SHOW:
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- or go back to the newest paste.
| 1 | - | (Simplified version an old problem, here with 8 bottles instead of 1000) |
| 1 | + | (Simplified version an old problem, here with 16 bottles instead of 1000) |
| 2 | ||
| 3 | - | A king has 8 bottles of wine of which one (unknown) has deadly poison in it. If one drinks even a drop of the poisoned wine one will die within three weeks. |
| 3 | + | A king has 16 bottles of wine of which one (unknown) has deadly poison in it. If one drinks even a drop of the poisoned wine one will die within three weeks. |
| 4 | ||
| 5 | The king will have a party in four weeks and wants to figure out before that which bottle is poisoned so that he can discard it. | |
| 6 | ||
| 7 | - | He has only a few servants who he is willing to sacrifice in order to test this. |
| 7 | + | He has some servants who he is willing to sacrifice in order to test this. |
| 8 | ||
| 9 | - | The typical solution here is to use the binary system so that you need to sacrifice 3 servants in order to test 8 bottles. |
| 9 | + | The typical solution here is to use the binary system so that you need to sacrifice 4 servants in order to test 16 bottles. |
| 10 | ||
| 11 | - | There is a problem though, namely the fact that people sometimes die for other reasons. For example if all 3 die, then that could be because bottle 7 was poisoned, but it could also be bottle 5 and that servant 2 died for some other reason. This would lead to discarding bottle 7 when it is actually bottle 5 that is poisonous. |
| 11 | + | There is a problem though, namely the fact that people sometimes die for other reasons. For example if the the 3 first servants die, then that could be because bottle 7 was poisoned, but it could also be bottle 5 and that servant 2 died for some other reason. This would lead to discarding bottle 7 when it is actually bottle 5 that is poisonous, so a fatal mistake. |
| 12 | ||
| 13 | My question is, how can one improve the certainty? How many servants are needed with your improved method? |
