So, I recently saw a video on carykh's channel on Youtube about Veritasium's 2 peg challenge. I wondered, how do we do this with 3 pegs?
The challenge is simple, how do we twist the string so the sign stays put when no pegs are removed, but when any single peg is removed, it falls?
Here's is my solution:
Each peg is going to be denoted with their own notation
As Cary said, if a peg's normal notation meets its inverse next to it, it cancels out. I decided to do all of it in my Notes app
My final solution is this:
A valid solution is the nested commutator:
[A, [B, C]]
Expanded:
A B C B' C' A' C B C' B'
B C B' C' C B C' B'
→ [B,C][B,C]⁻¹
→ e
The rope falls apart.
A C C' A' C C'
→ A A' C C'
→ C C'
→ e
The rope falls apart.
A B B' A' B B'
→ A A' B B'
→ B B'
→ e
The rope falls apart.