Problem!!!(BOMC-2)
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Let $a_1, a_2,... a_{20}$ be distinct positive integers not exceeding $70$. Show that there is some $k$
so that $a_i$ $-a_j$ = $k$ for four different pairs ($i, j$).
Edited, comment:Sorry, I didn't Latex the minus sign
so that $a_i$ $-a_j$ = $k$ for four different pairs ($i, j$).
Edited, comment:Sorry, I didn't Latex the minus sign
You spin my head right round right round,
When you go down, when you go down down......(-$from$ "$THE$ $UGLY$ $TRUTH$" )
When you go down, when you go down down......(-$from$ "$THE$ $UGLY$ $TRUTH$" )
Re: Problem!!!(BOMC-2)
$(i,j)$ and $(j,i)$ are different pairs for $i \not = j$, are not they?
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Nur Muhammad Shafiullah | Mahi
Use $L^AT_EX$, It makes our work a lot easier!
Nur Muhammad Shafiullah | Mahi
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Re: Problem!!!(BOMC-2)
The question didn't say ordered pairs...*Mahi* wrote:$(i,j)$ and $(j,i)$ are different pairs for $i \not = j$, are not they?
You spin my head right round right round,
When you go down, when you go down down......(-$from$ "$THE$ $UGLY$ $TRUTH$" )
When you go down, when you go down down......(-$from$ "$THE$ $UGLY$ $TRUTH$" )
Re: Problem!!!(BOMC-2)
When you use first brackets, the convention is to assume $(i,j)\neq (j,i)$. If you wanted to mean "not ordered pair" you could have used $\{i,j\}$ to remove the confusion.
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Use $L^AT_EX$, It makes our work a lot easier!
Nur Muhammad Shafiullah | Mahi
Use $L^AT_EX$, It makes our work a lot easier!
Nur Muhammad Shafiullah | Mahi
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Re: Problem!!!(BOMC-2)
Sorry , actually I just wrote what i saw in the question. And that's why I'm not confidently saying that the question doesn't mean ordered pairs...*Mahi* wrote:When you use first brackets, the convention is to assume $(i,j)\neq (i,j)$. If you wanted to mean "not ordered pair" you could have used $\{i,j\}$ to remove the confusion.
You spin my head right round right round,
When you go down, when you go down down......(-$from$ "$THE$ $UGLY$ $TRUTH$" )
When you go down, when you go down down......(-$from$ "$THE$ $UGLY$ $TRUTH$" )
Re: Problem!!!(BOMC-2)
Have you solved it yet? (If you have, with/without ordered pairs?)
Please read Forum Guide and Rules before you post.
Use $L^AT_EX$, It makes our work a lot easier!
Nur Muhammad Shafiullah | Mahi
Use $L^AT_EX$, It makes our work a lot easier!
Nur Muhammad Shafiullah | Mahi
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Re: Problem!!!(BOMC-2)
I found this problem in an N.T. work sheet.I couldn't remember how far i went then and even if I've solved this problem I've completely forget about that. Besides actually i want to see a nice solution of this problem....*Mahi* wrote:Have you solved it yet? (If you have, with/without ordered pairs?)
(and actually ordered pairs doesn't matter that much as if $a_i-a_j=k=a_j-a_i$ will imply $a_i=a_j$ and contradiction, so it's easy to guess we should work with only pairs )
You spin my head right round right round,
When you go down, when you go down down......(-$from$ "$THE$ $UGLY$ $TRUTH$" )
When you go down, when you go down down......(-$from$ "$THE$ $UGLY$ $TRUTH$" )
Re: Problem!!!(BOMC-2)
Sorry, a hour's load shedding
Yes, I figured that out then. But there must be $21$ elements in the set otherwise a contradiction can be built.
Solution:
For $20$ elements,contradiction:
I hope you will edit the question.
Yes, I figured that out then. But there must be $21$ elements in the set otherwise a contradiction can be built.
Solution:
Please read Forum Guide and Rules before you post.
Use $L^AT_EX$, It makes our work a lot easier!
Nur Muhammad Shafiullah | Mahi
Use $L^AT_EX$, It makes our work a lot easier!
Nur Muhammad Shafiullah | Mahi
- Phlembac Adib Hasan
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Re: Problem!!!(BOMC-2)
Solution:
Last edited by Phlembac Adib Hasan on Tue Apr 03, 2012 9:35 pm, edited 1 time in total.
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- Phlembac Adib Hasan
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Re: Problem!!!(BOMC-2)
How clumsy I am! A person without any patience. Always making silly mistakes.
Last edited by Phlembac Adib Hasan on Tue Apr 03, 2012 9:38 pm, edited 1 time in total.
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