Dividing a Square into Unique Rectangles

  1. For 1<=N<=8, divide an NxN square into the maximum number of non-overlapping rectangles with integral sides, such that each rectangle is unique in dimensions from any other. That is, between any two rectangles, the length or width or both must be different.
  2. Same as number 1, with the added constraint that no rectangle can be a square.
  3. Divide a checkerboard into the maximum number of unique rectangles. Here you have the added variable of color, so two rectangles of equal size can still vary by pattern.

Source: Original.

Mail to Ken