Sunday, March 25, 2018

logical deduction - Nine Bottles of Wine, One Poisoned, Two Mice, Two Tests


Came across this puzzle and couldn't think of a solution:




You are given nine bottles of wine out of which one is poisoned. Given two mice (that will die when taken a sip of poisoned wine), how can you find out which bottle is the poisoned one by only performing two tests?



Any ideas?


Edit: I misunderstood the exact meaning of test. I thought that each “drink/sip” was a test. Thanks for all the answers.



Answer




Number the bottles 0 through 8; these can be represented as 2 digit ternary numbers (example, 7=213). Call the mice Alice and Bob.



  • For the first experiment, have Alice drink from every bottle whose first ternary digit is 0, and have Bob drink from those whose second ternary digit is 0.

  • For the second experiment, replace every 0 in the previous sentence with 1.



After the two experiments, the experiment during which Alice died (if any) tells you the first ternary digit of the poisoned bottle: if she died on the first experiment, it is 0, on the second, it is 1, if never, it is 2. Similarly, Bob's lifespan tells you the second digit. Thus, afterwards you will know the bottle.

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