Even in Greek mythology.
Theseus was going to slay the minotaur so Ariadne sent him with string to use so he could find his way back as we wove his way through the maze of columns.
The challenge was that each time he went around a column, that length of string had to be greater than the time before. How many pathways could he find? Below is an example of 5 pathways that got longer with each turn.
Students worked on this for the whole class period, finally finding that 8 pathways was the most that could be found in the 5x5 grid.
For those students with extra time, they worked on the 8x8 grid. With this larger grid, they found that 14 pathways were possible.
We organized this data into a table of values and filled in the missing pieces.
We even connected it to Algebra and found the equation... 2g - 2 = p
Because of our limited time, I told the students that it would just take one counterexample to disprove our pattern.
Sure enough, today a student came in to class with 9 pathways.
Are 10 pathways possible?
So now, how many pathways could fit in the 8x8 grid?
Gotta love math!
