Puzzle
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Ponder This Challenge - August 2015 - Loopsless projections of a loop

Ponder This Challenge:

Find a way to fold a loop of string in three-dimensional space such that all three projections will be loop-free (i.e., you won't be able to make a path from a point to itself without backtracking).

Provide your answer as a list of integer 3D coordinates, where each pair differs in exactly one coordinate.

For example, the following list is loop-free on two projections (x,z) and (y,z), but forms a loop on the third projection (x,y):
[1,1,1],[1,1,2],[2,1,2],[2,1,1],[2,2,1],[2,2,2],[1,2,2],[1,2,1],[1,1,1].

Solution

  • A possible solution is:
    [0,0,0], [0,0,1], [0,0,2], [0,1,2], [0,1,1], [1,1,1], [1,1,2], [1,2,2], [2,2,2], [2,1,2],[2,0,2], [1,0,2], [1,0,1], [2,0,1], [2,0,0], [2,1,0], [2,2,0], [2,2,1], [1,2,1], [0,2,1],[0,2,0], [1,2,0], [1,1,0], [0,1,0], [0,0,0]

    Thanks to Robert Gerbicz who pointed us to the cover of Peter Winkel's book Mathematical Mind-Benders (http://ecx.images-amazon.com/images/I/416HFW9R1AL._SX331_BO1,204,203,200_.jpg), which shows a solution; and to David Greer who sent us a great animation showing the solution: http://imgur.com/1zkpt5Y.

Solvers

  • Robert Gerbicz (28/07/2015 08:56 PM IDT)
  • Gregory Giecold (29/07/2015 02:12 AM IDT)
  • Don Dodson (29/07/2015 08:56 PM IDT)
  • Gary M. Gerken (30/07/2015 07:33 AM IDT)
  • John Tromp (30/07/2015 08:39 PM IDT)
  • Kang Jin Cho (01/08/2015 06:02 AM IDT)
  • Shirish Chinchalkar (02/08/2015 03:41 PM IDT)
  • Daniel Bitin (02/08/2015 11:21 PM IDT)
  • Harald Bögeholz (03/08/2015 01:21 AM IDT)
  • Liubing Yu (03/08/2015 07:53 AM IDT)
  • Lucas Mirelmann (05/08/2015 01:53 AM IDT)
  • Florian Fischer (05/08/2015 11:59 AM IDT)
  • Uoti Urpala (07/08/2015 12:46 AM IDT)
  • Graham Hemsley (07/08/2015 06:58 PM IDT)
  • Alexandre Gilotte (08/08/2015 12:08 AM IDT)
  • Francis Golding (09/08/2015 07:41 PM IDT)
  • Yan-Wu He (10/08/2015 12:02 PM IDT)
  • David Greer (10/08/2015 09:28 PM IDT)
  • Todd Will (11/08/2015 08:16 PM IDT)
  • Paolo Farinelli (12/08/2015 03:24 AM IDT)
  • George Stoianov (12/08/2015 04:12 PM IDT)
  • Joseph DeVincentis (12/08/2015 07:46 PM IDT)
  • Jamie Jorgensen (12/08/2015 10:46 PM IDT)
  • Martin Husar (13/08/2015 09:10 AM IDT)
  • Jesse Rearick (19/08/2015 02:53 AM IDT)
  • Pino Ottavio (22/08/2015 12:59 PM IDT)
  • Michael Rosola (22/08/2015 08:16 PM IDT)
  • Bradley Sherman & Mason Bouffard (28/08/2015 08:11 AM IDT)
  • Jim Clare (31/08/2015 03:11 AM IDT)
  • David Dunkley (02/09/2015 02:45 AM IDT)

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