Method to the Madness
(Published on 4. January 2026, 17:31 by Merdock)
NOTE: I updated the way the fog unrolls. It's a little more difficult and, in my opinion, a little more enjoyable. I left the original up here, but between the two I would recommend this one.
Click here to solve the updated puzzle.
Rules:
Regular sudoku rules:
Place the digits 1-9 in every row, column, and box
XV:
The X symbol separates digits that sum to 10. The V symbol separates digits that sum to 5. Not all X or V symbols are given
Dynamic Fog:
Fog will revealed along a set path
Howling Mad Lines:
Purple lines do not follow any traditional line rule set. In fact, no other line rule set can go where a Howling Mad line is. (specific list provided below, as well as an image of impossible Howling Mad lines)
For this puzzle, Howling Mad lines are always three cells long and are always either strictly vertical or strictly horizontal. Additionally lines can not overlap each other. No sets of digits appear on more than one line. For example, if one line contains 1, 2, and 4, no other line can contain all three of those digits.
Given those rules, all lines are given. If a set of digits appear like they would form a line, but don't they violate an expressed rule. They are longer than three cells, they are not strictly vertical or horizontal, the set of digits already appear on another line, placing a line over the digits would cause them to overlap, or the digits are ordered in a way that prevents a line.
Lines that cannot replace Howling Mad Lines
| Line Type | Description |
|---|---|
| Renban | Consecutive non-repeating digits |
| Nabner | Non-consecutive non-repeating digits |
| Parity | Alternating even/odd |
| Entropy | Every 3 digits has a [1,2,3], [4,5,6], and [7,8,9] digit |
| Modular | Every 3 digits has a [1,4,7], [2,5,8], and [3,6,9] digit |
| German Whisper | Adjacent digits differ by at least 5 |
| Dutch Whisper | Adjacent digits differ by at least 4 |
| Palindrome | Digits read forward as they do backwards |
| Sequence | Adjacent digits all have the same difference |
| Region Sum | Box borders separate regions that all sum to the same number |
Note:
Normally I include ten lines as impossible lines for Howling Mad, but a commenter gladly pointed out that that does occur in this puzzle. I've this removed it from the list of impossible lines. My apologies
Examples of Impossible Howling Mad Lines:
Solution code: Column 6, read top to bottom
Comments
on 11. January 2026, 14:07 by Swiddow
This was quite fun, I couldn't put the puzzle down til I finished it. I have never played the howling mad lines before. Missing the "all lines are given" constraint the first read through had me scratching my head awhile. =)
Merdock: Thank you! I introduced the lines in my last puzzle, but I feel this was a much better exploration of the concept.
on 7. January 2026, 16:13 by Katchoo
Das war sehr knifflig aber auch sehr toll! Am Ende ist mein Gehirn etwas Karussell gefahren, und musste versuchen, Linien und nicht-Linien schön auseinerzuhalten. :)
on 6. January 2026, 03:49 by Merdock
Changed list of impossible lines and added note indicating that
on 6. January 2026, 02:56 by sparkymanu
I know you didn't mention it in sudokupad, but in the description you talk about "Ten lines" which would make box 9 wrong ; This puzzle is very hard but worth the time to stretch the brain!
Edit : I finally finished it and wow that was tricky... the negative constraint put me to sleep
Merdock: You are completely right, I didn't notice the ten-line failure. It looks like that's not the only spot. As this puzzle is already up, I'll just remove that from the list of impossible lines for this puzzle. Luckily it's not included in my picture of impossible lines, so I won't have to change that.
I'm sorry the negative constraint put you to sleep. How I had the dynamic fog unveil really puts more or less emphasis on it. Depending on when I reveal the very last of the fog, some of those negative deductions go away. Thank you so much for the feedback, I'll try to use it to improve future games.
Edit Spark : I didn't mean as a bad thing, I meant it took all my last brain power for the day to finish it haha, but I'm glad I pushed through!
on 5. January 2026, 20:27 by Merdock
Added an updated link to a slight more difficult slightly more enjoyable way the fog unravels.
on 5. January 2026, 00:06 by Merdock
Edited constraint rule on howling Mad lines
on 4. January 2026, 23:54 by gdc
r6c789 is *** in the finished grid. Am I misunderstanding the negative constraint?
Merdock: I'm sorry, I forgot to mention that lines can not overlap. I will update the rules on the page.
gdc: Thanks for the quick response. That makes scanning for the negative constraint a lot more straightforward.
