A Mathematical Miracle
(Published on 10. June 2026, 09:15 by Sudokujoker)
This is my attempt at a blank grid sudoku. Enjoy :)
Normal sudoku rules apply: place the digits 1-9 once each in every row, column and 3x3 box.
Cells within a chess king's or chess knight's move may not contain the same digit. Orthogonally adjacent digits may not be consecutive.
Two prime numbers, X and Y, can be added together to give another prime number, Z.
X is the digit in Row X, Column X, and also is in position X inside box Y.
Y is the digit in Row Y, Column Y, and also is in position Y inside box X.
To clarify, positions are read from left to right and top to bottom in usual western reading order.
Sudokupad link: https://sudokupad.app/f9i96469hi
Solution code: Row 9
Comments
on 20. June 2026, 19:22 by pmays123
Very cool puzzle! Its amazing how this solves so nicely with such little info. Thanks!
on 17. June 2026, 20:58 by Sudokujoker
Thanks to everyone for the feedback! Sorry that I phrased the rules in a way that was confusing for some ... I put that down to my efforts to keep the instructions succinct. Thanks for solving and please check out my other puzzles if you enjoyed this :) -SJ
on 16. June 2026, 22:08 by Maldivia
I enjoyed it, and didn't find the rules confusing; could they be rephrased slightly, sure, but I had no doubt about them.
As for the break-in, there are only two combinations of digits that can be X and Y, when taking into account that X and Y needs to be sudoku digits, and one of those combinations can be ruled out immediately. And after that, it's a straight forwards anti-knight/king/consecutive, basically solving one digits at a time.
on 14. June 2026, 04:53 by Davos
Yeah, the rules are unclear, which turns a 1 into an impossible puzzle
on 13. June 2026, 17:58 by VitP
"level 1".
you keep using that word. i do not think it means what you think it means.
in particular, you should give at least level 2 to the solver due to the effort they need to put in to figure out the INTENDED meaning of the rules, because it does not match the WRITTEN meaning, as defined by the rules of plain english.
for example, the usage ... COMMA ... COMMA AND ... creates a LIST etc.
(which results in absurdity ... NO digits qualify)
there are easy ways of writing the rules to make them perfectly clear
for example :
Two prime numbers, X and Y, can be added together to give another prime number.
ONE instance of X is in (Row X, Column X), and ANOTHER is in position X inside box Y.
ONE instance of Y is in (Row Y, Column Y), and ANOTHER is in position Y inside box X.
THAT is conceivable.
on 12. June 2026, 03:29 by Chenyekai
着色部分很漂亮。
on 11. June 2026, 11:36 by Rollo
Very nice, solved with a little bit of coloring ;-).
on 11. June 2026, 00:36 by Dr Logic
Interesting puzzle
on 10. June 2026, 23:49 by itsid
now.. finally got around actually giving it a shot; what a beautiful puzzle!
it is about the easiest miracle sudoku I solved in the last few days,
and -to me- it is certainly the most beautiful so far.
[sometimes the low hanging fruit is the sweetest]
Thanks for setting!
on 10. June 2026, 22:35 by Ol-Jay
Was this supposed to be a coloring sudoku..? Because I solved it without.. XD Lovely puzzle, thanks for setting!
on 10. June 2026, 22:33 by Vaurien
Beautiful puzzle! I sometimes forget how powerful the anti-king + anti-knight constraint is, and while it took me a bit to get the first set of digits in the puzzle, the more I did get the faster it filled in. ????
on 10. June 2026, 22:08 by drbs
Nice, the universe sang again.
on 10. June 2026, 20:52 by Fisherman
I think the rules are sufficient.
on 10. June 2026, 19:43 by itsid
*cough* w/o having the puzzle started yet, much less solved... I have to disagree with Lithum-Ion.
all primes in a sudoku cell are single digit.
two of which form a third...
One of those is blatantly obvious, and say we call that X
So again w/o having started I can place a digit.
in RxCx ... knowing that alone (and the rules of miracle sudoku) reveals the ONLY possible Y
And yes, I know X and Y without even starting the puzzle, and without a doubt. (tt0126765)
and with that 4 digits down without opening the link
on 10. June 2026, 18:00 by Frankster
Excellent puzzle
on 10. June 2026, 14:47 by boggles
fun! had to draw on a few different sudoku skills, but nothing too challenging. great stuff
on 10. June 2026, 14:11 by Lithium-Ion
Nice idea! However, I do not understand how this can be rated as one star difficulty since you need huge amounts of coloring. Moreover, the rules should be changed to clarify that the property holds not for all prime numbers X and Y whose sum is a prime, but only for one X and Y.
on 10. June 2026, 14:11 by Lithium-Ion
Nice idea! However, I do not understand how this can be rated as one star difficulty since you need huge amounts of coloring. Moreover, the rules should be changed to clarify that the property holds not for all prime numbers X and Y whose sum is a prime, but only for one X and Y.
on 10. June 2026, 12:22 by superkinkel
It's incredible how powerful the combination of the constraints is. The coloring is actually very easy. Figuring out the prime constellation was actually the hardest part. I had the possible candidates immediately, but excluding the impossible took me longer than it should have.
on 10. June 2026, 10:37 by phono
Very nice puzzle! Took me a little to figure out the prime constellation – and the rest flows nicely with the restrictions. Coloring helps a lot. Thank you!
