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| Solutions | ||||||
| The two old women | ||||||
| Since it is in any case impossible to know whether you are talking to the woman that is always lying or always telling the truth, there is no other way than to combine lie and truth. This can be easily done by asking the woman what the other woman would answer! Since there is exactly one lie in the final answer the woman will show you the way to hell so you have to take the other road that leads to heaven. | ||||||
| The magic dices | ||||||
| The assertion can be easily checked. In mathematical words we have found a non-transitive example! It is striking, isn't it!? | ||||||
| The goat problem | ||||||
| At first sight there seems to be a fifty-fifty chance to get the right door. But this reasoning is erroneous. Clearly, your chances in the beginning to get the right door are 1/3. Then the quizmaster opens a door with a goat. This process has no influence on the probability that you have chosen the right door in the beginning so it remains at 1/3. Consequently, the chances that the other door contains the car are 2/3! Therefore you should change your opinion and switch to the other door. Moreover, if you knew from the beginning that a goat is in door 1 (e.g. because you hear the goat bleating) then you should choose door 1! The quizmaster then shows you the second door with a goat and you can switch to the door with the car! | ||||||
| If you are still not convinced you can run a simulation on the following page: http://math.ucsd.edu/~crypto/Monty/monty.html |
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