Well, do you understand the illustration? How many square are there?
Now draw a corresponding illustration for the 3 by 2 and 3 by 3 grids. look for a pattern.
Hey all, I need some guidance on a problem I've been working on involving a grid formula. Please see the problem below:
(i) Consider a n x n grid of uniform size. Guess a formula for the number of different squares (of varying size) and prove it.
Above is an illustration for a 2 x 2 grid.
(ii) What is your answer when we consider the same problem for a m x n grid?
Not sure where to start off with this one....all help is appreciated!
Hi Plato, I've got a formula f(n,m) to count the number of squares an n by m generates. I've got a question on proving it. The smallest case is n=2,m=1 (I let n>m WLOG) so the formula must be shown to be true for any n>=2,m>=1. Using induction and assuming f holds for some (a,b), should I show that f(a+1,b) holds and f(a.b+1) holds. Given both of these cases hold f(n,m) holds for n>=2,m>=1, as requied?
I really do not understand what you are asking.
If you are asking how to prove
then by all means use induction.
However, as I said before I do not think that is the point of this question. I think you are to say why that sum counts the squares.
That why part b) is a generalization question.