6
$\begingroup$

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?

  • 0
    if you cut 144 equal sized square pieces this should work yes – 2017-02-20
  • 0
    @marmouset One cut! – 2017-02-20
  • 0
    If the breadth$=9$ units, how will it gain the other $3$ units? – 2017-02-20

1 Answers 1

4

enter image description here Essentially the same problem appears in Boris Kordemsky's puzzle book, with the solution as below. enter image description here

  • 0
    I think you don't have to divide to same shape. – 2017-02-20
  • 0
    @TakahiroWaki Whether the two pieces are the same shape or not was not specified in the question. – 2017-02-20
  • 0
    Here is no explanation why stair-step cut work well, and that is unique solution, so on. – 2017-02-21
  • 0
    @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. – 2017-02-21