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, $7=21_3$). 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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