#109 Masyu – rated easy
On a 10×10 grid (or any larger size), I can certainly force a Masyu with just 3 circles (and a few different ways at that) and I don’t think you can do better but it ignores a lot of the space though. Maybe the low count rule should be that the loop should touch all edges; in such a case I’d bet 15 can be beat by a couple, but its close to minimal.
Haha, yes I was going to add the caveat “and not be lame”. More precisely (for 10×10) the clues should not remain valid in a smaller grid size. Which covers what you suggested about touching each of the edges.I suspect you could probably lower the number a bit too, I only really noticed this when I was trying to add a 16th black circle to B9 that this was relatively sparsely clued..
I just sketched out a 10 clue Masyu (markup is failing me at including a link so I’ll just type it: http://www.stanford.edu/%7Etsnyder/Masyu-10clue.png ). If you want it to touch all corners, I can do that in 13. “Lame” might still qualify since the way to build a large loop is a bit gimmicky, but I’d wager the minimum may be at 9 (or 12 with corners).
Oh that’s definitely lame – but I guess the same was sort of true for those minimal yajilin a while back. The trouble is you want to draw a line (if you’ll excuse the pun) somewhere. You might start specifying something about the length of the loop, but then things are starting to get somewhat arbitrary.Hmm – not as interesting as I’d hoped for then. I think you’re probably right about it maybe being possible to lower to 9 (I can’t see why visiting all the corners has any special distinction beyond being slightly more fiddly) – however I think it’d be a dull and painful exercise to try and fiddle the right sort of loop, more so than the yajilin.
The statement about corners was in case someone wanted to make a point: “well, you don’t go anywhere in that 6×6 postage stamp corner”, as if the % of occupied cells, or going to all quadrants, or something else equaled the essential essence of a “proper” Masyu. I’d say a majority of the 10×10 Masyu I see are “lame” in the sense of uninteresting or completely forced from basic principles, so it’s not an exclusive feature of making a minimal clue puzzle, but I’d guess there are probably 12 or 13 clue Masyu that can have some intrigue.
Grant – if it’s any consolation that one is definitely also lame – I can solve that in my head!Thomas – I agree re a lot of 10×10 not worth being the bother. The ones I’ve put out recently have had an extra kick to them (I’m particularly proud of #100 – I’ve never seen that sort of logic in any sized masyu before). The trouble is lameness is awfully hard to quantify. Most definitions will morally extend to larger grid sizes by induction.I suspect that the more clues you reduce and yet still retain a legal (and non-gimmicky – another great technical definition) solve, the more and more trial and error you might need.