Batch 3 - Class 190 - Game of Thrones, Snails Strategy Game
Pre-Class Exercise
- (536Dudeney - 324) A squirrel goes spirally up a cylindrical pole, making a circuit in four feet. How many feet does it travel to the top if the post is sixteen feet high and three feet in circumference.
- Answer: Each circuit is 5 feet, so total 20 feet
Attendance Kushagra, Anshi, SiddharthM, SiddharthB, Rhea, Rehaan, Mahi, Arjun, Arnav, Damini, Smiti, Angad
Class puzzles
Game of Thrones
After years of fighting and tragedy without any resolution, the leaders of Westeros decide to convene to vote among themselves for the next Ruler of the Iron Throne. Tyrion, Dany, Sansa, Cersei and Jon are the five contenders. The vote will proceed as follows: Tyrion will first nominate one of the five of them. They will all vote yea or nay for his nominee, and if that person gets at least three “yea’s”, he/she will be named the ruler. Otherwise, Dany will have an opportunity to nominate someone, and then, if that person doesn’t receive at least three votes, Sansa will choose a nominee to put up for a vote, and then Cersei will. Finally, if Cersei’s nominee doesn’t pass with three votes, Jon will get to appoint the next ruler (with no voting necessary).
Their preferences are as follows:
Tyrion: T > D > S > J > C (Tyrion hates Cersei.)
Dany: D > T > S > C > J
Sansa: S > C > J > T > D
Cersei: C > J > S > D > T (Cersei hates Tyrion.)
John: J > D > S > T > C
Suppose that all five of them know each other’s preferences and are strategic and forward-looking. Furthermore, suppose that they cannot commit to vote against their own preferences in the future. Finally, if indifferent between possible nominees, everyone would prefer to nominate the ultimate winner. Who will Tyrion nominate and who will win?
- Answer: D. Work backwards from John. Since Cersei knows that John will nominate himself if his turn comes, Cersai will nominate herself and win (C,S,D votes). To avoid that, Sansa will nominate herself (S,J,D votes). To avoid that, D will nominate himself (D,T,J votes). Since Tyrion will loose if he nominates himself against D, T will nominate D and let D win.
Now suppose that Tyrion has a chance to institute a rule that no one is allowed to nominate (or appoint, in the case of Jon) himself or herself. Would he want to institute that rule? Who would he nominate and who would win?
- Answer: Work backwards again. T will still nominate D and D will win.
Slippery Snail
Play the game below with a friend. Four bugs are placed on certain spots on the snail. Take it in turns to move any bug, moving out towards the snail's mouth (the star). You can move a bug any number of spots but bugs cannot jump on or pass each other. When a bug reaches the snail's mouth (the star), it is out of the game.
The winner is the player who gets the last bug into the snail's mouth.
Can you find the winning strategy?
- Answer: Try to make two sets of adjacent bugs in your turn, and maintain that position
Homework Problem:
The Prisoner's Paradox
Three condemned prisoners share a cell. A guard arrives and tells them that one has been pardoned.
“Which is it?” they ask.
“I can’t tell you that,” says the guard. “I can’t tell a prisoner his own fate.”
Prisoner A takes the guard aside. “Look,” he says. “Of the three of us, only one has been pardoned. That means that one of my cellmates is still sure to die. Give me his name. That way you’re not telling me my own fate, and you’re not identifying the pardoned man.”
The guard thinks about this and tells him, “Prisoner B is sure to die.”
Prisoner A rejoices that his own chances of survival have improved from 1/3 to 1/2. But how is this possible? The guard has given him no new information. Or has he?
- Answer: This is same as the Monty Hall problem. A's chances of dying are still 1/3
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