## Medium puzzles

A rabbit sits at the bottom of a staircase with n stairs. The rabbit can hop up only one or two stairs at a time. What kind of sequence is depicted by the different ways possible for the rabbit to ascend to the top of the stairs of length n=1,2,3...?

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Solution

A. B & C live together and share everything equally. One day A brings home 5 logs of wood, B brings 3 logs and C brings none. Then they use the wood to cook together and share the food. Since C did not bring any wood, he gives \$8 instead. How much to A and how much to B?

Hint
Solution
Source: CSEblog
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Suppose you have a hotel which has one floor with infinite number of rooms in a row and all of them are occupied.
1) A new customer wants to check in, how will you accommodate her?
2) What if infinite number of people want to check in, how will you accommodate them?
3) Suppose infinite number of buses arrive at the hotel, each having infinite number of people, how will you accommodate them?

Hint
Solution
Source: CSEblog
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In this gambling game, a player can buy a ticket for Rs 1 on any number from 1 to 6. Three identical and unfair dice are rolled. If the booked number appears on 0, 1, 2 or 3 dice, player wins Rs 0, 1, 2 or 3 respectively, without returning the original Rs 1. What is expected money you can win after buying a ticket for Rs 1?

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Solution
Source: 50 puzzles in prob
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A group has 70 members. For any two members X and Y there is a language that X speaks but Y does not, and there is a language that Y speaks but X does not. At least how many different languages are spoken by the members of this group?

Solution
Source: Quantnet
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