Once upon a time in ancient times there was a king who was very found of wines. He had a huge cellar, which had 1000 different varieties of wine all in different caskets (1000 caskets in all). In the adjoining kingdom there was a queen who was envious of the king’s huge wine collection. After some time when she could not bear it any more show conspired to kill her by poisoning all his wine caskets. So she sent one sentry to poison all the caskets, but no sooner had the sentry poisoned only one wine casket, he was caught and killed by the Royal guards. Now the king had a major problem in his hand so as to identify the poisonous casket, which he gave to the Minister. But the situation had two peculiarities.
I: Any one who takes even one drop from the poisonous casket will die.
II: He will die only after one month.
The king also handed over few prisoners to the Minister as “taster” of those caskets, as their lives was of little value.
If the Minister is allowed only 1 month to find out the poisonous casket, what is the minimum number of prisoners he should use as “tasters”?  Choose the correct choice from the following:
A) 1023
B) 1024
C) 1025
D) 1026
E) 1027
Sol:   Study the following table carefully. Each of the prisoners drinks wine from whichever casket has a 1 in his place. If he does not drink there is a 0.   So if no one dies, Casket 1 is poisoned.   If P1 dies, casket 2 is poisoned.   If P1 and P3 die ⇒⇒ casket 6 is poisoned and so on.   So, if there are 3 prisoners, we can differentiate upto 2323 =8 caskets.   So for 1000 caskets [even 1024 caskets], we need only 10 prisoners as 210210 = 1024   Answer 1024
<result>B</result>
Once upon a time in ancient times there was a king who was very found of wines. He had a huge cellar, which had 1000 different varieties of wine all in different caskets (1000 caskets in all). In the adjoining kingdom there was a queen who was envious of the king’s huge wine collection. After some time when she could not bear it any more show conspired to kill her by poisoning all his wine caskets. So she sent one sentry to poison all the caskets, but no sooner had the sentry poisoned only one wine casket, he was caught and killed by the Royal guards. Now the king had a major problem in his hand so as to identify the poisonous casket, which he gave to the Minister. But the situation had two peculiarities.
I: Any one who takes even one drop from the poisonous casket will die.
II: He will die only after one month.
The king also handed over few prisoners to the Minister as “taster” of those caskets, as their lives was of little value.
If the Minister is allowed only 1 month to find out the poisonous casket, what is the minimum number of prisoners he should use as “tasters”?