Microsoft Interview Puzzles

This was astronaut Jose Perez’s fourth visit to Mars
and he had learned to speak Martian. He wanted to
find his Martian friend Doman, but in order to locate
him he had to know what group Doman belonged to.
The three groups in the area were: Uti, Yomi, and
Grundi.
The Uti always told the truth.
The Yomi always lied.
The Grundi sometimes told the truth but sometimes
lied.
Perez needed information. Three Martians, Aken, Bal
and Cwos, each of whom belonged to a different group,
agreed to help him. He asked each one of them two
questions: What group do you belong to? What group
does Doman belong to?
1. Aken said:
I am not a Uti.
Doman is a Yomi.
2. Bal said:
I am not a Yomi.
Doman is a Grundi.
3. Cwos said:
I am not a Grundi.
Doman is a Uti.
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You have 8 balls. One of them is defective and weighs less than others. You have a balance to measure balls against each other. In 2 weighing, how do you find the defective one?
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You have two jars, 50 red marbles and 50 blue marbles. You need to place all the marbles into the jars such that when you blindly pick one marble out of one jar, you maximize the chances that it will be red. When picking, you’ll first randomly pick a jar, and then randomly pick a marble out of that jar. You can arrange the marbles however you like, but each marble must be in a jar.
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100 prisoners are stuck in the prison in solitary cells. The warden of the prison got bored one day and offered them a challenge. He will put one prisoner per day, selected at random (a prisoner can be selected more than once), into a special room with a light bulb and a switch which controls the bulb. No other prisoners can see or control the light bulb. The prisoner in the special room can either turn on the bulb, turn off the bulb or do nothing. On any day, the prisoners can stop this process and say “Every prisoner has been in the special room at least once”. If that happens to be true, all the prisoners will be set free. If it is false, then all the prisoners will be executed. The prisoners are given some time to discuss and figure out a solution. How do they ensure they all go free?
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A certain town comprises of 100 married couples. Everyone in the town lives by the following rule: If a husband cheats on his wife, the husband is executed as soon as his wife finds out about him. All the women in the town only gossip about the husbands of other women. No woman ever tells another woman if her husband is cheating on her. So every woman in the town knows about all the cheating husbands in the town except her own. It can also be assumed that a husband remains silent about his infidelity. One day, the mayor of the town announces to the whole town that there is at least 1 cheating husband in the town. What do you think happens?
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People are waiting in line to board a 100seat airplane. Steve is the first person in the line. He gets on the plane but suddenly can’t remember what his seat number is, so he picks a seat at random. After that, each person who gets on the plane sits in their assigned seat if it’s available, otherwise they will choose an open seat at random to sit in.
The flight is full and you are last in line. What is the probability that you get to sit in your assigned seat?
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