Pigeonhole principle, Mathematics

Assignment Help:

By pigeonhole principle, show that if any five numbers from 1 to 8 are chosen, then two of them will add upto 9.   

Answer: Let make four groups of two numbers from 1 to 8 like that sum the numbers in a group is 9. The groups are as following: (1, 8), (2, 7), (3, 6) and (4, 5). 

Let us refer these four groups like pigeonholes (m). So m = 4. Take the five numbers to be choosen arbitrarily as pigeons that is n = 5. Take a pigeon and put in the pigeonhole according to its value. After placing 4 pigeons, the 5th has to go in one of the pigeonhole. That is by pigeonhole principle has at least one group that will contain [(5-1)/4]+ 1 numbers. So two of the numbers, out of the five selected, will add up to 9.


Related Discussions:- Pigeonhole principle

Convert measurements between the english system, Convert measurements betwe...

Convert measurements between the English system? To convert measurements between the English system and the metric system: 1. Look up the conversion between the two units of

Determine the laplace transform of the probability , 1. Let , where  ar...

1. Let , where  are independent identically distributed random variables according to an exponential distribution with parameter μ. N is a Binomially distribut

Integers, what are 20 integer equations that have multiplication, division,...

what are 20 integer equations that have multiplication, division, subtraction,and additon??

Trignometry, Sin3x ? Solution) THE FORMULA IS RIGHT ,SO sin3x=3sin...

Sin3x ? Solution) THE FORMULA IS RIGHT ,SO sin3x=3sinx-4sin 3 x

Find out the area of the region, Find out the area of the region enclosed b...

Find out the area of the region enclosed by y = x 2 & y =√x . Solution Firstly, just what do we mean by "area enclosed by". This means that the region we're interested in

Find out the center of mass, Find out the center of mass for the region bou...

Find out the center of mass for the region bounded by y = 2sin (2x), y =0 on  the interval  [0 , Π/2] Solution Here is a sketch (diagram) of the region along with the cent

Algebra, prove That J[i] is an euclidean ring

prove That J[i] is an euclidean ring

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd