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Both Masyu and Slitherlink puzzles have as their target a single closed loop that does not touch or intersect itself. So it seems natural to create a hybrid that uses both Masyu and Slitherlink clues. In this puzzle, your goal is to create a loop that satisfies all of the Slitherlink and Masyu clues. The numbers within the squares are Slitherlink clues, and indicate the number of sides of the square used by the path. The white circle and black square dots are Masyu clues: the path must past through the white circles without turning, but must turn at either the step before or after, or possibly both. The path must also pass through the black squares and turn, but must continue straight through the steps before and after. I hope you enjoy!

Grid

Solver Note: This puzzle is part of an ongoing series of studies for a future puzzle. While it has some interesting deductions, I don't think it is terribly difficult. So don't panic if you're making progress seemingly too easily!

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I will be using the Penpa editor: here's a link to the puzzle, if you want to solve along. (For nice input, go to "composite" and choose "loop".)


To start, some basic Masyu deductions:

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Some of the Slitherlink clues help make progress in a few different places:

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1 clues help us out:

The black dot in R2C4 can't go down, or it would trap the loop end in the upper left.

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And more progress can be made with the upper right 1: if it was satisfied by the segment under it, then that would force the right-side 3 to be a U, and then we'd have a problem: there would be a closed-off region in the upper right that had exactly three entrances/exits.

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Meanwhile, the 1 against the left wall has only one way it can be resolved.

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Finishing off some corners:

In the top right, we can't close the loop.
In the middle left, if the black dot goes down, then its region has 3 lines going into it again. This can't happen, so the black dot goes up.

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Now we can figure out the parity of the adjacent 3s. We also need to make sure not to close the loop too early:

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And now, that last white dot lets us finish off the puzzle!

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    $\begingroup$ Sniped me! Nice explanation. $\endgroup$ – bobble Oct 16 at 21:58
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    $\begingroup$ Darnit! I was most of the way through my own diagrammed explanation but its diagrams fall WAY short of the quality of yours, which are superb. I respectfully withdraw my write-up! A quality answer +1 $\endgroup$ – Stiv Oct 16 at 22:00
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    $\begingroup$ Seems my phone accidentally posted this on my post...I am not (generally) in the business of self-congratulation. Well done! Seems it was nontrivial if not too hard. Hope you enjoyed! $\endgroup$ – Jeremy Dover Oct 16 at 23:22
  • $\begingroup$ The editor you used seemed great for doing puzzles. Could I ask how you got numbers to appear at intersections of gridlines? $\endgroup$ – Alaiko Oct 17 at 15:18

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