Three men, Adam, Bertie and Charlie, agree to take part in a lethal three-way duel. They each have a pistol and several rounds of ammo, and they draw lots to see who will shoot first and who second. Then they stand an equal distance apart, and they take turns to fire. When it is a player's turn, he can take one shot at any target of his choice. Then, the turn passes to the next player. The duel continues until only one player is left alive.
For simplicity, we can ignore the possibility of a player becoming injured and unable to shoot: a player is either alive or dead. We also assume that each player chooses to play in such a way as to give himself the best chance of winning.
Now Adam and Bertie are crack shots and will always get a kill, but Charlie is only a moderate shot and will only get a kill two thirds of the time. All three men know this.
Of the three men, who has the best chance of winning the duel?
A man was found murdered on Sunday morning. His wife immediately called the police. The police questioned the wife and staff and got these alibis:
- The Wife said she was sleeping.
- The Cook was cooking breakfast.
- The Gardener was picking vegetables.
- The Maid was getting the mail.
- The Butler was cleaning the closet.
The police instantly arrested the murderer. Who did it and how did they know?
Three closed boxes have either white marbles, black marbles or both, and they are labeled white, black and both. However, you're told that each of the labels is wrong. You may reach into one of the boxes and pull out only one marble.
Which box should you remove a marble from to determine the contents of all three boxes?