Random ants | PuzzledQuant

New on YouTube: How Jane Street made $5B in India (and what SEBI says it did) - Watch now

Get quant-ready in 2026

⚡ Build the skills to land top-paying quant jobs. Offer ends in --d --h --m --s-- days -- hours -- minutes -- seconds.

Medium

Expected Value

$500$ ants are placed on a $1$ -foot string without any order. Assume independent uniform distribution for each ant. Each ant will move randomly towards either end of the string at a constant speed of $1$ foot per minute. The ants will keep moving until they reach the end of the string, and if two ants collide head-on, they will both immediately turn around and continue moving. Assuming that the size of the ants is infinitely small, what is the expected time for all $500$ ants to fall off the string?

Discussion (11)