A Winding Path: Yet Another Sudoku Variant Ruleset!

#Sudoku #SudokuSleuth

Today's Puzzle:

Uses yet another variant ruleset from Arbitary, an individual who is clearly a Sudoku variant construction machine!

Do let me know in the comments if you enjoyed the variant and wish to see some of the tougher puzzles that use it.

Link to Play Along:

A Winding Path by Arbitrary

Rules:

Normal sudoku rules apply.

Consecutive Sum Lines: Within each 3x3 box, the sum of digits along a contiguous line segment is consecutive with the sum along the red line segment in any box it directly connects to. If a line re-enters a box, each contiguous segment is a separate sum which may be different in value if permitted by other rules. For example, in box 9, the sum of [R8C7, R9C7, R9C8] and the value of R7C7 may be different but each differs from the value of R8C6 by exactly 1.

i.e. Lines behave like region sum lines, but the sum increases or decreases by 1 whenever the line crosses into a box.

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[matt_the_musician]

Wow, this kind is neat! I like the consecutive sum lines! I had not seen those anywhere else.

[anaayoung]

Another constraint? You always bring this new "stuff" and I love it!!🤩

I tought it would be a hard puzzle. But this video has 22 min and you started after 6min, so I decided to try it, and it was worth it! Started the same way was you. But I did a mistake in R8 C4C5 because I used 5 and 6, not 5 and 7 (as possible values of the line), almost at the end but I could not place 6 in box, come back, did again, but still got a very good time! 😊

Lovely puzzle, but I guess this one would be hard in the near future, doing things like 36 and 37, rather than 10 and 9. 😅

Thanks for this puzzle! You can do the hard one, and even if it is difficult, is ok, I like watch the solve too and we always can learn more! 🤗

[richardglover]

Simple but lovely. Or better still, simply lovely.

[jdyerjdyer]

An easy 17 and 45. After a very long work day, nice to have an easy one. Thanks!

[simonwstrong]

Neat solve. Looking forward to more of these.

[latze]

Beautiful puzzle!
Took me half-century to notice the 4 cell line in box 1... after that everything went smoothly

[Vernicho]

I had to watch your intro and initial start to fully understand how the variant worked but then it did flow nicely once I knew the whole sum line increased or decreased, not just the digit as lines crossed boxes. That meant I did not find the initial break in in box 1 myself so can't really consider it a solve but at least I know how to approach consecutive sum lines in future puzzles.

[neil]

Fabulous puzzle. I set one segment equal to its neighbor and had to rewind a bit to fix it, but other than that, very straight forward.

[psiphiorg]

This was an interesting constraint! I started by coloring the line to indicate odd or even totals (not knowing which was which to start with), and was about three boxes in before realizing that each box contained totals all with the same parity, and the parity changes between boxes. It makes a lot of sense, but it's not necessarily the case with this type of puzzle, because a line could cross a corner between four boxes and break that parity rule.

After watching your solve, I realize that I got lucky in assuming that the last segment that runs into row 9 has to have an 8 total rather than 10. If I had been mistaken there, I'm not sure how long it would've taken me to find the source of the mistake. As it turned out, my time was 7:09, solver number 245.

[oldguydoesstuff]

That's a really nice puzzle and an interesting rule set. Gotta keep your thinking cap on to keep from slipping into region sum lines (which I failed to do at one spot, fortunately without too much damage). I have seen a similar concept before using kropki dots between killer cages, with the cage totals limited by the dots. So there was a little bit of crossover reasoning available to me there. Very fun solve.

[ryuuguu]

Looking forward to another consecutive sum line video

[kvom]

31:42 took me a while to see the break-in

[jonbrowne]

Hats off for getting your head around this variant Sleuth. I couldn’t - very hard not to apply the region sum logic which continuously caught me out even when watching your video solve. You have inspired me to give it another try!