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You are the ruler of a medieval empire and you are about to have a celebration tomorrow. The celebration is the most important party you have ever hosted. You’ve got 1000 bottles of wine you were planning to open for the celebration, but you find out that one of them is poisoned. The poison exhibits no symptoms until death. Death occurs within ten to twenty hours after consuming even the minutest amount of poison. You have over a thousand slaves at your disposal and just under 24 hours to determine which single bottle is poisoned. You have a handful of prisoners about to be executed, and it would mar your celebration to have anyone else killed. What is the smallest number of prisoners you must have to drink from the bottles to be absolutely sure to find the poisoned bottle within 24 hours?

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Hi, I'm Vineet Patawari. I fall in love with numbers after being scared from them for quite some time. Now, I'm here to make you feel safe with numbers and help you come out of Maths Phobia!

comments

  1. krish says:

    hello…let me tell a tooo simpler solution for this.

    the question asked was “the smallest no. of persons required for testing”

    acc. to probability,i could be just one person enough with 1/1000 probability of finding the poisoned bottle.

    soo this is the minumum no. i think becoz it was said that “ONLY A HAND FULL OF PRISONERS ” and no number is mentioned!

  2. NANDEESH H N says:

    I have seen the answer in some other site. I do not want to copy and paste it here. However I want to write something in my own words.
    1. Suppose there are 1000 persons to test, each bottle will have a unique person to test and so whichever person dies will tell which bottle is poisoned.

    2. If the number of persons is limited to say 5.
    a. We have to assign 5 digit codes to bottles like ‘00000’ to ‘11111’.
    b. Assign first position of the codes to first person and ask him to test all bottles which have ‘1’ in the first position of the bottle codes.
    Similarly second person will test all bottles which have ‘1’ in the second position of the bottle codes.
    c. Depending on which of the 5 persons died, we can identify the poison bottle.

    3. But 1000 bottles cannot be given unique codes using only 5 digit codes. We need 10 digit codes to give unique codes to 1000 bottles since 2power10=1024.
    So the bottle codes will look like ’0000000000′, 0000000001′ etc. and lastly ’1111111111′.
    So we need 10 persons to test.
    If the bottle code is ’1100101001′ it will be tested by 1st, 2nd, 5th, 7th and 10th persons.

    4. After the testing, check which combination of 10 persons died of poisoning. This will reveal the code of the poison bottle.
    For ex: If none of the persons died, the bottle code is ‘0000000000’
    If all of them died, the bottle code is ‘1111111111’.
    If the second, fifth, sixth, eighth and tenth persons died, the code of the poison bottle is ’0100110101′.

    NANDEESH H N

  3. Rajnish says:

    none … catch hold of all the cats and the dogs in kingdom … and make them dring it ….

  4. VIJIT says:

    SOMEBODY PLEASE POST CORRECT ANS. WITH EXPLANATION.

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I am Vineet Patawari - PGDM (IIM Indore), ACA, B.Com(H). My passion for Mathematics, specially Vedic Maths encouraged me to start QuickerMaths

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