A little typo which i will correct : Omid Hatami wrote: $10000 \le f(n) \le 960000$ Should be : $10000 \le f(1384) \le 960000$ and a little defination for $n-$mino: We call a shape, a $n-$mino If and only if, it contains only $n$ equal squares such that from each vertic ,by using the sides ,you will be able to reach anyother vertices.

Is 1384 from the Persian calendar equivalent of 2005?

Yes in Persian calender 1384 is 2005

upper bound: $n^2/2$ A rectangle of sides $n/2$ and $n$

yes its a bound. I think the coordinators said the best bound is $nlog(n)=f(n)$ ,but i dont get the shape due (how on the earth did they get $nlog(n)$ ?

Of course we said that the best bound we got is $n\log\ n$