TL;DR
The 100 Prisoners and a Light Bulb: A canonical quantitative trading interview question at olympiad difficulty. Commonly asked at Jane Street, Two Sigma, HRT.
By Valenke Exam Prep Team·Last updated 2026-06-01
olympiadClever Arguments
The 100 Prisoners and a Light Bulb
Asked at: Jane Street, Two Sigma, HRT
Problem
100 prisoners are in solitary cells. There is a room with a single light bulb (initially off). Each day, one prisoner is randomly selected to enter the room. They can toggle the bulb or leave it. At any time, any prisoner can declare "all 100 of us have visited." If correct, all go free; if wrong, all are executed. Devise a strategy guaranteeing success.
Related concepts
Ready to practice for the Valenke Finance Exam?
Adaptive practice powered by Item Response Theory targets your weak areas. Start with 3 free sessions.
Start free practice →