Duty pairs
(Published on 20. August 2025, 19:09 by Adrian71)
• In this puzzle, there are four types of line constraints: German whisper, Region sum, Modular, Entropic (for definitions see below)
• Every line obeys exactly two of these constraints
• Any two lines of the same color together contain all four constraints
• For every possible combination of two constraints, at least one line is present in the puzzle
• The digit on the left side of the > sign is higher than the digit on the right side of it
Solve on SudokuPad
The lines of the same color are:
• R2C1-R5C1 and R6C8-R9C8
• R2C2-R2C5 and R4C4-R1C7
• R3C7-R6C7 and R3C9-R6C9
• R4C6-R7C6 and R6C1-R9C4
Definitions:
• German whisper: adjacent digits on the line differ by at least 5
• Region sum: border boxes divide the line into segments; the sum of the digits is the same for all segments on the line
• Modular: any set of three adjacent digits along the line has three different remainders when divided by 3
• Entropic: any set of three adjacent cells along the line must contain a low digit (123), a middle digit (456), and a high digit (789)
Solution code: The digits of row 8
Comments
on 2. September 2025, 03:28 by marajade
This puzzle was a stretch for me but I'm so glad I put in the time! I spent 2 hours on it yesterday only to realize I'd made a mistake early on (missed some combo possibilities for the 3+1 lines so I mis-assigned the salmon pink pair). Started over more carefully today, spent another 2 hours, and I got it! What a gorgeous puzzle; it was so cool to see all the deductions unfold just from these 8 lines.
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It's great to hear that you managed to finish the puzzle in the end, I truly admire your perseverance and not giving up! Thank you for your feedback, and thank you for also trying a puzzle with less solves, it is highly appreciated!
on 21. August 2025, 01:58 by rameshsrivats
Fabulous puzzle. Incredibly smooth and fun.
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Thank you for the solve and the comment, it is appreciated very much!
