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A Mobius strip is one of the basic concepts of topology. There are many interesting tricks using this strip (for example, interesting results of cutting the tape with a different number of turns). Also, the Mobius strip is actively used for the labeling of recycle packages.

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A quick search of the site with the keyword "Mobius" returned just a few relevant entries. The Mobius strip is used as a non-core idea for a solution to a puzzle.

I am looking for an idea for creating a visual puzzle based on the Mobius strip. This strip can be used as the formulation as a solution puzzle.

Here are two links on interesting topological puzzles:

Question. How can I use a Mobius strip when constructing a puzzle?

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  • $\begingroup$ Vi Hart created this wonderful story based on drawings on a transparent Möbius strip. That's pretty much certain to give you some puzzle ideas. $\endgroup$ – Bass Nov 18 at 22:49
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Here's one:

and another:

A completed, solved game puzzle 10 is a mobius strip made of multiple columns 24 and rows 22 of blocks 20, or block-like pieces. Each block 20 has opposing display surfaces and opposing connecting surfaces which are orthogonal to the display surfaces. The connecting surfaces have mechanisms such as a corresponding peg 30 and aperture 32, respectively, for connecting one block 20 to another block 20. The display surfaces exhibit a color, alphabet 28, number or symbol. The unsolved puzzle is one or more bands of blocks connected by and pivotable about an axis 26 extending through the center of each block 20 parallel to the display and connecting surfaces. The solution to the puzzle may be words or phrases spelled by aligned letters of individual strips, or a predetermined pattern formed from aligned colors or symbols. To solve the puzzle, the blocks of each strip must be connected adjacent the blocks of another strip at appropriate locations.

and another:

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  • $\begingroup$ Thank you for the reference on the patent. I think i can use the strip and the Mobius strip connected by glue, after cutting one can see the square with letters and numbers on the edges. $\endgroup$ – Nick Nov 18 at 15:00
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I'll give some info but I'm not sure how good it will be for making a puzzle. I know this site loves graph theory, so maybe there is something there.

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This picture is of a Youngs' Ladder and comes from my research into the Heawood conjecture.

Here are the properties (In this case n=7):

  • The numbers {1,..,3n-1; 3n+1} are present.
  • The three edges on each vertex should have the form (a+b=c)
  • The arrow indicates flow or adding/subtracting
  • There are four classes of construction, depending on the residual of n (mod 4). For cases 0 and 3, the ladder has Moebius topology.
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There were a couple of puzzles from the MIT Mystery Hunt that involved the Mobius strip either as a medium or a mechanism, found by searching this index of past Hunt puzzles for puzzles tagged "Mobius strip." Among these puzzles, we have

  • a crossword puzzle that involved creating a Mobius strip as part of the answer extraction step,
  • an Einstein-grid style logical deduction that required solvers to assign labels to towns on a Mobius strip,
  • and finally, most interestingly, a seemingly standard word/assembly puzzle that took it up one dimension and used the Klein bottle (the 3D analogue to the Mobius strip) as part of the assembly step.

Perhaps these can provide inspiration for a twisty mechanism of your own?

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I have read all the answers and looked at the links. Based on these materials, I formed the following idea of using the Mobius strip.

  1. Take two colored strips. Write numbers on the yellow strip and letters on the blue one.

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  1. Make the Mobius strip from the yellow strip, and the ring from the blue one.

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  1. Glue the ring and Mobius strip together.

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  1. Cut the blue ring in the middle.

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  1. Cut the yellow ribbon in the middle.

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  1. Match the letters and numbers from the squares' sides, and read the word.

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