Factory Loop
(Published on 13. July 2026, 11:20 by marty_sears)
Rules:
Normal sudoku rules apply.
Draw a loop, one-cell wide, that moves orthogonally between cells.
Two loop cells may only touch orthogonally if they are directly connected along the loop. Two loop cells may only touch diagonally where they are either side of a corner cell along the loop (ie; the loop doesn't 'touch itself' orthogonally or diagonally.)
A green circle is on the loop, and its digit indicates the number of cells in its box that are on the loop.
A red square is NOT on the loop, and its digit indicates the number of cells in its box that are NOT on the loop.
For any two neighbouring cells along the loop, dividing one by the other gives an exact integer (one is a multiple of the other.)
Solution code: Column 9 cells that are NOT on the loop, reading downwards
Comments
on 4. August 2026, 00:07 by Astraeus
Unbelievable! I am flabbergasted that so little could be placed in the grid and still define a unique solution, much less one that flows so naturally. Yet another work of sublime genius.
on 1. August 2026, 18:08 by yuripuppies
Had a lot of fun with this one! The way the loop came together in the end was very satisfying
on 26. July 2026, 21:36 by gren
How does he keep doing it
Spectacular as usual
on 24. July 2026, 22:23 by alanb
The loop never touched itself but it touched me deeply
on 24. July 2026, 20:42 by Muratmet
Superb setting as always, absolutely gorgeous all the way through!
on 20. July 2026, 16:54 by Blake Saligia
A stunning global chain reaction achieved with just the minimalist placement of only 3 circles and 2 squares. Amazing!!!
on 18. July 2026, 17:25 by Klausku
Brilliant setting! First you cannot believe that only 5 clues lead to an unique solution. But then th puzzle flows smoothly and concludes in an gorgeous ending. Wow. Thanks Marty.
on 16. July 2026, 14:08 by abw
A wonderful puzzle Marty, as usual.
I'm afraid I also struggled with the original wording, assuming that the loop could touch itself diagonally. Having read the more recent comments here clarifying the rules, it all fell into place nicely.
I personally think that "the loop may not touch itself, not even diagonally" is unambiguous, but perhaps that's just because it's the wording that I'm used to. However, I do appreciate that newer solvers might need the additional clarification.
Your updated description makes things much clearer.
Thanks again Marty! A very enjoyable solve after my initial setback.
on 16. July 2026, 09:59 by Nairurian
Very nice puzzle although I did struggle a bit with a section in the rules before realising it meant “the loop doesn't 'touch itself' not even diagonally”.
Marty: yes, I can see it is nicer to just read that shorthand if you are used to the rule. But you can see how its problematic for people that aren't...
Nairurian: Yes, it’s definitely something springing from being used to certain phrasings on this page and I’m not saying it should be switched in the description, just that it was something that gave me some pause at certain points during the solve when I needed to rule it out.
on 16. July 2026, 09:08 by stranger
given "the loop" is an indexed sequence of cells, loop cells may neighbour orthogonally if and only if their indices differ by one, and diagonally by two.
on 15. July 2026, 06:33 by MusicGusto
Absolutely brilliant
on 15. July 2026, 02:18 by Exigus
Incredible how little is needed for a unique solution. Thanks!
on 14. July 2026, 18:25 by tcmsurfer
Finally, a new Marty puzzle I get to actually solve. Thank you so much for that one, loved it.
As a novice with CTC's Simon knowledge, I was able to manage this puzzle, even though I got myself in trouble twice. Once because I didn't read the rules correctly (it's not the 3x3 surrounding cells that are counting, but the box it is in!) and once because I made a Sudoku error and a digit on the loop was wrong. Funny enough it solved the same in shape in the error state.
Thanks again1
on 14. July 2026, 13:38 by SennyK
Hats off for creating such a good puzzle with only 5 clued cells! :-)
on 14. July 2026, 11:42 by Miatc
Beautiful puzzle, such a simple setup
on 13. July 2026, 20:47 by blackjackfitz
Huzzah!
on 13. July 2026, 19:50 by Franjo
Thank you very much for creating and sharing another beautiful puzzle. You used these multiple/factor lines for your last DFM-puzzle already, so maybe it’s time to give them an official name? I’m sure that other setters will use them….
Marty: I've been calling them Multiple Lines. I've seen other people call them Factor lines though, which is fair enough... I am enjoying them at the moment!
on 13. July 2026, 19:13 by brskri
Neat puzzle, as expected from Marty. It's surprising how many restrictions can come from so little clues -- but the outcome of that is a tight solve path -- very nice.
on 13. July 2026, 19:01 by Piatato
Smooth and fun, thanks!
on 13. July 2026, 16:10 by highonlife
Ok, I struggled with this one more than I should have.
Nice Puzzle.
on 13. July 2026, 14:38 by sujoyku
Thank you for yet another wonderful puzzle, Marty!
on 13. July 2026, 14:38 by mscha
A new Marty Sears puzzle! It's been a while... :-)
Very nice one. I found the break-in fairly easy - it helps that we've had a few divisibility puzzles recently - after that it was a bit trickier, but I never got stuck.
on 13. July 2026, 13:45 by Sotehr
A true gem among Marty Sears puzzles!
on 13. July 2026, 13:36 by amirs
It took me some time in the beginning to convince myself it's not immediately broken and find the initial break in. After that it was very smooth and fun!
on 13. July 2026, 13:24 by vukkarak
I have struggled with the beginning but then it was a nice flow!
on 13. July 2026, 12:21 by pmays123
Magical puzzle! Thank you
on 13. July 2026, 12:08 by Christounet
Miraculous!
This must have taken a while to find the perfect location for the last clues.
on 13. July 2026, 11:58 by Prof.Dori
One of my favorite puzzles from Marty, just brilliant from start to finish.
