How many windows are there?
An HDTV has a resolution of – or about million pixels. In some augmented reality applications, it is required to check all windows of size pixels. How many windows are there?
The answer is 4000000.
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1 solution
Consider the screen to be a coordinate grid, with each pixel at a lattice point and the bottom left point at the origin. Each 1 9 × 1 9 window can be defined uniquely by its bottom left corner, which can be placed at any point ( m , n ) such that m , n ≤ 2 0 1 8 − 1 9 + 1 = 2 0 0 0 . Thus, there are 2 0 0 0 2 = 4 0 0 0 0 0 0 possible windows.