a collection of riddles

This project is maintained by davidtorosyan

You can find some that I’ve enjoyed working on below.

See the rest of my projects at davidtorosyan.com.

Can you help the prisoners communicate using just a light bulb?

There are 100 prisoners about to serve solitary confinement. While imprisoned, no prisoner will have contact with any other prisoner - in fact, they will usually never leave their cells. However, each day the warden will pick a prisoner (either at random or arbitrarily) and lead them from to a sealed interrogation room. In this room there is a light bulb, which the prisoner can toggle on or off. The warden will then ask the prisoner “Have I interrogated each prisoner at least once?” The prisoner can either reply “yes” or decline to answer. If they do answer and are right, all prisoners are released - otherwise, they’re all executed.

Before entering solitary confinement, the prisoners will have a chance to confer and come up with a strategy. Your job is to come up with such a strategy to ensure their survival while minimizing their time spent in the prison. Formally speaking, your plan must have a zero chance of getting killed and non-zero chance of freedom.

Check out the final solution, or scroll down to see the solution unfold.

Coming soon.

Coming soon.

What are your odds of winning a 100 million person lottery with these rules?

You are one of 100 million people playing in a lottery. On each drawing there is exactly one winner. What is the probability that you will win at least once before someone (could be any one of the other players) wins three times?

Check out the final solution, or scroll down to see the solution unfold.

Coming soon.

Coming soon.

Can you pick the optimal number to guess?

You are one of 10 people playing a game. There is a hidden number, from 1 to 100, that you want to guess. All 10 players submit their guess simultaneously, and the winning guess is the closest from either side (without wrapping around). You can expect the other players to guess completely randomly. What number should you guess?

Check out the final solution, or scroll down to see the solution unfold.

Coming soon.

Coming soon.