Time in a Bottle
(Published on 20. August 2020, 02:25 by cam)
If I could make days last forever
If words could make wishes come true
I'd save every day like a treasure and then
I'd play sudoku with you
Enough of that. This puzzle was made as a tribute to one of my favorite musicians, Jim Croce. The song can be found here. The inspiration for this puzzle comes from everyone's favorite setter, Richard. His original clock sudoku can be found here. This is the third in a series of puzzles that are played on a Klein Bottle.
Ordinary sudoku rules apply. This puzzle takes place on a klein bottle. The top and bottom of the grid are glued together--they obey periodic boundary conditions (see the example on the left). The left and right side are twisted and then glued together (see the right side). The circles in the grid represent clocks. The four digits surrounding a white clock must strictly increase in a clockwise fashion starting from any of the four cells. The four digits surrounding a black clock must strictly increase in an anti-clockwise fashion starting from any of the four cells. All possible clocks are marked. (Don't forget the negative constraint!) Let me know if anything is unclear in the comments :)
Here is the puzzle. Enjoy! :)
Here is a penpa link courtesy of panthchesh. Thank you!
Solution code: Row 4 followed by column 1
Comments
on 23. August 2020, 17:36 by cam
Thank you everyone for your comments! :)
on 22. August 2020, 11:52 by Voyager
@cam: You write: "The inspiration for this puzzle comes from everyone's favorite setter, Richard."
Now I will prove, that this your sentence is wrong.
My proof goes like this: I personally do not have any favorite setters, thus Richard is not my favorite setter, thus Richard is not everyone's favorite setter.
on 22. August 2020, 06:52 by Narayana
What a wonderful puzzle Cam.
on 21. August 2020, 11:35 by henrypijames
I have to say though, the opening - at least the one I've found - borders on bifurcation. Testing (in order to exclude) those false alternatives was just barely doable in my head without writing things done - but I still did to be sure, also because I'm not a purist.
Reply: The opening I intended must be different. I will leave it in a hidden comment here shortly:)
on 21. August 2020, 06:30 by henrypijames
@Greg: After re-checking my accepted solution against the grid, I can confirm there's no missing circle.
Forgive me for stating the patently obvious, but just in case you overlooked: Not all digits in a circle are ascending or descending - the beginning and ending digits are in the "wrong" order with respect to each other (like 1 and 12 on a real clock).
If you have filled out one entire row/column/box before breaking, you can post it and let us check if it's correct.
on 21. August 2020, 00:19 by cam
@jessica6 This is a case of same side vs same point. It is true that the klein bottle is a non-orientable manifold, but that only means that the surface can't have an orientation. Individual points on the surface can. You have to travel all the way around the klein bottle to get back to the same point on the sudoku grid. The non-orientability only poses a problem when one of the grid lines maps back to itself which doesn't happen in this puzzle. Imagine taking a mobius loop and drawing a circle around it. You end up joining that circle back with itself halfway through. However, if you started your circle off to the side of the original, this wouldn't happen. Once you get through half of the drawing, the points don't line up. You have to go all the way around to join back up. I hope that helps!
on 20. August 2020, 23:42 by jessica6
How is "clockwise" defined on a Klein bottle?
If I start on a circle in any direction, I will come back to the same circle but on the backside, where spin is reversed. Only if I continue in that direction until I come back to the same circle again, then it will be the normal spin again.
on 20. August 2020, 22:23 by cam
@henrypijames I made your comment hidden, but I really like what you said :)
on 20. August 2020, 14:07 by Nothere
Wonderful time travel!
on 20. August 2020, 07:35 by Richard
Thanks for the astronomical compliment cam!
You make me blush...
on 20. August 2020, 06:16 by cam
@panthchesh Thank you for the link! I really appreciate it. I added it to the description.
on 20. August 2020, 05:33 by panthchesh
here you go, a penpa link: https://tinyurl.com/y63cny6t :)
Hopefully I'll have some time to try this one later :)
