4-color killer sudoku #2
(Published on 3. April 2021, 04:45 by Nylimb)
This puzzle is based on the four-color theorem: Mapmakers sometimes color regions, such as countries, so that regions which share an edge have different colors. In 1852 Francis Guthrie noticed that he could always do that using just 4 colors, and he wondered if that was true for all maps. (This assumes that each region is contiguous; if some countries are split into geographically separate regions, then more than 4 colors may be needed.) This was finally proved in 1976 by Kenneth Appel and Wolfgang Haken, using many hours of computer calculation. No proof has ever been fully checked without using a computer.
This is a standard killer sudoku, except that the cage sums are not given:
Fill the grid with digits from 1 to 9, so that every row, column, and 3x3 box contains each of the 9 digits exactly once.
Digits may not repeat in a cage, defined by the dotted lines. The sum of the digits in each cage has one of 4 values, which must be deduced. Cages which share an edge have different sums. (If two cages meet only at a corner they may have the same sum.) So if you color each cage based on its sum, you'll have a coloring of the cages of the type guaranteed by the four-color theorem.
After publishing 4-color killer sudoku #1, I became obsessed with trying to find such a puzzle that has a unique solution without any given digits. It took a lot of time and effort, but I finally found one. Unfortunately I couldn't see how to solve it without bifurcating. But after testing a few slight variations of that, I came up with the puzzle above, which I think is a bit easier than the previous one.
You can solve this in the CTC-app.
Solution code: Row 5 and column 8.
Comments
on 26. July 2024, 20:21 by deleva
Awesome impressive achievement.
on 21. July 2024, 20:38 by Nylimb
Thanks to glum_hippo for recommending this on the CTC Community Discord server, and to all the recent solvers.
on 17. July 2024, 18:52 by Qodec
One of the most fun puzzles I've solved in a considerable time. So impressive!
on 17. July 2024, 13:55 by glum_hippo
Here's a working penpa version, with answer check, if anyone wants it
https://tinyurl.com/3wpdwnan
on 17. July 2024, 07:20 by Agent
A masterful construction, thanks! The ruleset is executed perfectly.
on 17. July 2024, 06:55 by applesauce
incredible achievement and a blast to solve!
on 17. July 2024, 01:20 by Wessel Strijkstra
Truly incredible construction, I'm not often this entertained by a sudoku, from start to end a fantastic and smooth solve. Very well done.
on 16. July 2024, 23:43 by Fool on Hill
Stunning setting - not easy though
on 16. July 2024, 22:40 by Phistomefel
Great puzzle and it is incredible to me that you managed to get a working constellation for this ruleset. Kudos, Nylimb!
on 16. July 2024, 04:31 by glum_hippo
Stunning! Was more than 3 stars for me but really well thought out
on 24. February 2024, 23:02 by Nylimb
Added CTC-app link, with answer check. Apparently all git.io links, like the one I used before, have stopped working.
on 24. February 2024, 07:45 by Nylimb
Added warning about broken penpa link.
on 18. February 2024, 17:41 by thorscouts
Currently, the link to the Penpa option says "404 not found, try again".
@thorscouts: Sorry about that! I'll recreate the link and check to see if any of my other puzzles are affected, as soon as I have time. It might be a few days.
on 15. June 2022, 17:41 by Vebby
Superb! The solve path was a lot smoother than its prequel.
on 6. June 2022, 21:15 by Yawnus
What a beautiful puzzle! Without knowing that you had already done this, I also tried so hard to create a puzzle with exactly the same constraints. Finally I had to give up the requirement to fill the whole grid. "Killer Quartet" (0008WS) was my best effort with a partial grid.
@Yawnus: I'm glad you liked it. Filling the whole grid definitely made it more difficult to create. I'm working on your puzzle now.
on 6. April 2021, 00:59 by marcmees
wow. tough one. kept me up late. >4* in my opinion. Thanks
on 4. April 2021, 14:30 by Johannes Quack
I've seen quite a lot of sudoku variant puzzles - this is one of the very best!! Unbelievable, that you managed to get this correct! And the solve is not easy but fun. Big Compliment!
on 3. April 2021, 07:22 by ranhothchord
that took me a LONG time, but it was great. getting the actual digits was slow going for me, but I'm very glad I stuck with it. overall, i think this had a wonderful theme and very interesting solve
