# king prisoner poison bottle puzzle

A king has a cellar of 1000 bottles of delightful and very expensive wine. a neighboring queen plots to kill the bad king and sends a servant to poison the wine. (un) fortunately the bad king’s guards catch the servant after he has only poisoned one bottle. But  the guards don’t know which bottle but know that the poison is so strong that even if diluted 1,000,000 times it would still kill the king. furthermore, it takes one month to have an effect. the bad king decides he will get some of the prisoners  to drink the wine. Being a clever bad king he knows he needs to murder no more than 10 prisoners – believing he can fob off such a low death rate – and will still be able to drink the rest of the wine at his anniversary party in 5 weeks time. Explain how?

Label the wine bottles from 1 to 1000. Each of the bottle number can be represented by a binary 10 bit number (since the maximum that can be represented by 10 bits is 2 power 10 = 1024).
Mark each of prisoners from 1 to 10.

Do the following for each of the bottles 1 to 1000:
Step 1: Take note of the bottle number
Step 2: In binary format check which bits are set to 1 and make those particular numbered persons drink that bottle
Example: Bottle 6 = 00 0000 0110
So person numbered 2 and 3 will drink the bottle.

Say at the end  number 1 and number 4 prisoners are dead which is equivalent to the following binary: 0000001001 which is bottle number 9  in decimal. Bottle numbered 9 is the poisoned bottle.

To increase your chance of living, which prisoner would you want to be?

The most five significant bits are the most interesting because they would always be on from 1001 to 1023. Since there are only 1000 bottles ,so all those people are missing out on 23 bottles of wine that they otherwise would have had to drink. so in order to increase your chance of living, you’d probably want to be prisoner 6 to 10.

prisoner         10 9 8 7 6 5 4 3 2 1
bottle (924)    1 1 1 0 0 1 1 1 0 0
Note that if the king was really trying to kill the least number of prisoners, he should have let 999 prisoners instead of 10 prisoners each take a sip from their respective bottle numerically (if he had that many prisoners at his disposal). that way only one prisoner would die, and there is a chance of 1/1000 that no one would die.