## Medium puzzles

At a party of N people, some have a symmetric friendship. Symmetric means that if A is friends with B, then B is in turn friends with A. Prove that there are at-least two people with same number of friends.

Solution
Source: Top Quant Interview
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p and q are two points chosen at random between 0 & 1. What is the probability that the ratio p/q lies between 1 & 2?

Hint
Solution
Source: Written Test
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Roll a die, and you get paid what the dice shows. But if you want, you can request a second chance & roll the die again; get paid what the second roll shows instead of the first. What is the expected value?

A very innocent monkey throws a fair die. The monkey will eat as many bananas as are shown on the die, from 1 to 5. But if the die shows '6', the monkey will eat 5 bananas and throw the die again. This may continue indefinitely. What is the expected number of bananas the monkey will eat?

Hint
Solution
Source: Self, to show an example of recursive probability
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What is the expected number of coin tosses required to get n consecutive heads?

Hint
Solution
Source: Top Quant Interview
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