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
Of course that result can be rigorously obtained, but who cares?
Combinatorics is Algebra and Algebra is Combinatorics.