\input zb-basic
\input zb-matheduc
\iteman{ZMATH 2016a.00861}
\itemau{Crans, Alissa S.; Rovetti, Robert J.; Vega, Jessica}
\itemti{Solving the KO labyrinth.}
\itemso{Math. Mag. 88, No. 1, 27-36 (2015).}
\itemab
Summary: The KO Labyrinth is a colorful spherical puzzle with 26 chambers, some of which can be connected via holes through which a small ball can pass when the chambers are aligned correctly. The puzzle can be realigned by performing physical rotations of the sphere in the same way one manipulates a Rubik's Cube, which alters the configuration of the puzzle. The goal is to navigate the ball from the entrance chamber to the exit chamber. We find the shortest path through the puzzle using Dijkstra's algorithm and explore questions related to connectivity of puzzle with the adjacency matrix, distance matrix, and first passage time analysis. We show that the shortest path through the maze takes only 10 moves, whereas a random walk through the maze requires, on average, about 340 moves before reaching the end. We pose an analogue of the gambler's ruin problem and separately consider whether we are able to solve the puzzle if certain chambers are off limits. We conclude with comments and questions for future investigation.
\itemrv{~}
\itemcc{K30 A20}
\itemut{KO Labyrinth; spherical puzzles; KO graph; Dijkstra's algorithm; shortest path; random walk}
\itemli{doi:10.4169/math.mag.88.1.27}
\end