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Rules of MASYU, for those unfamiliar: https://www.gmpuzzles.com/blog/masyu-rules-and-info/

Hey guys! So I just discovered this really cool puzzling site called the Puzzling Stack Exchange (puzzling.stackexchange.com), and it's really cool! Users create cool new puzzles to challenge each other. I really want to contribute to this site with a bold new puzzle. But I can't come up with any new ideas!

Here's the best plan I got so far: Since I really like MASYU, I'm thinking of creating a MASYU puzzle for PSE. But just an ordinary MASYU puzzle would be boring. For a site like PSE, I need it to be really special somehow! Specifically, I want this MASYU puzzle to be free-floating.

What's a free-floating MASYU?

A free-floating MASYU puzzle is a MASYU puzzle that has no edges.

Many MASYU puzzles require deductions using the edge of the board in the solution. I want a MASYU puzzle that, in a sense, takes place on an endless board, and is just "floating" in the middle, with no edges for its solution to grapple on to.

As an example, here's a possible attempt at creating a free-floating MASYU:

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However, this isn't a valid MASYU because more than one solution can be found:

2

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Your task is to create a free-floating MASYU puzzle with a unique solution... or prove that no such puzzle exists.

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    $\begingroup$ "MASYU" is also known as "Pearl", such as in Simon Tatham's Portable Puzzle Collection. (Prior to seeing this post, I only knew it under this name.) $\endgroup$
    – Joseph Sible-Reinstate Monica
    Jul 6, 2019 at 5:34
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    $\begingroup$ @JosephSible Tatham typically gives alternate names to all his puzzles, such as "solo" for sudoku, so I don't think pearl is a standard name given for masyu. $\endgroup$
    – greenturtle3141
    Jul 6, 2019 at 5:58

2 Answers 2

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I claim that

yes, it is possible: the below Masyu puzzle has only one solution.
free-floating puzzle

The proof:

Stacks of 3 (or more) vertical white dots must all be passed through horizontally.

enter image description here

The segments in the second and third rows must not continue horizontally, or one of the white dots they currently pass over would be violated. This also lets us determine that the white dots in the first and last column are passed vertically:

enter image description here

The black dots in the center can be finished, and so can the other ends of the segments in rows 3 and 6.
enter image description here

And finally, the remaining white dots must be passed horizontally, and the remaining segment ends in rows 2 and 7 must continue vertically, completing the loop.

enter image description here

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Deusovi came up with a very nice and simple solution. Here is the (much more convoluted) configuration that I came up with, if you were curious:

1

The line:

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    $\begingroup$ But for a puzzle to be interesting it does not always have to be simple! Yours looks interesting as a puzzle :) $\endgroup$
    – justhalf
    Jul 5, 2019 at 13:17

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