4-color killer sudoku #1
(Published on 18. February 2021, 04:42 by Nylimb)
Note: If you only want to solve one puzzle of this type, I recommend 4-color killer sudoku #2 instead of this one. It avoids the unsightly given digit, and is somewhat easier to solve.
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.
I had hoped to find a puzzle of this type with no given digits, but I eventually gave up. I don't know if such a puzzle exists. (P.S.: 6 weeks later, I finally found one: 4-color killer sudoku #2.)
The puzzle is available on Penpa.
Solution code: Row 1 and row 6.
Comments
on 27. July 2023, 01:17 by Nylimb
Added suggestion to solve 4-color killer sudoku #2 instead.
on 15. June 2022, 06:06 by Vebby
5/5 difficulty for me. Latter half was brutal, but once I got the ball rolling it was a joy to solve. Also enjoyed the interesting cage colouring phase which wasn't nearly as hard.
on 21. June 2021, 08:29 by Mody
Großartig. Es hat viel Spaß gemacht, die Farben und Werte herauszufinden.
Great. It was a lot of fun to figure out the colours and values.
on 3. April 2021, 04:49 by Nylimb
Added link to 4-color killer sudoku #2.
on 2. April 2021, 19:33 by Nylimb
Added '#1' to the name.
on 22. February 2021, 02:38 by Storm
Very challenging and interesting solve! Thanks for creating it.
on 22. February 2021, 02:10 by harrison
@Nylimb: I found this to be very difficult! I spend most of the weekend staring at the grid after finishing the coloring and only found a way through it today. I won't be surprised to see this get to 5*s.
Thanks for sticking with this, it was really enjoyable to finally solve.
on 19. February 2021, 19:15 by Bobby
Very nice and entertaining puzzle! Hopefully more people give it a go.
on 18. February 2021, 17:38 by Nylimb
Raised initial difficulty estimate.
on 18. February 2021, 14:17 by Jesper
Cool puzzle! It was fun to figure out the colors. Very challenging (but also interesting) killer. It wouldn't surprise me if the final difficulty rating will be considerably higher than 3 stars.
@Jesper: Thanks; I've raised the difficulty estimate to "hard". (I always have trouble judging that. By the time I'm ready to publish a puzzle, I've gone through the solution path, in multiple versions, so often that it seems fairly obvious.)
on 18. February 2021, 13:02 by bigger
Nice. But I suck at killer, it took me way longer than i expected. Totally worth it.
