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

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

No two rectangles can be the same size.

Yes you can and this is one way you can do it:

• 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? Apr 23 at 12:32
• All I meant was this is how you can do it.
– PDT
Apr 23 at 12:36
• 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. Apr 23 at 12:41
• @MatthieuM. Note that the two rectangles at the top left can be swapped.
– ACB
Apr 23 at 12:59
• @ACB: Good call. So there's at least 2 distinct solutions. 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.