There are 1000 wine bottles. One of the bottles contains poisoned wine. A rat dies after one hour of drinking the poisoned wine. How many minimum rats are needed to figure out which bottle contains poison in hour.

Question

Accepted Answer

I solved this puzzle using a short example. I took 8 bottles and feed three rats with wine. I fed each rat 4 bottles. Now, suppose three rats have the following wine configuration:

Rat 1 - 3 6 7 8 (0 0 1 0 0 1 1 1)

Rat 2 - 2 5 7 8 (0 1 0 0 1 0 1 1)

Rat 3 - 4 6 5 8 (0 0 0 1 1 1 0 1)

If no rat die then we can say that poison is in bottle 1, if rat 1 dies then we can say that poison is in bottle 3 as it was first bottle to fed by rat 1, similarly, if Rat 2 dies than bottle 2 was poisoned and if Rat 3 dies bottle 4 was poisoned. If both Rat 1 and Rat 3 die, then bottle 6 has poison. If Rat 1 and Rat 2 die, then we can say that bottle 7 has poison. If both Rat 2 and 3 dies, then bottle 5 have poison, and if all rats die then bottle 8 was poisoned. So making combinations, we can see that for 8 bottles you need 3 rats. Similarly, for 4 bottles you need 2 rats or in general, for 2^n bottles, you need n rats. So for 1000 bottles, you will need Log2(1000) which approximately comes out to be 10 ,so 10 was the answer of that puzzle. So just by taking shorter example I solved this puzzle and the interviewer was satisfied with my answer.

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