Can you re-arrange these rectangles to form another rectangle, but with different dimensions (dimensions commute in this case)?

random rectangles

  • $\begingroup$ Do you have to stay within the defined grid coordinate system (meaning you can't split up grid cells)? $\endgroup$
    – Aranlyde
    Commented May 15, 2019 at 7:13
  • $\begingroup$ A and 1 can be considered to be the same length. The beige right hand cell is 2*10, but can be rotated to 10*2. $\endgroup$
    – JMP
    Commented May 15, 2019 at 7:15

1 Answer 1


No. The rectangle has an area of $75$ square units. The only other rectangle with integer sides that would have the same area would be $3*25$ (or $1*75$ technically, I guess).

The rectangles you have are $3*6, 2*3, 3*2, 2*4, 4*2, 10*2$ and $9*1$. The $9*1$ needs a $9*2$ paired with it to fill those rows and prevent leaving a $1*x$ space that cannot be filled. This cannot be done.


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