Square Killer Quadruplets
(Published on 5. November 2020, 00:00 by SudokuExplorer)
Normal sudoku rules apply.
Rules about Killer Quadruplet Cages:
In a killer quadruplet cage, each digit appears exactly four times within the cage.
No two cells a knight's move apart, within the cage, can be equal (Anti-knight constraint inside the quadruplet cage).
Its cage sum is the total of all the digits in the cage.
For example, if a killer quadruplet cage has four 1s, four 2s, four 3s and four 4s then its cage sum is 4*1+4*2+4*3+4*4=40.
In this sudoku, the two cages are killer quadruplet cages with cage sums being square numbers.
Rule about Little Killer Clues:
The values (not necessarily distinct) on the diagonal, in the direction of the little arrow, sum to a square number.
You can try this on Penpa+ or F-Puzzles (the yellow and blue regions are the killer quadruplet cages/regions). I hope this is a fun one!
Have fun colouring!
Hint 2: (highlight white text below) What are the square numbers modulo 4?
That is, what are its possible remainders when divided by 4?
If 4x+3y is a square, then what can you say about y?
Solution code: Enter the first and last rows
Comments
on 10. November 2021, 16:52 by SudokuExplorer
@Vebby: Thanks for giving this a try, I'm really pleased you enjoyed the later disambiguation. :-)
It turned out better than intended thanks to the first few solvers who spotted an error in the initial version.
on 6. November 2021, 08:17 by Vebby
Loved it! The disambiguations towards the end were so much fun. Thanks S.E.! :)
on 31. July 2021, 20:47 by SudokuExplorer
Fixed labels/tags
on 11. January 2021, 20:12 by SudokuExplorer
Fixed title
on 7. November 2020, 13:34 by CaneloC
Very nice! So few clues, but they all guide the way.
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Thanks CaneloC for your feedback. I see what you did there ;-)
on 6. November 2020, 15:18 by bosjo
Great puzzle, even though I think the pentuplet still is my favourite of the puzzles I've solved in this series. The ruleset for this puzzle is simpler, so purists may like it better.
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Thanks for trying it bosjo, and for your feedback. :-)
I agree that the pentuplet puzzle is a bit better, because of the less obvious structure and the interaction of the different constraints. I had tried a month ago to fit two killer quadruplet cages, but couldn't. So I'm still pretty happy with this one.
on 6. November 2020, 03:36 by LongOrteil
Reworked the puzzle again. Got the same solution as last time. Entered the solution code and this time it worked! Phew! Really awesome puzzle S-Explorer!
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I initially had tried to make the fourth arrow easy, but this unfortunately led to two solutions. I'll be more careful the next time. I'm really glad you enjoyed it enough to retry the puzzle. Thank you :-)
on 6. November 2020, 01:38 by Dina
Fun solve! Really interesting logic after the colouring too! I'm happy I found this website.
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Welcome to LMD! I'm glad you were entertained. I'm sure you'll enjoy more puzzles on this wonderful portal. :-)
on 6. November 2020, 00:06 by TimE
Very nice puzzle! The colouring was fun and then the rest of the logic was both interesting and very unique! Don't worry about the mishap, it happens. I look forward to the next one :-)
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Thank you for you kind words, TimE. I'm pleased it was an interesting solve :-)
on 5. November 2020, 17:12 by panthchesh
Sudoku Explorer, I LOVE your puzzles! :) I just wanted you to know, even though this had a slight hiccup, I'm still looking forward to the next one! :D
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Thanks for your heart-warming comment. I'll be extra careful the next time. :-)
on 5. November 2020, 16:53 by marcmees
fun. thanks
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I'm really glad you enjoyed it! Thanks for trying the fixed puzzle :-)
on 5. November 2020, 16:10 by Storm
Really fun puzzle! Thanks for fixing it and my logic was the same as yours :-)
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Thanks for trying it after the fix! I'm glad it turned out to be enjoyable for you :-)
on 5. November 2020, 16:07 by ThrowngNinja
I will say even with the solution mishap, I found this puzzle quite enjoyable!
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My heart was in my throat, when I logged in to find multiple solutions. Your comment makes me feel better. Thanks! :-)
on 5. November 2020, 14:43 by SudokuExplorer
Big apologies to those who tried the initial version. Luckily I only needed to change one arrow clue, so most of the logic is the same as before.
on 5. November 2020, 13:20 by SudokuExplorer
I apologise for the multiple solutions... I thought I had systematically checked all the cases but I was wrong.
I'll deactivate in half an hour, and try to fix it soon. I'll try to keep the starting logic similar. Sorry for the frustration at the end.
on 5. November 2020, 12:08 by Sktx
I got to the "correct" solution code, and I think I ruled out the other possibilities logically, but the solutions found by other commenters do seem to work, I can't find the problem with the rules. It's troubling. But there might be a unicity problem with this one.
@panthchesh actually your first solution is mine too, and the code did work for me.
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I personally apologise for my oversight. I have now fixed it so that there is now only one solution.
