# Puzzle 20: Masyu

Another one from the Masyu series. This one I’m happy with. It just wouldn’t have made a good contest puzzle since no one would take the time to find the logical path.

EDIT: Solve at pzv.jp.

## 10 thoughts on “Puzzle 20: Masyu”

1. Tualha

Very nice one, difficult. I think it would have worked for a contest, though. Took me maybe 20 minutes? But that’s on Inkscape, much easier to play what-if, and this has a lot of what-if.

2. Tualha

Seems to me only the very simplest Masyu puzzles involve no what-if at all. I certainly can’t see any way to solve this one without some proof-by-contradiction lemmas.

3. rob Post author

Let’s say there’s a solution that’s very low on “what if”, assuming the Masyu basics. There’s one particular technique that needs to be applied in a couple of situations, I’ll try to give some hints of increasing explicitness (rot13’d):

* Vg unf gb qb jvgu juvgr pyhrf.
* Zhygvcyr juvgr pyhrf va n cnegvphyne neenatrzrag.
* Gel gb trarenyvmr gur snpg gung n Znflh pna’g unir n fvatyr juvgr pyhr qverpgyl va n pbeare.
* Ubj bsgra qbrf gur ybbc pebff n qvntbany bs juvgr pyhrf?

4. Tualha

I’m sorry, I don’t see what you mean. There are many ways [gur cngu pbhyq pebff gur juvgr pyhrf va n qvntbany], aren’t there? It happens a few different ways in this puzzle.

5. rob Post author

Sorry for being unclear! You’re right, there’s multiple ways, but every white clue causes the line to be crossed exactly once.

Check out this (broken) Masyu fragment: http://pzv.jp/p.html?mashu/10/10/0930909901900000000090010033030000

The top left corner being valid, top right invalid is what I was trying to hint at first.

Then, in the bottom left corner, there’s a non-obvious segment that can be placed (connect columns 3 and 4 in the last row). In the bottom right corner, you can mark an ‘x’ (between columns 8 and 9 in the last row.

6. Tualha

I think I follow you — you’re saying it’s sort of a Jordan curve thing? Even numbers work, because if you start on the “inside”, you end up on the inside? But odd numbers don’t work; you need to pass through once more, even if there’s no white clue there.

Still, it doesn’t seem like a hard-and-fast rule that can easily be applied. Maybe you can sometimes find an invariant, and either draw or rule out a line, but it seems like it would be hard to be sure of a conclusion.

7. Tom Collyer

Hi Rob, I’ve only just come across your blog. Enjoyed this puzzle a lot – took me about 5 minutes to crack in the end. In that respect I find that most hard masyu are a bit trial and error anyway – if I haven’t come across something very often (like this puzzle) then it’s at least semi obvious where I should be looking!

I’ll look forward to playing with this theme in a puzzle of my own later this year :)