### Yajilin by Palmer Mebane

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Theme: No Extra Numbers

Author/Opus: This is the 29th puzzle from our contributing puzzlemaster Palmer Mebane.

Rules: Standard Yajilin rules.

Answer String: Enter the length in cells of the horizontal loop segments from left to right in the marked rows, starting at the top. If the loop only has vertical segments in the marked row, enter 0. Separate each row’s entry with a comma.

Time Standards (highlight to view): Grandmaster = 3:30, Master = 5:15, Expert = 10:30

Solution: PDF

Note: Follow this link for other classic Yajilin. If you are new to this puzzle type, here are our easiest Yajilin to get started on.

• Andrew Brecher says:

Love this variant.

• drsudoku says:

Not to be too pedantic, but this got tagged as a “classic” puzzle because it uses the standard rules. The proper definition might be a twisted classic, which would fit with the week’s theme.

• Scott Handelman says:

I think, for most puzzle fans, there’s no such thing as “too pedantic.”

• Nikolai says:

A very enjoyable puzzle, thanks 🙂 (Didn’t feel as difficult as a Friday, though.)

I wonder – what is the minimum number of blank clues that you need to force a unique solution on an n times n grid?

• chaotic_iak says:

For n = 1, clearly there’s no solution no matter how many cells are marked gray.

For n = 2,3,4,5, I find the sequence 0,1,2,3. Of course this is not meant to be taken as evidence that n-2 gray cells is enough.

An easier version of the problem asks about the least number of black cells in an n-by-n Pure Loop puzzle. Interestingly, the exact same sequence of minimum number of black cells still applies at least until n = 5, although the solutions for n = 4,5 are wildly different.

• Nikolai says:

Ah, but the Pure Loop problem has been studied already. The best known bounds are n – 4 if n is at least 8 and divisible by 4, and n – 2 otherwise. See Chessics 12, 1981, p. 12, and The Games and Puzzles Journal 8-9, 1988-9, p. 143, at http://www.mayhematics.com/p/p.htm for details.

• chaotic_iak says:

I have now proven that the least bound for n divisible by 4 is n/2, although for personal reasons I’ll show it later.

I have also found a 5-cell puzzle for n=6 (R1C4, R2/4/6C3, R4C6), but no 4-cell yet.

• chaotic_iak says:

03:20. Dang, I almost interpreted it as a Pure Loop.

Can’t wait for Saturday’s puzzle to see what twisted thing we have. A Cross the Streams that is actually just Nonogram? Or Cross the Streams with question marks everywhere or God forbid asterisks everywhere? (That last one has non-unique solution for any board size except those with area 0.)

• Scott Handelman says:

If you were a Patreon supporter, you’d already know. Nyah nyah.

• chaotic_iak says:

Sheesh, not everyone has money to spend freely.

• Scott Handelman says:

No one has money to spend freely. The mere act of spending money makes “freely” no longer an apt adjective. 🙂

• Giovanni P. says:

Yeah, that doesn’t sound a bit condescending at all…

As to the puzzle, I will need to finish untangling it, but it’s nice to see something from Palmer. I hope we will see a little more of his work later in the year.

• Scott Handelman says:

I was kidding. Sheesh! I thought I made it clear I was being tongue in cheek with the “nyah nyah” at the end.

• drsudoku says:

I’ve had this puzzle for awhile (it was submitted alongside this other great Yajilin from Palmer we posted in September). But I too hope to see more submissions from him as the year goes on.

• Giovanni P. says:

I’m sorry Scott. I overreacted, when it was obvious it was a joke.

I just had a fear that the Patreon rewards could turn into a “haves versus have nots” thing, especially given that the patrons got a transcript to go along with the Saturday puzzle. My fear is probably unjustified, and I’ll think before I post in the future.

• drsudoku says:

Giovanni: I share this concern too; while we encourage patronage and do offer some rewards that are not otherwise available, we do not want it to seem that we are changing how our daily puzzles are experienced by most of our solvers and by newcomers as we grow our audience. We certainly do not want to start turning comment threads into an “us versus them” situation, particularly in a “well I already know what’s coming” kind of way which the early puzzle pdf reward is not meant to do.

So, even though I judged that this was intended in a joking way, I will watch for and try to moderate such discussions more carefully in the future.

• Giovanni P. says:

Dr Sudoku: If it’s obviously a joke, then it’s fine. The commenters here are nice people, so you won’t have to watch it that much. Thank you for your consideration, and have a nice afternoon everyone.

• Aaron Chan says:

I wanted to try making something like this for a while now. I guess since it has been done, I should search for another idea.

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