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May be I can sit here.. Oh no,again it forms a square:p

Posted: Fri Feb 24, 2012 11:13 am
by AntiviruShahriar
Let a class room having $n^2$ seats in $(n \times n)$ form.how many students at most can take their seat so that no 4 students form a square.

Re: May be I can sit here.. Oh no,again it forms a square:p

Posted: Fri Feb 24, 2012 2:48 pm
by nafistiham
$2n-1$ I think

Re: May be I can sit here.. Oh no,again it forms a square:p

Posted: Fri Feb 24, 2012 3:31 pm
by AntiviruShahriar
Proof?
I got $ \frac{n^2}{2} (n-1)$ but . . . . . . . . . . . . . . . .

Re: May be I can sit here.. Oh no,again it forms a square:p

Posted: Sat Feb 25, 2012 6:51 pm
by nafistiham
Oh! no.it should have been \[2n-1\]
The points can be just of two adjacent sides.
moreover, it can be proved that more than $2n$ points make at least a right triangle.(BdMO 2012 secondary 9)

Re: May be I can sit here.. Oh no,again it forms a square:p

Posted: Sun Feb 26, 2012 4:48 pm
by AntiviruShahriar
No,think about a classroom.h0w do students sit.
I think you have consider only the arms of that square.

Re: May be I can sit here.. Oh no,again it forms a square:p

Posted: Sun Feb 26, 2012 4:50 pm
by AntiviruShahriar
After sitting 2n-1 students,more student can also sit diagonaly or other position and dont form a square