## Search This Blog

### Challenging Mind puzzle

Challenging Mind puzzles - 23 August

You are the ruler of a medieval empire and you are about to have a celebration tomorrow. The celebration is the most important party you have ever hosted. You've got 1000 bottles of wine you were planning to open for the celebration, but you find out that one of them is poisoned.

The poison exhibits no symptoms until death. Death occurs within ten to twenty hours after consuming even the minutest amount of poison.

You have over a thousand slaves at your disposal and just under 24 hours to determine which single bottle is poisoned.

You have a handful of prisoners about to be executed, and it would mar your celebration to have anyone else killed.

What is the smallest number of prisoners you must have to drink from the bottles to be absolutely sure to find the poisoned bottle within 24 hours?

1. 10. Number the bottles, write that in binary, number prisoners from 1 to 10. Prisoner i drinks bottle n if bit i of n is 1. Each dead prisoner tells you that bit i of poisoned bottle is 1. q

2. 10. because 2^10 >1000. use binary.
label 10 prisoners 1 to 10.
prisoner 1 will drink from the bottle whose number has lowermost bit set.

3. 10 prisoners must sample the wine. Bonus points if you worked out a way to ensure than no more than 8 prisoners die.

Number all bottles using binary digits. Assign each prisoner to one of the binary flags. Prisoners must take a sip from each bottle where their binary flag is set.

Here is how you would find one poisoned bottle out of eight total bottles of wine.

Bottle 1 Bottle 2 Bottle 3 Bottle 4 Bottle 5 Bottle 6 Bottle 7 Bottle 8
Prisoner A X X X X
Prisoner B X X X X
Prisoner C X X X X
In the above example, if all prisoners die, bottle 8 is bad. If none die, bottle 1 is bad. If A & B dies, bottle 4 is bad.

With ten people there are 1024 unique combinations so you could test up to 1024 bottles of wine.

Each of the ten prisoners will take a small sip from about 500 bottles. Each sip should take no longer than 30 seconds and should be a very small amount. Small sips not only leave more wine for guests. Small sips also avoid death by alcohol poisoning. As long as each prisoner is administered about a millilitre from each bottle, they will only consume the equivalent of about one bottle of wine each.

Each prisoner will have at least a fifty percent chance of living. There is only one binary combination where all prisoners must sip from the wine. If there are ten prisoners then there are ten more combinations where all but one prisoner must sip from the wine. By avoiding these two types of combinations you can ensure no more than 8 prisoners die.

1. I don't understand what you do withcyhe 8 bottles? How do we find out at one go?

2. he copied it from a website... he himself didn't understand it. noob.

3. don't just tell us dush

4. Explaination as simple as it can be: You have only one chance to observe the results, becouse it will need 20 hours to be absolutely sure. The prisoner then is dead(1) or alive(0). Mark 10 of the prisoners with labels from 0 to 9. Mark the bottles with labes from 1 to 1000. Then you have the to ready the sample each one should drink. Lets say you want to make the sample for the 666 bottle. In binary its 1010011010 so give it to prisoner 1,3,4,7,9.(Its 2^1+2^3+2^4+2^7+2^9 if you dont get how binnary works). One single drop will be enough. So at the end if only 1,3,4,7,9 are dead, you should not open bottle No 666, unless maybe your mother in law is at the party. If prisoner 2 is dead too, this means that sample given to 1010011110 is bad. That means you throw bottle 670 (2^1+2^2+2^3... damn im lazy). For that with the 8 guys: bottles 991,959,895,767,511 are EXTREMELY bad for your prisoners :)

4. 10 ..Alternate solution.
------------------------
Arrange the bottles in the form of cube of dimension 10*10*10.
Choose 10 prisners and make them drink bottles in all the three dimensional arranegement. Now,after 24 hrs see, who are the prisoner died, now, depending upon the intersectin value of their axes, you can find the bottle which has the poison in it.

1. This comment has been removed by the author.

5. it cant be 10 sir. how would you know if which bottle has the poison, the symptoms or even death will take effect within 10 to 24 hours.. and you only have 24 hours to figure this out :)

6. 30 and only 3 need to die.
Same answer as above i.e 3D. You need 10 from each dimension. So call them X1-10, Y1-10 and Z1-10. Now your poisoned bottle is A? B? and C? of the 3 dead.

1. Extremely elegant solution. :)

7. i meant X?, Y? and C? :)

Since it has mentioned the person will die within 20 minutes.Ine one hour there is three cycle of 20 minutes and in 24 hours there will be 72.So you can make a slave drink diferrent bottles at interval of 20 minutes.Since minutest amount of poison can kill no need to make them drink more than one drop.
No two slaves will taste same bottle.
So by using 14 slaves you can make taste 1008 bottles in 24 hours.

9. @saidas, read the question again...

"Since it has mentioned the person will die within 20 minutes."????

10. well take the bottles divide it into 10 rows of 100 take 10 prisoners to drink a sip in a single row when on dies take the row and take the same 9 guys and add another prisoner to make 10, 11 men so far and divide it into 10 rows of ten then take the row from the guy who died and those ten are the last ones i think you can make due with 990 bottles of wine
hope it takes 10 hrs for each guy to die
not the best way i know but it is the simplest

11. 30 prisoners, if you design a grafic with x(10),y(10),z(10) where the prisoners are each number of a column and make them drink 100 potion each . based of who dies in each column you can determine the cordinate of the poison

12. the answer is 12, a ,b , and c . 12:4. you can easily determine what bottle is poisoned. :D

13. i would have said 20. have them stand in 2 rows of 10 to form a grid. and put all 100 bottles out. after each prisoner has drank their sips from 10 bottles then whichever two die you'd cross reference them on the grid to find the poisoned bottle

1. 5 rows of 200 in 2D gives you a better result. that's 10 slaves up front (5 from each dimension) which gives you an intersection of 4 bottles when 2 of the slaves die. now test 3 of the 4 left, and you have your answer for a total of 13

14. The correct answer is 33 prisoners. As the question asks the minimum number of prisoners, so the minimum time to die will be considered i.e 10 hrs. So in 24 hrs one prisoner can be tested twice. So considering 33 prisoners, each prisoner will be given 31 bottles to taste. 33*31= 1023. So 23 prisoners will be given 30 bottles and rest 10 will be given 31 bottles. After 10 hrs one prisoner will die. Balance prisoner left = 32. Balance time left = 14 hrs. Give rest 32 prisoner 1 bottle each. One prisoner will not receive any bottle as there are 31 bottles. After 10 hrs the bottle with poison will be identified as the prisoner will die. Still time left for kings party is 4 hrs.

1. Logic fail. It asks the minimum prisoners for ANY CIRCUMSTANCE, i.e. including the possibility that deaths take more than 10 hours.

Even if they all did die in 10 hours, your answer would be wrong; you can do it with 10 prisoners.

15. I figured out this solution using the 3D cube model that some of the others are talking about so the solution is 28 (30-2=28 since there is an overlap). For those that dont understand, arrange bottles into a 10x0x10 cube and have the prisoners correspond to the length, height and width. You will find that this requires 28 prisoners and your poisoned bottle can be pinpointed from your dead prisoners.

Sadly I found myself outdone when someone suggested using a binary system which means only 10 prisoners is sufficient to pinpoint the location
2^10=1024 unique combinations
Each bottle will be assigned a unique binary combination and label your prisoners for ease
Eg
ABCDEFGHIJ
And when the binary number =1 then the prisoner must drink
So let's say the combination for the first bottle is assigned 0000000001 then the prisoner at the 10th position (prisoner J) must drink
If the combination is 0001101100 then prisoner at the 4,5th position ED and 7,8th position GH must drink
Since each combination is unique, if the above combination was the poisoned wine then only EDGH will die and thus we know which bottle is poisoned

16. Yeah I'm not very smart..................

17. Just Think About ItMay 31, 2013 at 5:06 AM

They didn't have binary in medieval times...

1. Totally agree! Why doesn't someone post the solution just with logic and regular numbers so that everybody understands it?

2. first let us take 1 prisoner,he can drink one bottle if its poisoned he will die.so this way u will need 1000 prisoners
Take 2 prisoners and name them as a1,a2
their group
is like
a1
a2
a1,a2
none total:4=2^2
and make this four groups drink 4 bottles(named) if a2 alone dies u can identify that bottle

Take 3 prisoners a1,a2,a3.group them as
a1
a2
a3
a1,a2
a2,a3
a1,a3
a1,a2,a3
none total:8=2^3 if a1,a2 alone dead that wine bottle is poisoned

so to test 1000 bottle
2^n>1000

18. He is a King so i think he is rich enough to bring another 1000 wine bottles!!! Lol noob king

19. 1 prisoner
Because if the king gives a fews drops of wine to each
prisoner from a bottle (one bottle for each prisoner)
the prisoner who dies will show the corresponding bottle.

20. If I am the ruler, I will organise another 3000 bottles, 1000 for guest, 1000 for slaves & 1000 for prisnors, Lets enjoy everyone why to die to anyone????

21. One problem we are in medieval times so we won't be using binary numbers because we are too stupid!

22. what do the slaves have to do with it? How about, zero prisoners used or dead. Just serve up the wine, 1/1000 chance of being poisoned, likelyhood ~3 guests dead. You would get away with that in medieval times!

Correct answer is 10 for fewest prisoners used, vs 999 prisoners if you wanted fewest dead.

23. got to admit both the cube and the binary was better than my solution which required 32 people and required throwing out 2 bottles as it didn't pinpoint the bottle. arrange it as a 32*32 square with some empty spots empty(31 rows of 32 and 1 row of 8). number each prisoner 1-32 and assign them to a specific row and column. each prisoner drinks from each bottle in their row and column. if only prisoner n dies then the bottle at (n,n) is poisoned. otherwise if n and m die then either the bottle at (n,m) or (m,n) is poisoned. throw them both out and call it a day. still don't think the question hurt me too badly during my interview.

24. Number all bottles and prisoners 1 to 1000. Have every prisoner take 1 sip from their respective bottle. 1 Death.

25. Did they even have Binary system in Medieval times... :P :P

26. You need only 4 prisoners and only 1 of them will die. Here is how. Read full.

Guys stop using binary. You are all overthinking this.

None of you used the part where it says that the prisoner dies after 10-20 hours.

So here is the answer based on sequential time arrangement.

For Example if Prisoner 1 drinks Wine 1 at 0000 hours then he will die between 1000 to 2000 hours. So if you say that you want the sample to be taken after every hour then one prisoner can only drink 5 wines after every hour so that the last wine he drinks at 0400 hours will kill him between 1400 to 2400 hours.

All you need to do is record the time of death of the prisoner and you will know exactly which wine was it and only one prisoner will die.

For hourly sampling you will need 200 prisoners. For hour hourly sampling you will need 100 prisoners and for every minute you will need just 4 prisoners out of which only 1 prisoner will die.

Good Day.

27. 1? Have each drink from a bottle and the bottle of the one who dies is the poisoned one?

28. Also your method wont work @Ahmad. What if he drinks one at 00 hours and one at 001 hours, and dies at 0019 hours? How will we know which bottle killed him?