Sock

Probability Level 2

A men wears socks of two colours - black and white. He has altogether 20 black and 10 white socks in the drawer. Supposing he has to take out the socks in dark, how many must he take out to be sure that he has a matching pair? Find the minimum number of socks. Not assuming luck.

The answer is 3.

2 solutions

Shreyansh Mukhopadhyay
Feb 4, 2018

The socks are in the sets of $\boxed {2}$ colors -black and white. So, accoding to the Pigeonhole Principle to ensure atleast $\boxed1$ matching pair, we need $\boxed 3$ socks.

@Shreyansh Mukhopadhyay

Abe maine thoda PHP kya kiya school me tu toh uske piche hi padh gaya. Chl kal mai tujhe Congruences par probs dunga that 's the real stuff boi !!

Ayon Ghosh - 3 years, 4 months ago

did you check that question $24|n^2+23$

Shreyansh Mukhopadhyay - 3 years, 4 months ago

@Shreyansh Mukhopadhyay Sahi hai bhai. Chl ek aur deta hu : find all solutions to $x^4-2y^2 = 1$ . Aur net se mat tapna plz.

Ayon Ghosh - 3 years, 4 months ago

@Ayon Ghosh – are x and y both integers? ; Check my new question

Shreyansh Mukhopadhyay - 3 years, 4 months ago

@Shreyansh Mukhopadhyay – Yes bruh.obviously dono integers hi honge na...

Ayon Ghosh - 3 years, 4 months ago

@Ayon Ghosh – Bana ki nahi ? Around 5 baje prob diya tha abhi to 9 baj gaye.

Ayon Ghosh - 3 years, 4 months ago

@Ayon Ghosh – almost ban gaya

Shreyansh Mukhopadhyay - 3 years, 4 months ago

@Shreyansh Mukhopadhyay – Chl thike kal school me batana, Btw chl ek final easy problem deta hu jo tujhse 2 min me Maggi ki tarah ban jana chahiye. Surprisingly it is from IberoAmerican MO 1988 Problem 1....

A Triangle has its sides in A.P. and also altitudes in AP prove it is equilateral hahaha.

Ayon Ghosh - 3 years, 4 months ago

Suresh Jh
Feb 3, 2018

When he will take an odd number of socks then he will get all same or one different and other same or some such cases. So minimum odd number 3, you will get all same then you will get a pair, or one different other same then you will have 2 socks same colour then you will get a pair. No other cases are possible. This can also be clarified by the pigeonhole principle.