Proving the i,j Corner Relationship in a Divided Square

[monsmatglad]

Homework Statement

A square is divided into smaller n^2 smaller squares with corners (i,j)
Show that for every whole value of k, k= (i+1) + (n+1)*j and this is specific for every choice of i and j.

Homework Equations

The Attempt at a Solution

i see what i have to prove, but i don't know how to prove it.

 

[Mark44]

Homework Statement

A square is divided into smaller n^2 smaller squares with corners (i,j)
Show that for every whole value of k, k= (i+1) + (n+1)*j and this is specific for every choice of i and j.

This is not very clear to me. I understand that you are dividing a square into 1, 4, 9, ..., or n² smaller squares, but what does "corners (i, j)" mean?

I also don't understand where k fits into things.

Have you given us the exact wording of this problem?

 

[monsmatglad]

i and j are the corers of the smaller squares. the corner farthest down to the left would have i=0 and j=0. The next corner, moving to the right would be i=1 j=0.

K is just a value that according to the problem is related to the position of a corner.
if, for example i=1 and j= 2, then k would be k= (1+1) + (n+1)*2 which is a specific value for that specific pair of i and j.

mons

 

[jeppetrost]

It's really like counting.
Try like this: if you only change i, what is the maximum value you can get? (what is the maximum value of i?)
Now, let i be 0 again and change j by one. What is the difference between k(i_max,j=0) and k(i=0,j=1) ? Does this help you?

 

[monsmatglad]

aha. thank you, that solves it!