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

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

Unread post by AntiviruShahriar » Fri Feb 24, 2012 11:13 am

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.

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

Unread post by nafistiham » Fri Feb 24, 2012 2:48 pm

$2n-1$ I think
Last edited by nafistiham on Sat Feb 25, 2012 6:54 pm, edited 1 time in total.
\[\sum_{k=0}^{n-1}e^{\frac{2 \pi i k}{n}}=0\]
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AntiviruShahriar
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Re: May be I can sit here.. Oh no,again it forms a square:p

Unread post by AntiviruShahriar » Fri Feb 24, 2012 3:31 pm

Proof?
I got $ \frac{n^2}{2} (n-1)$ but . . . . . . . . . . . . . . . .

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

Unread post by nafistiham » Sat Feb 25, 2012 6:51 pm

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)
\[\sum_{k=0}^{n-1}e^{\frac{2 \pi i k}{n}}=0\]
Using $L^AT_EX$ and following the rules of the forum are very easy but really important, too.Please co-operate.
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AntiviruShahriar
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Re: May be I can sit here.. Oh no,again it forms a square:p

Unread post by AntiviruShahriar » Sun Feb 26, 2012 4:48 pm

No,think about a classroom.h0w do students sit.
I think you have consider only the arms of that square.

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

Unread post by AntiviruShahriar » Sun Feb 26, 2012 4:50 pm

After sitting 2n-1 students,more student can also sit diagonaly or other position and dont form a square

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