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Score Points: 3

You work for the census bureau. You call a random phone number and learn that the household has exactly two children and at least one of them is a girl. What is the probability that they are both girls?

5 Solvers
Score Points: 3

My wife and I recently attended a party at which there were four other couples. Various handshakes took place. No one shook hands with himself/herself or with his/her spouse, and no one shook hands with the same person twice. After all handshakes were over, I asked each person, including my wife, how many hands he/she had shaken. They all gave me a different answer. How many hands did my wife shake?

6 Solvers
Score Points: 5

45 Natives in a certain colony have a myth that there is a certain disease signalled by a blue mark on their forehead. All the natives have blue marks. If they find out that they have the disease, they must declare it the same day in the town hall meeting, and leave the colony. However, no one else tells others if they have a blue mark out of courtesy. One day, a foreigner comes in, and tells the whole society that he has seen at least one blue mark in the colony. If the day the foreigner came was day 1, on what day will the first person leave the village?

12 Solvers
Score Points: 2

There are three people standing in a queue so that the last person can see both people in front, the middle person can see one person in front, and the first person can't see anyone. Three hats, chosen out of three red and two blue hats, are placed one each on their head. The last person is asked the colour of hat on his head, and he says "I don't know". The middle person is asked the same and he also says "I don't know". Is it possible for the first person to answer “I know”? If yes, enter 0. If no, enter 1.

8 Solvers
Score Points: 5

10 prisoners are given a chance of survival by the jailer. The jailer tells them that the next morning, he will have them stand in a queue (so that the last person can see the nine people in front, the second last people can see eight people in front of him, and so on), and then place either a red hat or a purple hat on each person's head. The person hence will be able to see the color of hat for people in front of him (but not his own hat). The jailer will then start from the last person, and ask each person "What is the color of hat on your head". The person can answer "red" or "purple".

10 Solvers

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