Kra-Z Cages
(Published on 30. January 2023, 02:07 by yanggang)
Normal sudoku rules apply. There are nine "doubler digits" in the puzzle whose value is counted as twice the digit in the square for the purposes of the renban lines and cage sums. There is one doubler digit per row, column and 3x3 box, and each of the numbers 1-9 is a doubler digit somewhere. Cells on a grey renban line contain a consecutive set of values (not necessarily in order). Values in cages must sum to the total in the top-left of the cage.
Cages may not contain duplicate digits (as this would break sudoku for a 3x3 box) but CAN contain two cells contributing the same value to the sum (for example: a doubled 3 and a 6 in the same cage is allowed). On the other hand, a renban line may not contain duplicate values but CAN contain cells with the same digits if allowed by other rules (for example: a 2, 3, and doubled 2 is allowed on a line).
CtC App: Link
F-puzzles: Link
Solution code: The solution code is the seventh row (9 digits).
Comments
on 30. January 2023, 19:12 by AryaSV
I have taken two attempts, have spent more than 3 hours in total. For the love of god, I seem to have gotten some deduction wrong which leads me to a conflict in the end :( Hoping to get this right soon
Edit: I spiralled into confusing values vs numbers on lines. Finally got the solution today morning! Very nice puzzle, had lots of fun time with this one.
Reply: Glad you enjoyed! Sorry for the confusion. - yanggang
on 30. January 2023, 17:00 by yanggang
Clarified rules thanks to a comment by Allagem.
on 30. January 2023, 08:28 by Allagem
VERY tricky puzzle. Trying to make deductions while accounting for the possibility of doublers is very challenging, especially on renbans. I'm sorry to admit I needed to use a single, relatively short bifurcation near the beginning of the puzzle (looking ahead ~8 moves to eliminate a possibility). But otherwise I think I proved every step. Renbans have some particularly confusing relationships with doublers. I can tell you worked very hard on this, well done and good puzzle!
My advice for other potential solvers: renban lines cannot have duplicate values while killer cages cannot have duplicate digits. (I hope it's clear that value includes the x2, but digit does not). In this way, they treat the doublers differently and it takes some mental effort to keep those straight.
EDIT: Holy cow, I just realized this is your very first published puzzle! What a crazy puzzle to debut with!
