We need 10 rats to figure out the poisoned bottle. The result is based on binary number system. We get 10 using ⌈ Log 2 1000 ⌉. The idea is to number bottles from 1 to 1000 and write their corresponding binary numbers on the bottle. Each rat is assigned a position in the binary numbers written on bottles. Let us take an example.
What happens if bottle number 42 is poisoned?
Let us take an example. Rat 1 represents first bit in every bottle, rat 2 represents second bit and so on. If rat numbers 5, 7 and 9 die, then bottle number 42 (Binary 0000101010) is poisoned. Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above
How to find the poisoned bottle of wine?
Answer to Riddle #61: Finding the Poisoned Bottle of Wine 61. A bad king has a cellar of 1000 bottles of delightful and very expensive wine. A neighbouring queen plots to kill the bad king and sends a servant to poison the wine. Fortunately (or say unfortunately) the bad king’s guards catch the servant after he has only poisoned one bottle.
What happens in a king, 1000 bottles of wine and 10 drops of poison?
Soon after, the Queen discovers that one of the senators is trying to assassinate the King by giving him a bottle of poisoned wine. Unfortunately, they do not know which senator, nor which bottle of wine is poisoned, and the poison is completely indiscernible. However, the King has 10 prisoners he plans to execute.
Can a mouse poison be more than one ingredient?
But that’s not the case. In fact, poisons can be powder, pastes, and even semi-solids. Most mouse poisons don’t use only one ingredient, but several, using a deadly poisonous element mixed with something delicious to entice them.
What was the number of the poisonous bottle?
Translate the number 0101010101 into decimal to determine which bottle it was. 101010101 = 256 + 64 + 16 + 4 + 1 = 341. Hence, bottle number 341 was the poisonous bottle. Pretty clever, isn’t it? Because there are 10 prisoners and each prisoner has two states (dead or alive), this system has a grand total of 1,024 different combinations.
How can you tell which bottle of wine is poisoned?
Therefore, a unique combination of rats will die telling us which bottle is poisoned. Carrying on, with 3 rats we can actually find the poisoned bottle out of 8 bottles. Table built on the same logic as the ones above. Depending on which rats die and live, we can figure out which bottle was poisoned.
