4-color killer sudoku #2
(Eingestellt am 3. April 2021, 04:45 Uhr von 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.
Lösungscode: Row 5 and column 8.
Kommentare
am 24. Februar 2024, 23:02 Uhr von Nylimb
Added CTC-app link, with answer check. Apparently all git.io links, like the one I used before, have stopped working.
am 24. Februar 2024, 07:45 Uhr von Nylimb
Added warning about broken penpa link.
am 18. Februar 2024, 17:41 Uhr von 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.
am 15. Juni 2022, 17:41 Uhr von Vebby
Superb! The solve path was a lot smoother than its prequel.
am 6. Juni 2022, 21:15 Uhr von 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.
am 6. April 2021, 00:59 Uhr von marcmees
wow. tough one. kept me up late. >4* in my opinion. Thanks
am 4. April 2021, 14:30 Uhr von 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!
am 3. April 2021, 07:22 Uhr von 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
