My Favorite Riddles

Three Coin Flips

Three mathematicians in separate rooms must flip a coin while blindfolded. Then, each is informed of the results for the other two, but not for their own. Each has the choice to either guess the result of their own flip, or pass. If any one of them guesses incorrectly, they are all killed. If nobody guesses correctly, they are all killed. What is the best strategy? Answer

Split the Coins

You are blindfolded. There are 100 pennies on the table, 70 heads, 30 tails. How can you split them all into two groups, each containing the same number of heads? Answer

Unbalanced Billiard Balancing

You have 13 pool balls and a balance. One ball is a different weight than the others. How many times do you need to use the balance to find it? Answer

Endless Powers

x^(x^(x^...)) = 2. What is x?

I'm thinking of a number...

I am thinking of an integer in [1, 27]. You can ask me 3 yes/no questions. What strategy ensures you will find the number?

Prisoner Counting Switches

There are 21 prisoners in separate rooms. Every day, one prisoner is taken to a special room and must flip exactly 1 of 2 light switches. No matter how many days have passed, every prisoner will still enter the room again at some point. At any time, any prisoner may claim that all the prisoners have entered the room. If he is right, they are all freed. Otherwise, they are all killed. What strategy could they have come up with before being imprisoned that would ensure their freedom? Answer