Master Lock Speed Dial, why there are 7501 states

*correction 9:30
if the the last move is left, we end up on a white
if the last move is up, we end up on a black
if the last move is right, we end up on a color ( i say black in the video)


My attempt at describing why there are 7501 reachable states for  MasterLock Speed Dial style locks, and how a wheel works. There are an infinite number of input sequences but they all lead back to one of 7500(+1) wheel configurations.  The state space is greatly reduced (compared to 15^4) by the fact that the last move forces 3 wheels into a known relationship.


Links:
mh's paper paper covers all of these concepts and you should read it https://toool.nl/images/e/e5/The_New_...


to experiment on your own you should check our prevarikation's cool new port of mh's visualizer at https://prevarikation.com/mh-visualizer/ also check out her channel @prevarikation