> if it actually wrapped around on itself with a half-twist, wouldn’t the letters wind up backwards too? Then 6-Down wouldn’t be MESSENGER but rather MESSENGER, and so on.
This premise is assuming the Mobius strip is transparent, which the header image clearly isn't. No letter-reversals or any symmetry is needed. On normal, opaque paper, you can just make a crossword as a normal long loop. (proof: Write GGGGGGG on one side of a paper, and write it upside-down on the other side. With a twist, you'll get one long GGGGGGGGGGGGGG... looping as if it were one boring single-sided loop).
A true Mobius strip doesn't have "sides" like the paper model of one does. You can see that in the quote from Martin Gardner where he talks about a creature completing a loop becoming a mirror image with respect to it's friends. I assume the author wanted the paper model to mimic that property.
Incidentally, the author's choice makes for a much more interesting puzzle than the one you would have them use (IMO)--yours would be indistinguishable from a puzzle written on a cylinder.
I agree it's an interesting puzzle! Just thought he made the jump to transparent paper without introduction in a way that confused me. It seemed instead like a non-transparent Mobius strip would join itself upside-down after a full loop, which wasn't obviously untrue.
My partner publishes crosswords and it's always fun to see how much artistry goes into authoring a puzzle. You can play with the structure/grid, the theme of course, every minute detail of the fill, etc.
Never would have thought of a Mobius-strip though, insane.
qxw [https://www.quinapalus.com/qxw.html] is a wonderful open source app that lets you make crosswords with interesting topologies, complete with grid filler support, if anyone wants to experiment with them.
For anyone trying to solve the examples, the toroidal crosswords example image has a copy-paste error from the post author (not present in the original): the numbers for Down are 1, 3, 5 and 6 (and not 1, 2, 4, 7).
Not sure why. Refer to the original puzzles linked for the correct clues.
This premise is assuming the Mobius strip is transparent, which the header image clearly isn't. No letter-reversals or any symmetry is needed. On normal, opaque paper, you can just make a crossword as a normal long loop. (proof: Write GGGGGGG on one side of a paper, and write it upside-down on the other side. With a twist, you'll get one long GGGGGGGGGGGGGG... looping as if it were one boring single-sided loop).
Incidentally, the author's choice makes for a much more interesting puzzle than the one you would have them use (IMO)--yours would be indistinguishable from a puzzle written on a cylinder.
Each edge of the ribbon was a linked list, connected to each other by rungs. It looped back on itself but connected crosswise .
Then if you nuked all the rungs it was clear you still got a connected piece that you could traverse over.
Never would have thought of a Mobius-strip though, insane.