Traffic light stop

What this traffic-light optimization puzzle tests

This is a medium-difficulty puzzle that combines conditional probability with decision-making under uncertainty. It asks you to reason about the relationship between your current observation, the underlying cycle, and your expected future cost — a pattern that appears frequently in trading and operational research.

The key insight is that what you observe now (the current light color) contains information about where you are in the cycle. A candidate must set up the problem by considering all possible phases of the traffic light at the moment of observation, weight them correctly by probability, and then compute the expected wait time for each scenario. The puzzle rewards clarity of reasoning over memorization.

• Conditional probability and Bayesian reasoning
• Arrival-time distributions and cycle time
• Expected value computation given partial information
• Decision-making with incomplete state knowledge