Question

What is Pigeonhole Principle?

Answer 1

Are you still there?

Answer 2

I guess not...

Answer 3

Hmmm.I think its when some x terms are are put into n pigeonholes where x is always greater than n...so 1 pigeonhole must contain more than 1 x item .........

Answer 4

u mean the text way or your mathematical term bhaiya??

Answer 5

Basically it says:
When you have n items to be placed in n-1 locations, at least one location will contain two or more items.
Example: if you try to put 10 pigeons in 9 holes, you will end up with at least one pigeonhole containing 2 or more pigeons.

Example quiz using the pigeonhole principle:

Five points are marked on a sphere. Show that it is always possible to draw a circle on the surface of the sphere such that at least four points are on one side of the circle. Assume that a point on the circle itself is considered to be on either side.

Answer 6

Ishaan, exercise for you, prove that in a group of 6 people there must be at least 2 people who has same amount of friends.

Do you need to know this principle for JEEEE?

Answer 7

formulation and examples.If n pigeons are put into m pigeonholes (n greater than m), there's a hole with more than one pigeon

Answer 8

Correction to formulation of example problem.
Five points are marked on a sphere. Show that there is a hemisphere that contains at least four points, assuming that points at the intersection of the hemispheres is considered to be on both hemispheres.

Answer 9

Another one:
Five points are drawn inside of a square of side 1 cm. Show that there are two points which are less than 0.75 cm apart.

Answer 10

It has 4 forms. The basic one says that if there are nk + 1 pigeons and n pigeonholes then there are at least k pigeons in 1 pigeonhole.