I hope that question makes sense. I’m an adult and maths may as well be a foreign language for me. This is my secret shame.
Anyway, let’s say I have a sheet of paper and I want to draw 4 vertical and 4 horizontal lines, how do I figure out that I will actually get 25 squares without counting?
In: Mathematics
Let n be the number of vertical lines you draw and m be the number of horizontal lines you draw. Any space* will be cut into (n+1)*(m+1) areas. Multiplying this out give you n*m+n+m+1 spaces. As to why you get n+1 and m+1 spaces, just look at the case where you draw 1 vertical line and no horizontal lines. The one vertical line gives you 2 areas; this can also be extrapolated from the fact that a line cuts a plane into two half-planes.
In the case of 4 vertical lines and 4 horizontal lives you get 5*5=25 or 4*4+4+4+1=16+4+4+1=25. This works for any number of vertical or horizontal lines.
* Just a note here, when I say any space I really mean any 2D space. 3D or higher spaces tend to get really picky about lines actually cutting/separating things into unique spaces.
(H+1)x(w+1)
You start with one unit. Each line adds one to that dimension. If you have 2 vertical lines you have 3 columns. 5 vertical lines is 6 columns. Etc. Just multiply columns times rows.
Multiply. 4 lines makes 5 sections, just like in tic tac toe 2 lines make 3 sections. So just add 1 to the number of lines and multiply cause you will always have +1 extra section created by x number of lines. In the case of tic tac toe, (2+1)*(2+1) = (3)(3)
For your other example, (4+1)*(4+1) = (5)(5)
asterisks messed up my post
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