Dr. Sudoku Prescribes #27 – Masyu

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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: Smiley Face – our first (but probably not last) use of this theme here.

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 = 1:00, Expert = 3:00, Novice = 10:00

Solution: PDF

  • Ravi says:

    yes finally close to Master level 1:25
    Excellent design.

  • Scott Handelman says:

    The clock said 1:48 but I had to stop because my daughter was crawling towards things she shouldn’t, so I’m gonna say that actual time was closer to 1:40. Only one real moment of pause at the left eye; everything else fell nicely into place. I should really just add the “black diagonally adjacent to two whites” deduction to my natural arsenal. I’m not exactly *relearning* the rule every time, but it doesn’t come as naturally as a lot of other deductions I take for granted.

    Hopefully by typing this, it’ll set that one in stone.

  • Jack Bross says:

    About 1:15. My guess based on a lot of Nikoli solving is that the fast time on Nikoli’s timing system would be 2 minutes on this one, since I usually beat those pretty easily at about 1/2-2/3 of their suggested time for Masyu. Your Master timing isn’t unreasonable, since I definitely can think of a few solvers who I’d expect to do this in about 40-45 seconds.

  • I was also going to comment on the “black diagonally adjacent to two whites” deduction, but in the opposite way: this is probably the very first pattern of Masyu that I figured out, at about the same time as obvious things like two whites adjacent or one space apart on the edge. I’m always surprised at how rarely I get to use it; I think it just happens to have been used a bunch of times in one of the first puzzles I solved. It makes me nostalgic for the very first USPC I ever did, which was also the first Masyu puzzle I ever saw, thinking “wow, these are some creative puzzles they invent for this test! What a cool rule set!”

    • hagriddler says:

      Can I ask what exactly do you mean with the “black diagonally adjacent to two whites” deduction ?

      My break in (after the obvious edges) were the 2 blacks and 2 whites in row 4-6 col 2-4 (one of the eyes). Is that what you mean ?

      • Jack Bross says:

        Yeah, the reason that the black pearls in the left eye can’t just directly connect is the diagonally adjacent pair of white pearls. That situation (usually with only one black pearl) is fairly standard. If there are three white pearls diagonally next to a black pearl, both directions of the black pearl are determined.

        Joshua: I dove in at the deep end for my first USPC as well, and was surprised that I did OK. I think it was a forgiving test, or up my alley or something. The next year, I was only moderately more prepared, and felt like I got clobbered. It was at that point I decided I better either learn how to solve the most standard puzzle types properly or give it up.

        • Scott Handelman says:

          Ah, you’re the guy who got the same score as me at last year’s USPC, but did it slightly quicker, knocking me out of the top 25.

          Know that you have a mortal enemy!!!

      • Para says:

        Yeah, it’s important to note that it’s a black diagonally adjacent to 2 white in a V-pattern. Otherwise it does hold true.

  • drsudoku says:

    I started the week thinking I’d make a hard puzzle around the black/diagonally adjacent white thing, but decided against it. It’s not that hard an observation but is a very good test of the “Nikoli-ness” of the solvers’ experience since they almost never use it but it pops up in other sources regularly.

    While I did something different for the Friday “Hard” puzzle, to set everyone’s expectations: I consider Masyu the “entry” loop puzzle genre, the easiest of the loop puzzles. Sure it has nice emergent properties, but it is also nice in part because it is usually quite simple. So love Masyu for what it is, and love these puzzles for what they are too.

    • Tom Collyer says:

      32 seconds here (in paint).

      Interesting that you consider Masyu to be the “entry” loop puzzle. I think I’d argue the case for slitherlink there. I know masyu is supposed to be ultra culture independent, but the point remains that you still need to explain what the black and white pearls actually mean. With slitherlink, as long as you are familiar with arabic numerals, it’s immediately obvious what you are supposed to do with the puzzle as soon as you know you have to draw a loop.

      That said, I still prefer Masyu in terms of solving, the rules mean that once you know what you are doing the solving process becomes a wonderfully fluid experience in a way that you don’t really get with most slitherlink.

      And whilst its fair to say that there aren’t too many tricks you need before you can be a proficient masyu solver – and indeed you say that part of the beauty is in this particular simplicity – but I think there is plenty of difficulty, subtlety and beauty that can be achieved with Masyu. Even in 10×10 format. I still consider this one of the greatest puzzles I’ve ever made: http://tcollyer.blogspot.co.uk/2011/07/friday-puzzles-114_9464.html

      • drsudoku says:

        Certainly Slitherlink is another good style — it is the other one I’ve chosen for my first series — but I’ve found in my personal experience giving Nikoli styles out to other people that Masyu is the easier one to grab onto completely. Much of Slitherlinks complex deductions are more indirect (like corners through 2’s) where Masyu’s are right at the circles and so the focus of the solving feels more direct or simpler. At least that has been my opinion.

        Thankfully, both styles can have a range of puzzle difficulties so both are interesting enough for real exploration.

  • skynet says:

    From the times that i see posted here.A thing or 2 is sure to me
    Either this must be a very famous puzzle known to quite a lot or there must be some predetermined patterns which decide the course of the loop based on the placement of the circles.
    All times under 2 >>>>>Are you making a joke out of this puzzle??So roughly speaking you guys wil be doing 7-8 masyu puzzles in the time that i do one???Oh no ..This is ridiculous…I may as well not attempt these puzzles..

    • drsudoku says:

      A whole lot is knowing a few predetermined patterns – so don’t worry if you haven’t solved several dozen yet. Just practice and you’ll get much faster too.

    • Scott Handelman says:

      skynet, realize that most of the people who are posting under 2 minutes times have literally done hundreds of Masyu puzzles. The patterns and deductions are second nature at this point. I don’t have to think about the fact that, say, if a black circle is against the edge, then the path must extend two squares away from the edge. I just do it. The line is drawn before I really think about what I’ve done.

      Don’t worry about the time so much. Everyone will have longer times on puzzle types they’re not as familiar with. I don’t generally even bother posting my sudoku times because I just don’t solve them at a competitive level. I just solve them for the fun of it and don’t let other people’s obvious superiority at sudoku take that fun away from me.

    • Ravi says:

      Hi Skynet,
      I completely agree with Dr.Sudoku and Scott Handelman.
      When I started solving puzzles it used to take more time for me to solve (sometimes to understand as well :)), because of constant practice I improved myself.

      For example take Masyu, this puzzle in my initial stages took more time for me to solve and now I have improved myself a lot because I have started creating them. I am not bragging but honestly while solving this one I did not wait even for a second because I know all the deductions right away.

      In my opinion once can improve a lot by constructing puzzles or solving larger grids directly no matter how much time it takes to solve.

  • skynet says:

    Thnks for the comments..I should not push myself so much i think and try to solve the puzzle for fun which is always good….

  • Giovanni P. says:

    Honestly, Masyu was the first Nikoli type I really picked up on, and it was the main subject of the first Nikoli book I ever bought (Masyu and Sudoku).

    It’s definitely a simple puzzle with a simple rule set, but a lot can still be done with it in terms of artistry as Tom Collyer noted. A good example is the twisted symmetry of the giant Masyu in Nikoli 141–that could not have been an easy puzzle to lay out. Several of juno’s puzzles are good examples as well.

    On the other hand, a puzzle type like Masyu can be enhanced with the right variation–look at MellowMelon’s optional black Masyus for a good example. Personally, I wonder what one could do with a puzzle where you take the Masyu loop out of the puzzle, and make the goal fitting the loop back into the grid. I may have to build a proof of concept sometime soon.

  • Carl W says:

    5:41 It’s funny to see all the comments here about the pattern of a black next to two whites in a V pattern.

    I haven’t really done a whole lot of Masyu, and on this one I totally missed that break-in. After the trivial edge pieces, I paused until I found a break-in based on the symmetric layout of 5 black circles on the right side. I finally got over to the left eye near the end of the solution, and kicked myself since it was obvious at that point that it was the initial break-in I had been missing.

    Hopefully that whole experience shoved that pattern into memory for next time.

  • mokrton says:


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