction. For example, here once the 8 is chosen there is no way to get to level 5. But a different choice can lead to a 10-level maze. Here one would have to choose 6 after 7, and that could lead to
```
0   9   4   7   6   5   8   3   2   1  10.
___ ___ ___ ___ ___ ___ ___ ___ ___ ___ ___

```
Another strategy is to decide to live with the 8-level maze you have constructed. Since levels 5 and 6 were not used, levels 7, 8, 9, 10 have to be renumbered as 5, 6, 7, 8. This yields
```
0   7   4   5   6   1   2   3   8.
___ ___ ___ ___ ___ ___ ___ ___ ___

```