Logic for wine drinking!!

1000 wine bottles were ordered for a feast by a king. 4 days before the feast, a person was caught mixing poison in a wine bottle, it is known that poison is present in only one wine bottle. King has 10 expendable workers, which he can order to drink wine. Now by using only those 10 people how can you separate that poisonous wine bottle, given that it takes 3 days for poison to kill a person.

Note by Vivek Bhagat
3 years, 8 months ago

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I am familiar with this puzzle. The solution uses binary mapping.

Flag each bottle with an unique \(10\) digit binary representation, As \(1000 < 2^{10}\), such representation is possible. For example,

\[1^{st} \; \textrm{bottle will be flagged as 0000000001}\] \[2^{nd} \; \textrm{bottle will be flagged as 0000000010} \] \[3^{rd} \; \textrm{bottle will be flagged as 0000000011} \] \[.\] \[.\] \[1000^{th} \; \textrm{bottle will be flagged as 1111101000} \]

Let the workers be \(A_1, A_2, A_3, A_4, A_5, A_6, A_7, A_8, A_9\) and \(A_{10}\)

And each binary representation represents an unique drinking combination. For example the \(3\)rd bottle represents,

\[ \begin{Vmatrix} A_1 & A_2 & A_3 & A_4 & A_5 & A_6 & A_7 & A_8 & A_9 & A_{10}\\ 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 1 & 1 \end{Vmatrix} \]

means only \(A_9\) and \(A_{10}\) will drink the 3rd bottle.

Another example, 1000 th bottle represents

\[ \begin{Vmatrix} A_1 & A_2 & A_3 & A_4 & A_5 & A_6 & A_7 & A_8 & A_9 & A_{10}\\ 1 & 1 & 1 & 1 & 1 & 0 & 1 & 0 & 0 & 0 \end{Vmatrix} \] means \(A_1, A_2, A_3, A_4, A_5\) and \(A_7\) will drink the 1000 th bottle.

And after \(3\) days we can uniquely determine which bottle is poisoned, observing which workers die. For example, If \(A_1, A_2, A_3, A_4, A_6, A_8\) and \(A_{10}\) die after \(4\) days, this will represent,

\[ \begin{Vmatrix} A_1 & A_2 & A_3 & A_4 & A_5 & A_6 & A_7 & A_8 & A_9 & A_{10}\\ 1 & 1 & 1 & 1 & 0 & 1 & 0 & 1 & 0 & 1 \end{Vmatrix} \]

means the \(1111010101_2 = 981_{10}\) th bottle is poisoned

Tasmeem Reza - 3 years, 4 months ago

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1000 has 10 digits of binner. So we can separate that poisonous bottle with 10 person

Hanif Adzkiya - 3 years, 4 months ago

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can't we ask the person who was mixing the poison????? just having fun!

Parth Tandon - 3 years, 8 months ago

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hehe, nice try, i should mention that all the bottles look exactly identical! so even he wont be able to tell that

Vivek Bhagat - 3 years, 8 months ago

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