# Math solution for number of possible window monitor positions using 1, 2, or 3 divisions

Hello,

What math equation describes the number of possible window positions when dividing a computer screen (rectangle) using one, two, & three sections in one or both (horizontal & vertical) axes?

For example, one division obviously has 1 possibility:
And it appears that with one or two divisions in each direction there are 4 + 2 + 2 = 8 possibilities:
But what about with one, two, or three divisions? I initially counted 9 + 3 +3 + 4 + 12 = 31
but then I realized I had forgotten the 2-3 combinations so that's 12 more (ie 31 + 12 = 43).
I suspect there may be others because 43 seems like a bit of an odd total. That's why it needs math!

And what about having up to four divisions? I didn't even try to start doing that graphically.

Thanks
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Commented:
the problem is not well defined yet. why should rectangles (0, 0, 8, 12) and (4, 0, 8, 12) be valid solutions (3rd and 5th yellow) but (0, 0, 6, 12) is not?

if you say all windows must have same size and a solution covers the whole screen, you nicely have

-           0 split lines 1 window
-           1 split line   3 windows
- up to 2 split lines 5 windows
- up to 3 split lines 7 windows

Sara
0

Finance AnalystCommented:
Is it not a simple mathematical function:

(Vertical Dividers +1) x (Horizontal Dividers +1)

Examples:
Vert      Horiz
0+1  x   0+1 = 1
1+1  x   0+1 = 2
2+1  x   1+1 = 6

Thanks
Rob H
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Author Commented:
Thanks for the responses.

the problem is not well defined yet. why should rectangles (0, 0, 8, 12) and (4, 0, 8, 12) be valid solutions (3rd and 5th yellow) but (0, 0, 6, 12) is not?
Apologies for the ambiguity in my OP. I did state that the possibilities for a given number of divisions includes those for a lower number but I neglected to account for the lower numbers and create a total . In other words:

1 division = 1 possibility
2 divisions = 1 (from 1 division) + 8 (as stated in OP) = 9 total possibilities
3 divisions = 1 (from 1 division) + 8 (from 2 divisions) + 43* (as stated in OP) = 52 total possibilities

To avoid the same head scratching among other experts, I think the best step is to award points and close this thread and then re-post the question in a new thread.

Thanks again for the input.
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Author Commented: