Can you tile a 15x16 rectangle using eight rectangles whose sizes are 1x2, 2x3, 3x4, ... 8x9?

No two rectangles can be the same size.


2 Answers 2



Yes you can and this is one way you can do it: enter image description here

  • $\begingroup$ When you say "this is how you do it", do you mean there's a unique solution (modulo symmetries), or is it just some introduction text? $\endgroup$ Apr 23 at 12:32
  • $\begingroup$ All I meant was this is how you can do it. $\endgroup$
    – PDT
    Apr 23 at 12:36
  • $\begingroup$ Oh :x I was trying to see if there are possible variations and it's not obvious to me. The top-right and bottom-right rectangles force the bottom-right to stick to an edge, or a self-contradiction is reached. So there may well be a unique solution, but I'm not sure. $\endgroup$ Apr 23 at 12:41
  • 3
    $\begingroup$ @MatthieuM. Note that the two rectangles at the top left can be swapped. $\endgroup$
    – ACB
    Apr 23 at 12:59
  • $\begingroup$ @ACB: Good call. So there's at least 2 distinct solutions. $\endgroup$ Apr 23 at 13:28

Already answered, just to say there are ten ways to do it. I would have trouble counting them but my tiling program normally gets it right... if I type in all the parameters correctly. I think the right hand two are the pair already posted. The other eight correspond to 2x2x2 as there are three flippable pairs.

enter image description here


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