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10 June 2008 @ 06:53 pm
Total Masyu  
So, in a pre-preview of the USPC, which I expect will have a Masyu on it again this year, I thought I'd post a Masyu variant I was experimenting with over the weekend. The concept was suggested to me by rpipuzzleguy actually, and is a really good idea (although I still have my own Masyu variant ideas on the backburner for when/if I start to work on a logic puzzle site with onigame).

Basically, the concept is this: What if a Masyu puzzle had all its possible white circles/black circles revealed? Could you write a puzzle where the "absence" of circles now meant something?

The result, at first called Tyler/Thomasyu to credit both the idea's source and these puzzles' author, has been more appropriately named "Total Masyu" which can be used by the puzzle community in a better way.

In the Total Masyu puzzles below, draw a single-closed loop in each grid. The loop must pass through each cell containing a white circle and must pass through each white circle in a straight line, with an immediate 90 degree turn one square away from the white circle on at least one of the two sides of the circle; the loop must pass through each black circle and must make a 90 degree turn when passing through a black circle, extending at least two cells beyond the black circle before turning again. Also, all cells that obey either the white/black circle rules have been marked, so any empty cell cannot mark a 90 degree turn that extends two cells in both directions before turning again (black) or a straight segment that turns in one of the adjoining cells (white).

The result is an interesting new type with some fairly different chase-the-loop around logic than a regular Masyu, with white and blank squares taking over the power from black squares. I have an easy and two medium-hard samples for you to try below. One has the obvious "no black circle" theme that is possible with a Total Masyu puzzle, but both it and the other large ones have some new logic for you elite solvers to discover.

1: Welcome to Paradise (Easy)

2: White Flag (Hard)

3: Who's Crying Now (Hard)

garethmoore on June 11th, 2008 03:24 pm (UTC)
Nice variant
I really enjoyed these. Once you realise how the line must wiggle if there isn't a symbol there I'd say they are similar in difficulty to regular Masyu, except I imagine that actually making them is much trickier because of the way you need to make sure the 'wiggly bits' are forced to line up with each other as intended!?
motrismotris on June 11th, 2008 04:45 pm (UTC)
Re: Nice variant
There was a little bit of tweaking necessary on each of my initial "hard" designs to go from, say, 2 non-unique wiggles to a unique one. That often involved just adding in another circle somewhere to the path. But I think the general puzzles were as easy to construct as standard masyu as I had in mind what I wanted the loops to do and then just drew something that seemed to have blank cells where I wanted. Drawing a valid and somewhat minimal masyu with symmetric clues is probably actually harder, and I'm not sure I'd try symmetric black/white clues here.
thedan on June 11th, 2008 05:36 pm (UTC)
For what it's worth, I found #3 more straightforward than #2... Although I was missing something silly on #2 for a while, so it might have been easier if I'd gotten over that hump more quickly.
stigant on June 11th, 2008 10:27 pm (UTC)
mmm, its a bit hard to separate difficulty and unfamiliarity. Most things are easy once you know how to do them. I definitely took some techniques from 2 to 3, but I also found that with a higher density of dots, the 3rd puzzle had more standard masyu deductions than the 2nd.

One of my favorite variants of slitherlink is the one where you have 12 loops instead of 1 and each loop traces out the perimeter of a different pentomino. I've always wanted to try solving a masyu with that same theme. Unfortunately I'm not very good at making puzzles in the first place, and I couldn't see how to force both the long edges and the small turns (ie turns without being between straight segments) necessary without having some sort of path on the inside of the pentominoes. However, with this variation of Masyu, it may be possible to make it happen. The blank squares have a nice property that they must either make the loop go in long straight bits between white circles, or completely bent paths, plus it looks like it would be possible to force non-paths in larger groups of squares (ie it might solve the problem of not having paths inside the pentominoes).
stigant on June 11th, 2008 10:30 pm (UTC)
of course, since you can't remove any dots, it might be trivial to just find the spots that each pentomino can occupy via pattern recognition.
motrismotris on June 11th, 2008 10:52 pm (UTC)
My difficulty ratings for these were based on the "newness" of rules you'd need for them, and 2/3 seemed to have two different kinds of rules to use in places although 3 is more masyu-like in the sense of using global loop closure rules.

I actually find the pentomino/tetris fences puzzles to be rather hard and rather unlike normal fences puzzles as most constructors don't give you a lot of fence information to work with. So I almost give them their own category as my joy of slitherlink is far removed from a tetris fences puzzle.

Still, your suggestion intrigued me and before your second comment I mapped out the 12 pentominos in this way to think about a masyu form. Without some relaxation of the rules, the presence of black circles will give you the L, V, U, P, and Z pentominoes immediately. Then pattern matching can likely get the N, Y, I very easily including orientation, and the T, F, and W can be identified but not necessarily yet placed as each has two rotational placements (barring reflections which takes the F up to 4). X gets no circles, so it is fit by edge toughing constraints I suppose for uniqueness.

I'm actually thinking a "caves" pentomino packing puzzle is due, if it hasn't been done by somebody yet, as that kind of "how many cells do you see from here" info is orthogonal to what the fences form gives you but should have similar intellectual depth to make a satisfying puzzle.
thesubro on November 29th, 2010 01:01 pm (UTC)
Catching up on some of your older stuff ...
Very nice variation. Would enjoy more if the wiggling can be kept fresh. Thanks.