[Guest]

You have 240 barrels of wine, one of which has been poisoned. After drinking the poisoned wine, one dies within 24 hours. You have 5 slaves whom you are willing to sacrifice in order to determine which barrel contains the poisoned wine. How do you achieve this in 48 hours?

[Guest]

Hi,

I am adding explanation to the Elwa's answer in the comment#23 to make it simple (Explaining about the logic behind it to make it generic).

The trick when you are giving some group of poison bottles to some group of bottle and if they die then you should have enough slaves remaining to pinpoint the bottle in that group.

So here is the solution with bit of more explanation

- If you are using 5 slaves to drink some group of bottles and if they die, you should pinpoint the bottle among the group. So in this case the number of bottles that all the slaves drink is 1. And the combinations of selecting 5 slaves from 5 is 5C5 = 1. So no. of bottles = 1X1 = 1

- If you are using 4 slaves to drink some group of bottle and if they all die, you still have one slave remaining. You can use this slave to see which is poisonous bottle among the group of 2 bottles. And the combinations of selecting 4 slaves from 5 is 5C4 = 5. No. of bottles = 5X2 = 10

- If you are using 3 slaves to drink some group of bottle and if they all die, you still have 2 slaves remaining. You can use these 2 slaves to see which is poisonous bottle among the group of 4 bottles. And the combinations of selecting 3 slaves from 5 is 5C3 = 10. No. of bottles = 10X4 = 40

- If you are using 2 slaves to drink some group of bottle and if they all die, you still have 3 slaves remaining. You can use these slaves to see which is poisonous bottle among the group of 8 bottles. And the combinations of selecting 2 slaves from 5 is 5C2 = 10. No. of bottles = 10X8 = 80

- If you are using 1 slave to drink some group of bottle and if he/she dies, you still have 4 slaves remaining. You can use these slaves to see which is poisonous bottle among the group of 16 bottles. And the combinations of selecting 1 slave from 5 is 5C1 = 5. No. of bottles = 5X16 = 80

So far we used 1+10+40+80+80 = 211 bottles (for the first 24 hours).

In any of the slaves dies in above condition, we can easily figure out the poisonous bottle using the remaining slaves as i mentioned above.

If none of slaves dies, that means the poisonous bottle is among the remaining 29 bottles, and we have 5 slaves remaining. Using the binary combination with 5 slaves 2^5 = 32 >29, we can determine the poisonous bottle among these 29 bottles within the next 24 hours (24-48 hours)

So by the end of 48 hours we can identify the poisonous bottle using the above logic. (As a Note, actually we can identify from max of 243 bottles. Because we have left 3 binary combinations unused in the second step of above solution)