4-color killer sudoku #1
(Eingestellt am 18. Februar 2021, 04:42 Uhr von 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.
Lösungscode: Row 1 and row 6.
Kommentare
am 27. Juli 2023, 01:17 Uhr von Nylimb
Added suggestion to solve 4-color killer sudoku #2 instead.
am 15. Juni 2022, 06:06 Uhr von 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.
am 21. Juni 2021, 08:29 Uhr von 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.
am 3. April 2021, 04:49 Uhr von Nylimb
Added link to 4-color killer sudoku #2.
am 2. April 2021, 19:33 Uhr von Nylimb
Added '#1' to the name.
am 22. Februar 2021, 02:38 Uhr von Storm
Very challenging and interesting solve! Thanks for creating it.
am 22. Februar 2021, 02:10 Uhr von 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.
am 19. Februar 2021, 19:15 Uhr von Bobby
Very nice and entertaining puzzle! Hopefully more people give it a go.
am 18. Februar 2021, 17:38 Uhr von Nylimb
Raised initial difficulty estimate.
am 18. Februar 2021, 14:17 Uhr von 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.)
am 18. Februar 2021, 13:02 Uhr von bigger
Nice. But I suck at killer, it took me way longer than i expected. Totally worth it.
