Home » Ask & Discuss » Mathematics. » Algebra « Back to Discussion

Algebra

Blazing goIITian

Joined:	27 Dec 2010
Post:	1474

11 Feb 2012 08:52:05 IST

0 People liked this

255

beauitful!!

Mathematics

determine the number of ways to choose 5 numbers from the first 18 positive integers such that any 2 differ by at least 2.

Share this article on:

Comments (6)

sathyaram

Blazing goIITian

Joined: 25 Jul 2011

Posts: 322

11 Feb 2012 10:00:25 IST

Like 0 people liked this

136 ?

prahlad kumar sharma

Cool goIITian

Joined: 21 Jul 2010

Posts: 88

11 Feb 2012 10:33:12 IST

Like 0 people liked this

'do hazar do' sahi uttar hain sathyaram bhai !

sathyaram

Blazing goIITian

Joined: 25 Jul 2011

Posts: 322

11 Feb 2012 14:30:21 IST

Like 0 people liked this

patha nehi kaisse karna hai???madhad karo bhai!

Pls be active in gmail.I want to tlk with u personally...

hemang

Blazing goIITian

Joined: 27 Dec 2010

Posts: 1474

11 Feb 2012 23:41:01 IST

Like 0 people liked this

since the answer has already been told by prahlad, i will give the solution.

it is a tough problem.so don't get disheartened.

for any selection of 5 integers from the first 18 positive integers, we can make a unique set of 5 integers whch lie lower than or equal to 14 satisfying the given conditions.

i will tell you how.

suppose we chose {18,17,16,15,14}

we can do {14,15-3,16-6,17-9,18-12} = {14,12,10,8,6} which satisfies our condition.

so we get a one - one mapping between any selection from the first 18 integers to a unique correspondance in 1 - 14.

i need prahlad to prove the uniqueness part (if it exists!!!)

do it prahlad bhai!

Abhishek Bandiya

Cool goIITian

Joined: 7 Jul 2011

Posts: 59

12 Feb 2012 01:20:55 IST

Like 0 people liked this

i dont know i am right or wrong but i want to say

i think we have to select such numbers in which difference in any two is greater than or equal to 2

i.e suppose if we choose any number say 12 than we cant choose 11 and 13

we cant choose its neighbouring number

it is like 18 persons are sitting and we have to choose 5 in which no two are neighbour

now it is very easy, because it is equal to selection of five seats out of 14 seats

i.e.

so answer 2002

sathyaram

Blazing goIITian

Joined: 25 Jul 2011

Posts: 322

15 Feb 2012 17:24:46 IST

Like 0 people liked this

out of 14...How?

Quick Reply

Reply

	Some HTML allowed.
	Keep your comments above the belt or risk having them deleted.
	Signup for a avatar to have your pictures show up by your comment
	If Members see a thread that violates the Posting Rules, bring it to the attention of the Moderator Team