Entropy threshold
(Published on 22. January 2026, 12:43 by fractalminding)
Normal sudoku rules apply. Each 2x2 box in a grid has contain low digit {1,2,3}, middle digit {4,5,6} and high digit {7,8,9}.
Solution code: row 1 (9 digits)
Comments
yesterday, 18:56 by Djirt
Спасибо, отличное судоку!
yesterday, 18:23 by Qodec
Very rewarding solve! Hard to believe this even works!
yesterday, 15:41 by Mad-Tyas
I'm very excited to see this puzzle. And also sort of relieved. I would like to explain why.
Questions like "What is the minimum number of givens/clues to achieve a unique solution with a certain variant/ruleset?" always fascinated me. And when I invented the Entropy constraint more than four years ago and started to explore it, there was of course this question: What is the minimum for Entropy?
It's hard to estimate how much time I put into the search. And I managed to find more than 100 arrangements with 7 given digits, but never achieved 6.
Until now I had myself quite convinced that 6 is probably not possible. But it still bothered me to not really know it and so I very likely would have started again to search for it at some point :D
Thank you very much for creating and publishing this puzzle, which now allows me to complete this chapter as well!
A really great achievement! Congratulations :)
Reply: Thank you. I'm glad to see your comment! I know you often comment on entropy sudokus, and that's actually what motivated me to look for six-digit sudoku. I've also always wanted to solve a challenging math problem, even though I'm not a mathematician. It was quite challenging, but I'm glad it happened. If you could tell me how to contact you, I'd be happy to send you other six-digit sudokus that apparently have no human solution. I'd also tell you how to find the others. I'm sure you can create your own version that will have a more beautiful or more complex solution.
yesterday, 10:05 by Snookerfan
Great puzzle! I really liked the quite difficult and challenging endgame, which was very interesting and fair! Thanks
yesterday, 09:01 by Onkel_Dagobert
The low rating is totally undeserved. I think this is a brilliant puzzle. There is zero bifurcation needed, it stays interesting until the very end, and the logic required is challenging, but completely fair.
on 22. January 2026, 23:42 by apendleton
This was fun! Surprisingly tricky endgame. I thought I had it in the bag and was about done, but the last couple of disambiguations took me quite a bit longer than I expected.
Reply:
Apparently, this is the reason why this sudoku received a low rating. But I created it with the idea of using the smallest possible number of digits: 6. And this is the best implementation I found. I'm glad you liked it. Thanks for the feedback.
