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| Have fun with these puzzles and games! | ||||||||||||||||||||||||||||||||
| The two old women | ||||||||||||||||||||||||||||||||
| Suppose you are walking on a road and suddenly arrive at a fork. There are two roads available to you: one leads to hell and one leads to heaven. Beside the fork there is a house where two old women live. You know that one of them is always lying while the other one always tells the truth, but unfortunately they are twins and there is no way to distinguish them. It is your task to ask exactly one question to one of the women in order to decide, which road leads to heaven. | ||||||||||||||||||||||||||||||||
| Solution | ||||||||||||||||||||||||||||||||
| The magic dices | ||||||||||||||||||||||||||||||||
| Look at the following set of dices: | ||||||||||||||||||||||||||||||||
| Dice 1 | 1 | 2 | 16 | 17 | 18 | 19 | ||||||||||||||||||||||||||
| Dice 2 | 3 | 4 | 5 | 20 | 21 | 22 | ||||||||||||||||||||||||||
| Dice 3 | 6 | 7 | 8 | 9 | 23 | 24 | ||||||||||||||||||||||||||
| Dice 4 | 10 | 11 | 12 | 13 | 14 | 15 | ||||||||||||||||||||||||||
| It is easy to verify that dice 2 is better than dice 1 because it wins in 24 out of 36 cases. Similarly dice 3 beats dice 2 and dice 4 beats dice 3 with probability 2/3. Common sense says that dice 4 is much better than dice 1, but a careful inspection of the numbers shows that dice 1 is better than dice 4. Explain why this is no contradiction and create your own dices to astonish your friends. | ||||||||||||||||||||||||||||||||
| Solution | ||||||||||||||||||||||||||||||||
| The goat problem | ||||||||||||||||||||||||||||||||
| You are in the final round of a quiz show and you have to choose a door out of three. Behind one door there is a wonderful new car and behind the other two doors there is a goat, respectively. After you have chosen the door the quizmaster opens a door with a goat (since there are two doors with a goat he can do so in any case). Now, you have the chance to switch to the other remaining door. What would you do? And why? | ||||||||||||||||||||||||||||||||
| Solution | ||||||||||||||||||||||||||||||||