Easy | Discrete Maths |

There are 10 black socks and 10 white socks (no left-right distinction) in the wardrobe. Your task is to draw the minimum number of socks at random to be sure you have a pair of a single color. How many socks should you draw?

Hint

Pigeonhole principle

Answer

3

Solution

This is the easiest example of a very powerful tool called the Pigeonhole principal, which says that if there are (N+1) pigeons to fit in N holes, atleast one hole will have 2 or more pigeons. Hence, if you pick 3 socks to come with 2 color categories, at least one category will have 2 or more socks, i.e. a pair is guaranteed with either red or black color.

Source: Common

Enable Like and Comment Easy | Discrete Maths |

Assuming that temperature varies continuously, prove that there are always two opposite points on the Earth's surface that have the same temperature.

Solution

Aritro Pathak: consider any great circle.. T(x) is the temp at the point x .. let f(x)=T(x)-T(x+pi), then f(0)=T(0)-T(pi)..f(pi)=T(pi)-T(2pi)=T(pi)-T(0) then f(0) and f(pi) have different signs, so using mean value theorem, you have that f is 0 at some point.

FunFact: There are uncountable number of such pairs.

Here is a video explanation:

https://www.youtube.com/watch?v=5Px6fajpSio

An alternate version of this puzzle is the Mountain Man

http://www.techinterview.org/post/521419748/mountain-man

FunFact: There are uncountable number of such pairs.

Here is a video explanation:

https://www.youtube.com/watch?v=5Px6fajpSio

An alternate version of this puzzle is the Mountain Man

http://www.techinterview.org/post/521419748/mountain-man

Source: Top Quant Interview

Enable Like and Comment Medium | Discrete Maths |

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...?

Hint

Recursion

Answer

Fibonacci Sequence.

Solution

Suppose f(n) are the number of ways to reach nth stair. Notice that the final hop is either a single jump or double jump, i.e. its from (n-1)th stair or (n-2)th. Thus f(n) = f(n-1) + f(n-2), where f(0)=f(1)=1. This is Fibonacci sequence.

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

Its not 5 & 3

Solution

Since each person consumed 8/3 woods. A gave 5-8/3 = 7/3 woods to C and B gave 3-8/3 = 1/3 woods to C.

So, Out of the 8 dollars, A gets 7 and B gets 1

So, Out of the 8 dollars, A gets 7 and B gets 1

Source: CSEblog

Enable Like and Comment 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

8 choose 4 is 70

Source: Quantnet

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