Unequal parts

It is easy to dissect a rectangle into similar unequal triangles.
Find another dissection with three triangles. For which rectangles is it possible ? Solution

The dissection into 3 triangles fails if we start from a square (the green and blue triangles become equal)
How many triangles are then necessary ? Solution

Dissect a rectangle into rectangles similar to each others is not hard.
(here 2×4, 4×8 and 5×10 inside a 9×10 rectangle)
But if all rectangles, including the big one, have to be similar and unequal ? Solution

How many rectangles at least if all rectangles have integer dimensions ? Solution

A square into similar non equal rectangles ? Solution

A square into all unequal squares ? Solution
Details

 

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