Medium puzzles




Medium Discrete Maths

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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Medium Strategy

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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Medium Probability

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?

Hint
Answer
Solution
Source: 50 puzzles in prob
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Medium Discrete Maths

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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Medium Probability

A and B are in a team called AB, playing against C. If AB team wins it gets Rs 3, nothing otherwise.

Game is: A and B are placed in 2 separate rooms far away. A will toss a coin and B will also toss a coin; A will have to guess outcome of B's toss and B will guess A's. If both guesses are right, team AB wins Rs 3, nothing otherwise.
Should they play the game, by giving Rs 1 in start to C.

Hint
Answer
Solution
Source: Top Quant Interview
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