This is the first in a set of monthly puzzles, curated by Peter Winkler. This one was originally suggested by Richard Stanley.

You can sign up to hear his description of the answer at http://momath.org/mindbenders

3Blue1Brown

A mathematical puzzle involving a ladybug performing a random walk on a clock face. Starting at 12, the ladybug moves randomly to neighboring numbers each second until all positions are visited. The challenge is to calculate the probability that position 6 is the last number to be colored. This is part of a monthly puzzle series in collaboration with mathematician Peter Winkler and MoMath Museum.

The ladybug clock puzzle