## 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.
___ ___ ___ ___ ___ ___ ___ ___ ___

Return to Constructing a new 12-level labyrinth

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*
Tony Phillips*

Math Dept SUNY Stony Brook

tony@math.sunysb.edu

May 18, 1997