### Puzzles

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##### Monty Hall Problem

Suppose you're on a game show, and you are given the choice of three doors. Behind one door is a car, behind the others, goats. You pick a door, say number 1, and the host, who knows what's behind the doors, opens another door, say number 3, which has a goat. He says to you, "Do you want to pick door number 2?" Is it to your advantage to switch your choice of doors?

##### Variation of Monty Hall Problem

There are three prisoners A, B and C. A knows that two of the three are going to be released. Obviously the probability that A is released is 2/3. Now A becomes curious and asks the jailor, "Which two of us will be let go?" the jailor replies, "Well, I cannot tell you that, but B is going to be set free. That is all I can tell you." A gets disappointed and goes back to his cell and starts thinking about the new probability of his discharge. Has the probability really changed? If no, why? and if yes why and what is the new value?

##### Five Thieves and Bounty

Five thieves have just looted a bounty of 1000 gold coins. The loot has to be divided among them and therein lies the problem. It is then decided that the youngest one will come up with a strategy of division, and the rest will put the strategy to vote. If the strategy is voted with a majority, it will be accepted and will be carried out. Otherwise, the youngest one will be shot and the second youngest will be asked to do the same...and so on. So the problem is, if you are the youngest thief, what will be your strategy, to maximize your share of the bounty? (Assume all thieves have different ages.)

##### Game of Two

Two immensely intelligent players, A & B, engage in a game, the rules of which are as follows. For some natural number N, the board consists of numbers from 1 to N. Each player takes turns to strike off a number from the board, with the added condition that if a number is struck off, then all its divisors should also be struck off. The player to strike off the last number on the board wins. A plays first. Is this game fair? If not, who has a winning strategy for each N and what is it? Else find the best strategy for each player. Click here to learn more.

##### The Two Men of Tibet

Two men are located at opposite ends of a mountain range, at the same elevation. If the mountain range never drops below this starting elevation, is it possible for the two men to walk along the mountain range and reach each other's starting place, while always staying at the same elevation?