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I am trying to find a solution for the rectangle packing problem. In this problem we have a plate of width $w$ which is given by the problem and we have $n$ rectangles to place inside it. Each rectangle is defined by a pair of values $x_i$ and $y_i$. The objective of the problem is to place all the blocks inside the rectangle and minimize the total height $h$ of the plate.

I was wondering, can I assume that in one of the possible solutions (given moving the blocks) there is at least one in which the rectangle with the biggest area is at the bottom left corner?

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For $w=6$, I think the diagram below shows a counterexample. enter image description here

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