Three logic puzzles, with one thing in common: Gun fight!
A revolver is loaded with three bullets in three consecutive chambers. [Hence there are three chambers with bullets, and three empty ones.] Once the barrel is spun, each player points the gun at his own head and pulls the trigger. If he doesn’t die, the gun is passed to the other player. There are only two players. The game ends when one player dies. Would you prefer to be the first player to pull the trigger or the second one, or does it make any difference?
Imagine a gun fight between three people. Ina is the worst shot; she hits the target once every three trials. Mina is better; she hits the target twice every three shots. Dika is a dead shot; she never misses. Each gets one shot (i.e. only one round). As the worst shooter Ina goes first, then Mina, and then Dika. Whom should Ina aim for her one shot?
Three men are fighting in a truel. Andrew is the worst shot; he misses 2/3 of the time. Bob is better; he misses 1/3 of the time. Connor is the best shot; he always hits. Each of the three men have an infinite number of bullets. Each shot is either a kill or a miss. They have to shoot at each other in order until two of them are dead. To make it more fair they decide to start with Andrew, followed by Bob, and then Connor. We assume that they choose their strategies to maximize their probability of survival. At whom should Andrew aim for his first shot?
I will post the answers next week.
The second and third puzzles are from Tanya Khovanova’s Math Blog.
Pic Courtesy: Wikipedia
Answer to the first puzzle: see the comments section below.
Answer to the second puzzle: See the image below – click to embiggen.
Three scenarios are considered for Ina (who goes first): Ina shoots at Mina, Ina shoots at Dika, and Ina shoots in the air. As explained in the diagram below, the probability that Ina dies is lowest in the third scenario. Hence, she should fire the shot in the air (as Ramanand correctly inferred in the comment section below.)
Note that I’ve made a couple of assumptions: (1) These players are bloodthirsty – so if Ina kills Mina with her first (and only) shot, Dika would still kill Ina even if she poses no threat to her. (2) If it’s Dika’s turn, and both Ina and Mina are alive, then Dika will randomly kill either Ina or Mina. Changing this assumption (to “Dika would always kill Mina”, for instance) doesn’t change the conclusion though.
Answer to the third puzzle: I actually don’t have the correct answer for this puzzle. If anyone does have a solution, please do share!