You have 3 jars that are all mislabeled. One jar contains Apples, another contains Oranges and the third jar contains a mixture of both Apples and Oranges.
You are allowed to pick as many fruits as you want from each jar to fix the labels on the jars. What is the minimum number of fruits that you have to pick and from which jars to correctly label them?

Let's take a scenario. Suppose you pick from jar labelled as Apples and Oranges and you got Apple from it. That means that jar should be Apples as it is incorrectly labelled. So it has to be Apples jar.
Now the jar labelled Oranges has to be Mixed as it cannot be the Oranges jar as they are wrongly labelled and the jar labelled Apples has to be Oranges.
Similar scenario applies if it's a Oranges taken out from the jar labelled as Apples and Oranges. So you need to pick just one fruit from the jar labelled as Apples and Oranges to correctly label the jars.

General Custer is surrounded by Indians and he's the only cowboy left.
He finds an old lamp in front of him and rubs it. Out pops a genie. The genie grants Custer one wish, with a catch. He says, "Whatever you wish for, each Indian will get two of the same thing." Custer ponders a while and thinks:"If I get a bow and arrow they get two. If I get a rifle they get two!" He then rubs the bottle again and out pops the genie. "Well," the genie asks "have you made up your mind?"
What did Custer ask for to help him get away?

It was a Pink Island. There were 201 individuals (perfect logicians) lived in the island. Among them 100 people were blue eyed people, 100 were green eyed people and the leader was a black eyed one.
Except the leader, nobody knew how many individuals lived in the island. Neither have they known about the color of the eyes. The leader was a very strict person. Those people can never communicate with others. They even cannot make gestures to communicate. They can only talk and communicate with the leader. It was a prison for those 200 individuals.
However, the leader provided an opportunity to leave the island forever but on one condition. Every morning he questions the individuals about the color of the eyes! If any of the individuals say the right color, he would be released. Since they were unaware about the color of the eyes, all 200 individuals remained silent. When they say wrong color, they were eaten alive to death. Afraid of punishment, they remained silent.
One day, the leader announced that "at least 1 of you has green eyes! If you say you are the one, come and say, I will let you go if you are correct! But only one of you can come and tell me!"
How many green eyed individuals leave the island and in how many days?

All 100 green eyed individuals will leave on the 100th night.
Consider, there is only one green eyed individual lived in the island. He will look at all the remaining individuals who have blue eyes. So, he can get assured that he has green eyes!
Now consider 2 people with green eyes. Only reason the other green-eyed person wouldn't leave on the first night is because he sees another person with green eyes. Seeing no one else with green eyes, each of these two people realize it must be them. So both leaves on second night.
This is the same for any number. Five people with green eyes would leave on the fifth night and 100 on the 100th, all at once.
Search: Monty Hall problem
Why it's important for the solution that the leader said the new information "at least 1 of you has green eyes", when they must knew from the beginning, that there are no less than 99 green-eyed people on the island? Because they cannot depart the island without being certain, they cannot begin the process of leaving until the guru speaks, and common knowledge is attained.
Search: Common knowledge (logic)

Four people need to cross a rickety bridge at night. Unfortunately, they have only one torch and the bridge is too dangerous to cross without one. The bridge is only strong enough to support two people at a time. Not all people take the same time to cross the bridge. Times for each person: 1 min, 2 mins, 7 mins and 10 mins. What is the shortest time needed for all four of them to cross the bridge?

It is 17 mins.
1 and 2 go first, then 1 comes back. Then 7 and 10 go and 2 comes back. Then 1 and 2 go again, it makes a total of 17 minutes.

The Pope, Beyonce, POTUS, and Bill Gates are on the same plane.
There are only 3 parachutes left for the 4 of them.
POTUS says: "As the President, I think I should have the right to have a parachute, because I rule millions of people in the greatest nation of all."
Beyonce says: "As one of the greatest singers of all-time, I think I should deserve to be safe. I bring tears and laughter to millions of people, and I'm an important contributor to pop music."
Bill Gates says: "As one of the richest successful company owners, I think I should live because I'm on top of the economics cycle, creating jobs and incomes for millions of people. I am a wealthy and intelligent man."
Finally, the Pope says: "I'm an old, religious man. I lived a life that's full, I helped millions of people find their way through God, I'm ready to let go of a parachute and to face my fate."
Which one of them will abandon the parachute and die?

Did I ever mention that the plane was crashing? No one's gonna die.

A bad 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.
Fortunately (or say unfortunately) the bad king's guards catch the servant after he has only poisoned one bottle.
Alas, the guards don't know which bottle but know that the poison is so strong that even if diluted 100,000 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 in his vast dungeons 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 (999 bottles) at his anniversary party in 5 weeks time.
Explain what is in mind of the king, how will he be able to do so?

Think in terms of binary numbers. (now don’t read the solution, give a try).
Number the bottles 1 to 1000 and write the number in binary format.
bottle 1 = 0000000001 (10 digit binary)
bottle 2 = 0000000010
bottle 500 = 0111110100
bottle 1000 = 1111101000
Now take 10 prisoners and number them 1 to 10, now let prisoner 1 take a sip from every bottle that has a 1 in its least significant bit. Let prisoner 10 take a sip from every bottle with a 1 in its most significant bit. etc.
prisoner = 10 9 8 7 6 5 4 3 2 1
bottle 924 = 1 1 1 0 0 1 1 1 0 0
For instance, bottle no. 924 would be sipped by 10,9,8,5,4 and 3. That way if bottle no. 924 was the poisoned one, only those prisoners would die.
After four weeks, line the prisoners up in their bit order and read each living prisoner as a 0 bit and each dead prisoner as a 1 bit. The number that you get is the bottle of wine that was poisoned.
1000 is less than 1024 (2^10). If there were 1024 or more bottles of wine it would take more than 10 prisoners.

In olden days you are a clever thief charged with treason against the king and sentenced to death.
But the king decides to be a little lenient and lets you choose your own way to die.
What way should you choose?
Remember, you're clever!

Your friend pulls out a perfectly circular table and a sack of quarters, and proposes a game.
"We'll take turns putting a quarter on the table," he says. "Each quarter must lay flat on the table, and cannot sit on top of any other quarters. The last person to successfully put a quarter on the table wins."
He gives you the choice to go first or second. What should you do, and what should your strategy be to win?

You should go first, and put a quarter at the exact center of the table.
Then, each time your opponent places a quarter down, you should place your next quarter in the symmetric position on the opposite side of the table.
This will ensure that you always have a place to set down our quarter, and eventually your oppponent will run out of space.

You have two jugs, one that holds exactly 3 gallons, and one that holds exactly 5 gallons. Using just these two jugs and a fire hose, how can you measure out exactly 4 gallons of water?

Fill the 5-gallon jug to the top, and then pour it into the 3-gallon jug until the 3-gallon jug is full. You now have 2 gallons remaining in the 5-gallon jug. Pour out the 3-gallon jug, and then pour the 2 gallons from the 5-gallon jug into the 3-gallon jug. Finally, fill the 5-gallon jug to the top and pour it into the 3-gallon jug until it's full. Since there was only space left for 1 more gallon in the 3-gallon jug, you now have exactly 4 gallons in the 5-gallon jug.