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!

  • 5
    $\begingroup$ 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. $\endgroup$ Oct 13 '19 at 6:19

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.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.