
4 Attachment(s)
TicTacToe problem
Hi guys, hopefully this is an easy one for you.
Given a grid of nxn squares, where each square has an id, the first(top left) square has id 0 (so a 5x5 grid will have ids 024) like below:
Attachment 23365
I need to generate all diagonal solutions of length Y. So if Y is 3, then some of the solutions will be:
Attachment 23366
and
Attachment 23367
but obviously NOT
Attachment 23368
Any ideas how these solutions can be generated?

Re: TicTacToe problem
Hello, Kratos!
Quote:
Given a grid of $\displaystyle n\times n$ squares, where each square has an ID.
The first(top left) square has IDd 0 (so a 5x5 grid will have IDs 024) like below:
Attachment 23365
I need to generate all diagonal solutions of length Y. So if Y is 3, then some of the solutions will be:
Attachment 23366
and
Attachment 23367
but obviously NOT
Attachment 23368
Any ideas how these solutions can be generated?
We have an $\displaystyle n\times n$ grid.
And we want diagonals of length $\displaystyle y.$
Across the top row, there are $\displaystyle n  y + 1$ diagonals.
And there will be $\displaystyle ny+1$ such rows.
Hence, there are $\displaystyle (ny+1)^2$ diagonals of this form $\displaystyle \searrow$
. . and $\displaystyle (ny+1)^2$ diagonals of this form $\displaystyle \swarrow $
Therefore, there are: $\displaystyle 2(ny+1)^2$ diagonals of length $\displaystyle y.$

Re: TicTacToe problem
Wow, that makes sense. Thank you Soroban.