This picture was posted in the math building at my college! So there has to be some sort of math puzzle/meaning behind it. Here is the picture of the puzzle and the instructions.
I have tried this several times and still cannot get it.
Here are the instructions
Let me know what you guys come up with! Thanks!
Hint: no math magic, just informed trial and error. These are often easier if you work backwards from the goal. You have only one path for the first eight steps backward, then a guess. One of the options brings you back to where you were, but having arrived from the other color. That should give you confidence that it is the correct path, as constructors of puzzles like things like that. I find a solution that has $40$ steps.
In reverse, I get $\def\ot{\gets}\text{GOAL}\ot * \ot \otimes\ot Z\ot Y\ot X\ot W\ot O\ot L\ \\ \ot G \ot A \ot B \ot G \ot L \ot O \ot W \ot X \ot Y\\ \ot Z \ot S \ot R \ot J \ot I \ot D \ot E \ot F \ot K \\ \ot T \ot V \ot \otimes \ot * \ot V \ot T \ot K \ot F \\\ot E \ot D \ot C \ot B \ot A \ot START$
I suspect this is the intended solution because of the two big loops retracing steps.