10

Good day to all of you!

I have a puzzle which I just cannot solve. I attached a photo of it. The task is to transform the shape on the left into a 9x9 square (on the right) using ONLY 2 "cuts" - dividing it into 3 separate objects. Mirroring, rotating of them is allowed. You do not have to cut in a straight line, creating zig-zags, etc. is allowed. (please ignore the random functions at the bottom). Do you have any suggestions or potential solution? Thank you very much!

Puzzle

Jam
  • 10,632
  • 3
  • 29
  • 45
David Kosztyu
  • 99
  • Almost got it for $2$ cuts into $4$ pieces. Are we sure this has a solution? https://i.imgur.com/eloJmXV.png – Jam Oct 01 '17 at 21:20
  • Thank you for your effort! It was given as an extra task for bonus points at my friend's university - prof claimed that there is a solution but it cost also him a fair amount of time. So I am pretty sure there is a solution. – David Kosztyu Oct 01 '17 at 21:36
  • Ah, I see. Thanks for explaining where the problem came from :) It's kind of a trivial point but the right side edge of the shape is $>9$ so one cut has to end on the right side edge. – Jam Oct 01 '17 at 21:51
  • I can come up with $2$ ways of doing it in $5$ pieces but nothing better, yet. https://imgur.com/qnI99hg https://imgur.com/cs9qUeL – Jam Oct 01 '17 at 22:24
  • Another one with $5$ pieces. https://imgur.com/k2mhAi2. – Jam Oct 01 '17 at 22:54
  • This paper https://web.cs.umass.edu/publication/docs/2011/UM-CS-2011-028.pdf gives an algorithm for computing the dissection. I think I've almost got it with $3$ pieces: https://imgur.com/thtxeSM – Jam Oct 01 '17 at 23:41
  • 2
    Are you sure the 1x1 square is not on the right side of the 4x4 square? Then it would be the famous Sam Loyd's A Square Deal puzzle. However, on the left side it would cut the long thin piece into two. – Momo Oct 01 '17 at 23:58
  • I asked my friend to double-check and confirm that the drawing is correct - I let you know once I get the answer. However, the picture was taken during class - copied from the whiteboard, so I tend to be positive about its correctness. But I will make it sure. The Sam Loyd's puzzle is a brilliant input here, thank you Momo. If this turns out to be an incorrect puzzle I owe you all a beer. Or more. – David Kosztyu Oct 02 '17 at 06:55
  • Jam the one "almost good" with 3 pieces, only missing one square is impressive - but if the cutting is so complex I do not wonder I got utterly stuck with it. – David Kosztyu Oct 02 '17 at 06:57

1 Answers1

12

$\color{white}{Blah blah, I must write some words, I am a human.}$ enter image description here

Simply Beautiful Art
  • 76,603
Donald Splutterwit
  • 37,323