Yoyoproblem (BOMC2)

 Posts: 461
 Joined: Wed Dec 15, 2010 10:05 am
 Location: Dhaka
 Contact:
Yoyoproblem (BOMC2)
Prove that, we can choose $2^k$ different numbers from $0,1,2$.......$3^k1$, so that three numbers are in arithmetic progression will not occur.
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: Yoyoproblem (BOMC2)
"three numbers are in arithmetic progression" মানে??? একটু বাংলায় বলেন........sourav das wrote:Prove that, we can choose $2^k$ different numbers from $0,1,2$.......$3^k1$, so that three numbers are in arithmetic progression will not occur.
A man is not finished when he's defeated, he's finished when he quits.

 Posts: 461
 Joined: Wed Dec 15, 2010 10:05 am
 Location: Dhaka
 Contact:
Re: Yoyoproblem (BOMC2)
মানে হল, তোমার নেওয়া ঐ $2^k$ সংখ্যক সংখ্যার মাঝে যদি তিনটা সংখ্যা $a,b,c$ নেয়া হয় তাহলে $a,b,c$ দ্বারা কোন সমান্তর ধারা তৈরি করা সম্ভব হবে না। মানে $a+b=2c$ এই রকম কখনই হবে না।
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: Yoyoproblem (BOMC2)
The proof is easy by induction, though I have not found an $NT$based proof yet. I'll post it as soon as I get one.
Proof:
Proof:
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