A king is hosting a party with 4 bottles of wine. As the guests are about to arrive, it was found that one of the bottles is highly poisonous, and whoever drinks from it would die instantly. The king had some prisoners to be hanged anyway next day. He can ask four of them to drink “one drop” separately from each bottle. But the king wants to engage “minimum” prisoners. How many does he require?
Two prisoners are enough to identify the wrong bottle. A consumes Bottle 1; and B takes from bottle 2. Then both A and B consume from bottle 3. If either A or B die, bottle 1 or bottle 2 is poisonous respectively. If both A, B die bottle 3 is the spurious. If nobody dies bottle 4 has the poison.
What is the minimum number of persons required to test 8. Just 3 prisoners are enough. A takes first bottle, B takes second, C consumes third one, and then A and B from bottle four, B and C bottle five, A and C bottle six; and finally A, B and C from bottle seven. If A dies first bottle, B 2, C 3, in case A and B both die bottle 4, if all die the bottle 7 and if nobody dies, 8th bottle is poisonous.
Suppose the king is giving a lavish party involving 1,000 bottles, then how many prisoners does he require? Just 10…! Surprised? Yes. On the principles of permutation that if 2 prisoners can consume from 4 bottles, 3 can test 8, 4 can check 16; 5 can test 32; and 10 can verify 1024.
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