Masyu/Yajilin puzzles

Hi everyone, I was just wondering if anyone else finds that they can have a really good go at number puzzles, but when it comes to drawing loops in puzzles such as masyu and yajilin (and nurikabe for that matter) it is a totally different ball game?

I'm trying to fathom out masyu at the moment, and although I have a good understanding of the rules, after having drawn in a few lines around the edges of the grid, I haven't a clue where to start after that. I wondered if there were any experts out there who could pass on a few tips! Thanks.

in masyu you can look for patterns, like a black with two whites diagonally next to it like this

wxw
xbx

with x empty and b/w black/white. then you know the black doens't go up because if it did the whites would have no solution one side, whichever way the black goes. since it must go left/right.

every black must go up or down nd every black must go right orleft so you can use patterns like this to help start.

dave

Continuing with patterns:

3 Whites together in a row or column can never be "shish kebabed", because the exits of the middle White will both be straight and that breaks the rules. That means the exit lines of the 3 Whites run parallel to each other.

Using the walls as you do is the place to start. A White next to a wall means the exits to the White run parallel to the wall.

Blacks are interesting in that a line exiting them must travel 2 squares straight. If you cannot draw a straight line from the center of the Black 2 squares away in length, the line cannot exit the Black that way. Put a small 'x' on that grid line exit. Also, this tells you that the path must go 2 squares in the opposite direction of where you put the 'x'!

If you do Slitherlink, Christine, then some of the skills from that puzzle can apply to this one. The main one being "a line that enters a square must exit through a different grid line and there is only 1 way in and 1 way out for a box. That sounds obvious, but there are sometimes alleyways and boxed areas that when entered do not have an exit ... so you can 'x' those exits. I find that when I 'x' grid lines that I know that path cannot exit (as I do with Slitherlink) I can see alleyways, boxed areas, and path potentials that will break the rules much easier.

The interesting thing with Masyu is that the loop does NOT have to go through every square in the puzzle.

Spittledung's tips cover all the main starting points for Masyu. Three or more whites in a row is a great starting point, and his penultimate point is often the secret to making progress - look out for local closed loops that would be forced if the line were to go a certain way; you can eliminate these options!

More generally you can count line ends:

• An even number of line ends 'trapped' in an area is potentially fine
• An odd number of line ends 'trapped' in an area cannot be correct!

It's easy to see why - an odd number of line ends cannot all connect together. So if you're unsure which way a line goes, if it can seal off an area with one particular direction, count the line ends in that region - you'll know if it can't go that way. (and if it's the only segment that could possibly go that way, you'll also find out if it must go that way)

Furthermore, if there is part of the loop in an almost-enclosed area that isn't connected to anything else then there must be at least two more line segments entering that area, so sometimes you can run two lines alongside one another through part of the puzzle, which forces a lot more.

You can apply this to Yajilin too - put most simply if there is an area of the puzzle which must have part of the loop in then you know that there must be a second part of the loop coming in - perhaps you can draw part of that in already. It's rare that a Yajilin won't require you to make use of this observation.

Finally, one rule I have only used once when solving is the observation that to form a loop there must be an even number of line segments crossing every row and column, so when the grid is nearly full you can use this to make quick deductions sometimes (but usually these can be made by just general observation anyway). (If there weren't an even number, you couldn't have a loop)

Of course all these apply equally to Masyu, Slitherlink and Yajilin. There are many more possible tips - for example in Yajilin working out where shaded squares would seal off areas or make it impossible to place 'in and out' loop segments is a big part of the solving process too.



Edited 1 time(s). Last edit at 11/23/2009 03:43PM by gareth.

Thank you for taking the time to reply everyone. I have managed (with a little help) to complete my first every Masyu! I found the tips really useful, It's amazing how some things are obvious but you still need them pointing out to you, like the point about the three while circles in a row!. As a complete novice at this type of puzzle, I was also forgetting to check that a line had to be able to travel two sqaures away from a black circle. Anyway, I've got a taste for this puzzle now and will be seeking out a few easy examples to practise on and really get used to the rules!

I think the beauty of having a forum to go hand in hand with the puzzle magazine is that it does encourage you to have a go at new types of puzzles because there is usually someone on hand to help out!

You also raise a good point about the difficulty level - I shall put a couple of beginner's Masyu and Yajilin in the next issue to help ease people in! Maybe I can add a 'tip of the month' to some puzzles too. (And don't worry, I'll still keep the harder puzzles too! )

Incidentally in issue 1 the first Masyu is moderate and the second one is pretty tough, relative to the size of the puzzles.

Thanks to your encouragement I have now got to grips with this puzzle and have found several samples to practise on with some success!

Funnily enough I have managed to solve the second masyu in the magazine but keep going wrong in the bottom left hand corner of the first one, so must print off another copy and try again!

Now to have another look at yajilin.



Edited 1 time(s). Last edit at 11/26/2009 07:49AM by Christine.