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Yesterday my brother asked me a question.

Suppose you have a carpet of size $16×9$. Now you have to cut this carpet in such a way that after cutting it and arranging pieces, the dimension is $12×12$. You can only cut the carpet once. You can arrange the obtained pieces in any way you like. How can you do this?

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  • $\begingroup$ if you cut 144 equal sized square pieces this should work yes $\endgroup$ – marmouset Feb 20 '17 at 14:28
  • $\begingroup$ @marmouset One cut! $\endgroup$ – Parcly Taxel Feb 20 '17 at 14:31
  • $\begingroup$ If the breadth$=9$ units, how will it gain the other $3$ units? $\endgroup$ – Nick Pavini Feb 20 '17 at 14:36
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enter image description here Essentially the same problem appears in Boris Kordemsky's puzzle book, with the solution as below. enter image description here

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  • $\begingroup$ I think you don't have to divide to same shape. $\endgroup$ – Takahiro Waki Feb 20 '17 at 17:07
  • $\begingroup$ @TakahiroWaki Whether the two pieces are the same shape or not was not specified in the question. $\endgroup$ – Parcly Taxel Feb 20 '17 at 17:09
  • $\begingroup$ Here is no explanation why stair-step cut work well, and that is unique solution, so on. $\endgroup$ – Takahiro Waki Feb 21 '17 at 2:54
  • $\begingroup$ @TakahiroWaki I don't have to prove that the solution is unique, nor "why the stairstep cut works well". The proof is the picture; I only have to give one solution. $\endgroup$ – Parcly Taxel Feb 21 '17 at 2:57

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