## Yo-yo-problem (BOMC-2)

Discussion on Bangladesh National Math Camp
sourav das
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### Yo-yo-problem (BOMC-2)

Prove that, we can choose $2^k$ different numbers from $0,1,2$.......$3^k-1$, 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......
(-$from$ "$THE$ $UGLY$ $TRUTH$" )

Hasib
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### Re: Yo-yo-problem (BOMC-2)

sourav das wrote:Prove that, we can choose $2^k$ different numbers from $0,1,2$.......$3^k-1$, so that three numbers are in arithmetic progression will not occur.
"three numbers are in arithmetic progression" -মানে??? একটু বাংলায় বলেন........
A man is not finished when he's defeated, he's finished when he quits.

sourav das
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### Re: Yo-yo-problem (BOMC-2)

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......
(-$from$ "$THE$ $UGLY$ $TRUTH$" )

*Mahi*
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### Re: Yo-yo-problem (BOMC-2)

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:
Use $L^AT_EX$, It makes our work a lot easier!