Counting and complements · Brainteaser · difficulty 2 of 5

Ants on a triangle

An ant sits on each corner of a regular polygon with 3 corners. At the same moment, each ant picks one of the two edges at its corner, independently and with equal probability, and walks along the polygon's edges in that direction forever, all at the same speed. What is the probability that no two ants ever meet?

Answer with a probability. First lock in a gut guess with an 80% range, then solve it properly, then watch a simulation settle on the truth.

Play it

More counting and combinatorics puzzles

No two dice alike · Dice
Someone shares your birthday · Office party
The Chevalier's bet · Dice
Best of three · Sports
Birthdays in the locker room · Sports
Dealt a full house · Poker

All counting and combinatorics puzzles · All puzzles · Market making game