Castle in the Sky
(Published on 23. April 2023, 12:35 by filuta)
Möbius strip
The grid of this puzzle forms a Möbius strip, the left and right edges are connected as indicated by the letters a-g/A-G (the top and bottom edges work normally). Each full (Möbius strip) row is therefore circular and consists of two standard rows of the grid.
Rules of the puzzle:
- (loop) Draw an oriented loop without intersections connecting orthogonally centers of some cells. The orientation of the loop must be deduced.
- (squares) The gray squares are not visited by the loop. The number in a square is equal to:
(1) the number of the steps on the loop going towards the cell minus the number of the steps going away from the cell in the cell's column,
PLUS
(2) the number of steps to the right minus the number of steps to the left OR the number of steps to the left minus the number of steps to the right in the cell's full (Möbius strip) row.
The choice in (2) must be deduced for each square, but it is the same one for all cells enclosed by the loop and then the opposite one for all cells not enclosed by the loop.
(A cell is enclosed by the loop if it cannot be connected to the (Möbius strip) edge without crossing the loop.)
Example (see the figure below):
-The blue cells show one full Möbius strip row with two gray squares.
-There are 3 steps to the right and 5 steps to the left in the blue row. Here the -1 clue (not enclosed by the loop) gets 3-5=-2 from the row (steps to the right minus steps to the left) and it gets 2-1=+1 from the column.
-Now all clues not enclosed by the loop get "right - left" contribution from the row. For instance the 0 clue gets 1-2=-1 from the row and +1 from the column.
-All clues enclosed by the loop now get "left - right" row contribution. The +3 clue gets 5-3=+2 from the row and +1 from the column. The -4 clue gets 1-4=-3 from the row and -1 from the column.
Solve online via penpa+ link.
Solution code: For every standard row of the grid (from top to bottom) the number of turns of the loop (14 numbers).
Comments
on 14. September 2024, 07:30 by polar
This puzzle truly sits in a Hall of Fame for being totally unforgettable, yet re-solving it still felt like a new and immensely satisfying journey.
I have however found a flaw filuta… that nothing else seems to come close to this puzzle’s Valhalla; nor do I expect anything to anytime soon.
on 13. September 2024, 22:08 by Tacosian
What can I do except agree with what everyone else has said? This is the hardest and best puzzle that I've solved. Thank you for this unforgettable experience.
on 24. April 2024, 09:55 by filuta
@Phistomefel - now I'm lost for words, it really makes me so happy everyone - now including you as well - enjoyed this puzzle so much.
and congrats for the solve ofc!
on 23. April 2024, 23:47 by Phistomefel
Wow! I am awestruck, words fail to describe the beauty of this puzzle. It took me more than two weeks to gather enough information to even start it. The break-in was magical, but the puzzle didn't stop there. It was relentless, demanding, brutal at times, but every deduction felt so very satisfying. Thank you so, so much for this epic construction, filuta! This is the best puzzle I ever solved.
on 4. April 2024, 17:02 by polar
@Silverstep: Guilty as charged. One of the very few puzzles I observe here for email notifications on when it gets solved.. Because it's {insert superlatives here} and was my personal mission for it to get more solves for far too long :)
on 4. April 2024, 08:35 by Silverstep
It's interesting how this has seven solves and eight observers. Who are you, the one who watches from afar? What is your purpose?
on 25. February 2024, 04:27 by zzw
Jaw-droppingly amazing. The other comments weren't lying, this is super difficult but so mindblowing to finally solve.
It took me months to get the insight necessary to do *anything*, which was wild enough on its own, but the way the puzzle unfolded after that might be even better. It's simply perfectly constructed.
on 2. October 2023, 14:43 by wisty
I don't know how to describe how wonderful this puzzle is without sounding like an understatement. Fascinating? Well-made? Rewarding? Fun? Brilliant? I think the only way to properly appreciate is to solve it. It is well worth the undertaking. The beginning steps are one of a kind and the mid-solve is very very difficult but fair and immensely rewarding. Jesper's Castle Wall Deltas are definitely a prerequisite, but this is honestly a must-solve for anyone who loves this website and what this community has to offer.
on 2. October 2023, 14:35 by wisty
I love you
on 27. September 2023, 07:56 by The Book Wyrm
This puzzle is utterly amazing.
It is very hard - it took me several hours over a couple of days, and I even broke it a couple of times.
It is absolutely worth it though - this puzzle has some of the most ridiculous and cool deductions I've seen, and is a truly impressive construction.
on 23. July 2023, 01:29 by Myxo
I feel like I need to rest for a few weeks after solving this one. This may be the hardest puzzle on the website, and also one of the most satisfying ones when you finally understand it.
on 21. July 2023, 08:42 by polar
This puzzle is criminally under loved/solved :')
on 23. April 2023, 13:05 by polar
An epic tribute to an already brilliant puzzle. It's been a while since I sweated as much as I did solving this one, but it was worth every minute of it. Sheer madness, in the best possible way!
