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Can you divide a 7x13 rectangle into 13 rectangles all of different area? Can you find multiple solutions? Note that rotations and mirrors don't count as separate solutions.

Here is a similar puzzle for a 4x7: 4x7 rectangle divided into 7 different rectangles

Good luck!

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    $\begingroup$ I'm not so sure this larger version adds all that much to the other one to be homest. Most solutions there generalise directly to any $k\times(2k-1)$ rectangle made of $2k-1$ smaller rectangles of different areas. $\endgroup$ – Jaap Scherphuis Oct 13 at 6:19
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This can be done with a method similar to the one I used in the prequel question.
In fact,

This "two stairs" combined to make a rectangle would work for any $n\times(2n-1)$ rectangle. Also, this is one method used to prove the triangular number formula!

The numbers are displayed below in base 13 to keep the square-ness. (A for 10, B for 11, C for 12 and D for 13)

 7 7 7 7 7 7 7 6 6 6 6 6 6
 8 8 8 8 8 8 8 8 5 5 5 5 5
 9 9 9 9 9 9 9 9 9 4 4 4 4
 A A A A A A A A A A 3 3 3
 B B B B B B B B B B B 2 2
 C C C C C C C C C C C C 1
 D D D D D D D D D D D D D
 

Rotations, reflections, and permuting rows would give other solutions.

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