Masyu

Rules and Tips for standard puzzle types, and their variants
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pinkagape
Posts: 210
Joined: Mon 30 Apr, 2012 4:11 pm

Masyu

Post by pinkagape » Wed 17 Feb, 2021 9:55 pm

Nikoli defines Masyu as follows:

Make a single loop with lines passing through the centres of cells, horizontally or vertically. The loop never crosses itself, branches off, or goes through the same cell twice. Lines must pass through all cells with black and white circles. Lines passing through white circles must pass straight through its cell, and make a right-angled turn in at least one of the cells next to the white circle. Lines passing through black circles must make a right-angled turn in its cell, then it must go straight through the next cell (till the middle of the second cell) on both sides.

Loop puzzles can be tricky and use different kinds of logic, but hopefully this walkthrough will help introduce some of the key ideas.

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The walls can be good places to look. Black circles must make an L shape, so there must be a vertical line and a horizontal line of length 2. If it can't go up, it must go down. If it can't go left, it must go right. This forces the red lines shown. The white circle must have a line going straight through it, so it must go up and down.

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This forces the white circle in the centre to go up and down since it can't crash the line on its right. It also forces the red line coming out of the black circle for the same type of reason.

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My next reasoning is that the path through the white cell has to continue up because it can't turn before that, and since the black cell has to have length 2 cells coming out of it, it must go left as if it went right it would only be length 1.

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For the loop to continue from the white circle, it has to go all the way along to the right and has to connect with the existing loop section. At the bottom, it has to turn because it has to turn in one of the adjacent cells, and it hasn't turned in the top cell. The bottom right white circle had to go straight, so that could have been continued down at any point up until now, really. The very top left cell of the grid must continue along the loop and hence go down.

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The left hand white circle hasn't had its turn yet, so it must turn below. The right of the two adjacent white circles can't go up and down, so it goes left and right, which forces the other one to go left and right too.

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For the loop to close, the loop sections must join as shown.

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pinkagape
Posts: 210
Joined: Mon 30 Apr, 2012 4:11 pm

Re: Masyu

Post by pinkagape » Wed 17 Feb, 2021 9:55 pm

Here are two more small examples for you to try. The second follows after the comments regarding corrections from Sam and Freddie.

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Last edited by pinkagape on Thu 18 Feb, 2021 10:15 am, edited 1 time in total.

Feadoor
Posts: 224
Joined: Thu 17 May, 2018 7:08 am

Re: Masyu

Post by Feadoor » Thu 18 Feb, 2021 2:11 am

The second of those follow-up examples appears broken!

Puzzle_Maestro
Posts: 114
Joined: Mon 11 Mar, 2019 5:23 pm

Re: Masyu

Post by Puzzle_Maestro » Thu 18 Feb, 2021 7:33 am

I suppose the circle in R4C6 is supposed to be white, not black.

pinkagape
Posts: 210
Joined: Mon 30 Apr, 2012 4:11 pm

Re: Masyu

Post by pinkagape » Thu 18 Feb, 2021 10:14 am

Yes. That's what happened. Here's the corrected version. I'll delete the incorrect one. Thanks for checking!

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pinkagape
Posts: 210
Joined: Mon 30 Apr, 2012 4:11 pm

Re: Masyu

Post by pinkagape » Thu 25 Feb, 2021 8:26 pm

Here are some practice puzzles written by Neil Zussman, who has written the competition puzzles. Most are good checks to see that you've understood the rules, and the last one is a nice challenge to see if you're ready for the competition!
Attachments
Masyu Practice Set - NZ.pdf
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