4 Line Theorem
(Published on 19. December 2025, 22:56 by Manta-Ray)
Normal sudoku rules apply.
Every line in the puzzle conforms to one of 4 constraint types, listed below. No two orthogonally adjacent lines (i.e. two lines that pass through a pair of orthogonally adjacent cells) may be of the same constraint type.
- Renban: Digits along a Renban line form a non-repeating set of consecutive values.
- German Whispers: Adjacent digits along a German Whispers line differ in value by at least 5.
- Region Sum: Box borders divide a Region Sum line into segments of equal value. Different Region Sum lines may have different segment values.
- Parity: Digits along a Parity line alternate between odd and even values.
Solve on SudokuPad
Solution code: The number of times each constraint is used (in the order listed in the rules), followed by the sum of each Region Sum line's individual segment value, all separated by a '-' (e.g. 2-4-5-1-55)
Comments
on 20. February 2026, 07:11 by Zanno
What a wonderful puzzle! Thanks for sharing!
on 25. December 2025, 15:37 by SparkNights
Is a hybrid line (ie a line conforming to at least 2 of 4 types) vaild in this puzzle
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Hi! Every line only conforms to one of the 4 rules
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emmmm...... I'd like you to edit the rule to clarify it, for example, "Hybird line (like 49272, which is a hybird of Parity and German Whisper) is NOT allowed"
on 23. December 2025, 16:58 by War
Beautiful puzzle! More approachable than a 5* for sure.
on 23. December 2025, 03:45 by Tacocat
Very good and challenging puzzle, thank you!
Nice reference to the 4 color theorem which comes handy in the resolution.
on 22. December 2025, 20:55 by Jrosas
Nice logical flow to the puzzle. The Solution code instructions required some thought.
on 22. December 2025, 17:15 by henrypijames
The puzzle is only 4¼ difficulty for me, but the solution code is definitely 5+ difficulty!
on 20. December 2025, 18:04 by Bankey
Tough but great fun. Thanks, @ Manta-Ray :).
on 20. December 2025, 16:18 by Snookerfan
Superb puzzle! Very interesting ruleset. A challenging solve up to and including the solution code. Thank you
