Calculation of Total no. of Triangles form joining any 3 points in a Given Figure.
 Calculation of Total no. of Square form joining any 4 points in a Given Figure.
 Calculation of Total no. of Rectangle form joining any 4 points in a Given Figure.
I suggest you start with squares; that looks easiest to me.
You can have squares that are 1 by 1; 2 by 2; 3 by 3; and 4 by 4.
EDIT: You should also count the squares that are at 45 degrees to the grid.
There's an easy pattern to this, so finding that is a good beginning to the harder rectangle case.
Last edited by bob bundy (2013-09-29 09:13:07)
You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei
In mathematics, you don't understand things. You just get used to them.
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.