You are in a room with two doors. One door leads to freedom and the other leads to death. There are two guards, one by each door. One guard always tells the truth and the other always lies. You can ask one guard one question to determine which door leads to freedom. What do you ask?
You are outside a room with three light switches: One of the switches controls a light bulb inside the room, and the other two switches do nothing. You can turn the switches on and off and leave them in any position. You can open the door to the room only once to check the light bulb. How do you determine which switch controls the light bulb?
The Bridge and Torch Problem: Four people need to cross a bridge at night. They have one torch and the bridge can only hold two people at a time. The four people take 1, 2, 7, and 10 minutes to cross respectively. When two people cross the bridge together, they must move at the slower person’s pace. How do they all get across the bridge in the shortest time?
The Two Rope Burn:
You have two ropes of different lengths. Each rope takes exactly 60 minutes to burn from one end to the other, but they do not burn at a consistent rate (i.e., half the rope does not necessarily take 30 minutes to burn). How can you measure exactly 45 minutes using these ropes and a match?
The Three Hats: Three people are wearing hats. Each hat is either red or blue, and each person can see the other two hats but not their own. The first person says, “I don’t know what color my hat is.” The second person then says, “I don’t know what color my hat is either.” Finally, the third person says, “I know what color my hat is.” What color is the third person’s hat and how does he know?
