**Google Interview Puzzles**

**1)**You have to get from point A to point B. You don’t know if you can get there. What would you do?

**2)**Imagine you have a closet full of shirts. It’s very hard to find a shirt. So what can you do to organize your shirts for easy retrieval?

**3)**What method would you use to look up a word in a dictionary?

**4)**Every man in a village of 100 married couples has cheated on his wife. Every wife in the village instantly knows when a man other than her husband has cheated, but does not know when her own husband has. The village has a law that does not allow for adultery. Any wife who can prove that her husband is unfaithful must kill him that very day. The women of the village would never disobey this law. One day, the queen of the village visits and announce that at least one husband has been unfaithful. What happens?

**5)**You have eight balls all of the same size. 7 of them weigh the same, and one of them weighs slightly more. How can you fine the ball that is heavier by using a balance and only two weighings?

**6)**How do you cut a rectangular cake into two equal pieces when someone has already taken a rectangular piece from it? The removed piece an be any size or at any place in the cake. You are only allowed one straight cut.

**7)**How many piano tuners are there in the entire world?

**8)**What gives you joy?

**9)**Mike has $20 more than Todd. How much does each have given that combined they have $21 between them. You can’t use fractions in the answer. Hint: This is a trick question, pay close attention to the condition)

**10)**How many times a day a clock’s hands overlap?

**11)**Two MIT math graduates bump into each other. They hadn’t seen each other in over 20 years.

The first grad says to the second: “how have you been?”

Second: “Great! I got married and I have three daughters now”

First: “Really? how old are they?”

Second: “Well, the product of their ages is 72, and the sum of their ages is the same as the number on that building over there..”

First: “Right, ok.. oh wait.. I still don’t know”

second: “Oh sorry, the oldest one just started to play the piano”

First: “Wonderful! my oldest is the same age!” Problem: How old are the daughters?

**12)**If you look at a clock and the time is 3:15, what is the angle between the hour and the minute hands? (The answer to this is not zero!)

**13)**Four people need to cross a rickety rope bridge to get back to their camp at night. Unfortunately, they only have one flashlight and it only has enough light left for seventeen minutes. The bridge is too dangerous to cross without a flashlight, and it’s only strong enough to support two people at any given time. Each of the campers walks at a different speed. One can cross the bridge in 1 minute, another in 2 minutes, the third in 5 minutes, and the slow poke takes 10 minutes to cross. How do the campers make it across in 17 minutes?

**14)**If the probability of observing a car in 30 minutes on a highway is 0.95, what is the probability of observing a car in 10 minutes (assuming constant default probability)?

**15)**In a country in which people only want boys, every family continues to have children until they have a boy. if they have a girl, they have another child. if they have a boy, they stop. what is the proportion of boys to girls in the country?

**16)**You have an empty room, and a group of people waiting outside the room. At each step, you may either get one person into the room, or get one out. Can you make subsequent steps, so that every possible combination of people is achieved exactly once?

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