Dr. Sudoku Prescribes #29 – Masyu

Masyu by Thomas Snyder


or solve online (using our beta test of Penpa-Edit tools in linex mode where left click+drag draws lines and right click marks X’s)

Theme: Almost Twisted! – Slightly imperfect, but more difficult as a result.

Rules: Standard Masyu rules.

Answer String: Enter the length in cells of the horizontal loop segments from left to right in the marked rows, starting at the top. If the loop only has vertical segments in the marked row, enter 0. Separate each row’s entry with a comma.

Time Standard: Masyu Master = 2:00, Expert = 6:00, Novice = 20:00

Note: Advice on solving this puzzle has now been posted in “Ask Dr. Sudoku #5

Solution: PDF and solving video.

  • Blah… I spent 7-8 minutes finding the deduction in the lower right corner (nice), and then another couple finishing off the top (the final break in the top right corner is pushing my limit of what’s forward reasoning and what’s trial and error).

    • Avatar photo drsudoku says:

      This puzzle definitely stretched my testers between going to “bifurcation” space for speed, or simply persisting to find all the loop/parity constraints throughout. I’m glad you found and enjoyed the first of the two key breakthroughs. The other is indeed on the left/top that finally completes the upper-right. I’ll probably sketch them out as this week’s lesson in loop puzzles on Sunday.

      • Ravi says:

        Nice construction, I see that in this one cannot use the constraint ‘Unique Solution’.
        As you said everywhere it is loop/parity constraint that drives the complete solution.

      • Tom Collyer says:

        I seem to be on a different solving planet again. I spotted one of my favourite loop-trapping tricks with the blacks in R7C5, R10C6 and R8C7 and the rest of the puzzle fell reasonably quickly.

        That said, the trick in the lower right referred to is probably easier than that!

  • Ravi says:

    2:20 (Close to Master level :))
    Excellent construction.
    “Imperfection” I guess its difficult to make 10X10 hard Masyu with symmetry.
    When I construct, most of the times I end up in adding extra circle but as you said those puzzles will prove difficult sometimes.
    Now I have to analyze the way you have constructed it 🙂

  • bromp says:

    No time – but big thanks for this wonderful construction. I don’t believe that a symmetric set of clues could have made this puzzle any better.

  • TheSubro says:

    5:49 … Great construction on many levels. Loved the universal constraints that drove most of the puzzle’s progress. Very impressive how you fit all of that in just a 10×10.

    Probably would have been under 5 minutes. if I had worked out top left quicker at the end. Just kept seeing two solutions, until I realized the turn constraint on the top white circle at R1C5. Duh …

    Thanks for a great friday gift.


  • Jack Bross says:

    2:00 flat — I think this is the first puzzle where I nicked the “master” time. Although you said that chasing down the parity constraints seemed give testers a little pause, for me they were all pretty quick. It was a series of fast “what has to happen in this corner? this!” moments. Also helped that I wasn’t so zonked out on cold medicine today that I forgot what day it was (sigh…).

    To clarify the loop/parity thing: I think the major tip/solving trick that hasn’t been covered yet that new solvers need to learn for this one is “end counting”. In any region of the puzzle, there can’t be an odd number of “loose ends” with no way to escape the region. A lot of the choices in this puzzle come down to this trick.

    Fun puzzle!

  • skynet says:

    8 : 48 s!!
    Did 75% of the puzzle in under 4 mins and after that the 2nd quadrant tripped me a bit before i could see how the loops could get connected.
    So 3 valuable mins wasted over there to push me just below the expert level.But still happy compared to the miserable times that i posted earlier.

  • Aaron Chan says:

    First Masyu I did on this website. The puzzle itself didn’t give me too much trouble. The input on the other hand……

    • Avatar photo drsudoku says:

      I will agree the Masyu input is probably the hardest of the set I use, but is the most common form used at other competition sites too for this type. In part I think the problem is that counting values, as on Slitherlink and Tapa, are more natural when using whole squares. Since Masyu’s loop is square-centered, the counting of horizontal lengths sometimes tends to be 1 higher than what it actually is.

      • Aaron Chan says:

        I haven’t done much of any competition outside of USPC/WPC, so I am not aware of the input method at all. I did not even know whether you have to put 1’s or 0’s for vertical segments, (turns out to be neither, unless the row has no horizontal segments), and variations of whether to put number of grids vs number of crossings. Maybe an example would be nice.

  • Carl W says:

    6:14 Funny that I had almost the same time on this Friday puzzle as on the earlier Wednesday Masyu. I think “end counting” comes relatively naturally to me.

  • mokrton says:


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