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

For students of class 11-12 (age 16+)
AntiviruShahriar
Posts: 125
Joined: Mon Dec 13, 2010 12:05 pm
Location: চট্রগ্রাম,Chittagong
Contact:

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

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.

nafistiham
Posts: 829
Joined: Mon Oct 17, 2011 3:56 pm
Location: 24.758613,90.400161
Contact:

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

$2n-1$ I think
Last edited by nafistiham on Sat Feb 25, 2012 6:54 pm, edited 1 time in total.
$\sum_{k=0}^{n-1}e^{\frac{2 \pi i k}{n}}=0$
Using $L^AT_EX$ and following the rules of the forum are very easy but really important, too.Please co-operate.

AntiviruShahriar
Posts: 125
Joined: Mon Dec 13, 2010 12:05 pm
Location: চট্রগ্রাম,Chittagong
Contact:

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

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

nafistiham
Posts: 829
Joined: Mon Oct 17, 2011 3:56 pm
Location: 24.758613,90.400161
Contact:

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

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.

AntiviruShahriar
Posts: 125
Joined: Mon Dec 13, 2010 12:05 pm
Location: চট্রগ্রাম,Chittagong
Contact:

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

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

AntiviruShahriar
Posts: 125
Joined: Mon Dec 13, 2010 12:05 pm
Location: চট্রগ্রাম,Chittagong
Contact:

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

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