The ladybug clock puzzle

2026-01-16 · Source: 3Blue1Brown · Field: Science & Research — Mathematics & Computational Sciences · Depth: Intermediate, quick

Summary

A mathematical puzzle, dubbed "The Ladybug Clock Puzzle," describes a ladybug starting at the 12 on a clock face. Each second, the ladybug moves randomly to an adjacent number, either clockwise or counterclockwise. As the ladybug touches a number, it is colored red. The simulation continues until all numbers are colored. The puzzle asks for the probability that the number 6 is the very last number to be colored red. This is the first in a series of monthly puzzles presented in collaboration with mathematician Peter Winkler, with solutions discussed in monthly Zoom calls hosted by MoMath Museum's Year of Math program.

Key takeaway

For mathematicians and puzzle enthusiasts interested in probability and random walks, consider analyzing the symmetry and boundary conditions of the clock face to determine the likelihood of the number 6 being the final uncolored spot. Your approach should account for the ladybug's random, step-by-step movement to adjacent numbers.

Key insights

The puzzle asks for the probability that a specific number is the last to be visited in a random walk.

Principles

• Random walks involve probabilistic movement.
• The "last to be visited" concept is key.

Topics

• Ladybug Clock Puzzle
• Mathematical Puzzles
• Probability Puzzles
• Random Walks
• Peter Winkler

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Editorial summary, takeaway, and curation by AIssential. Original article published by 3Blue1Brown.