Birthday Loop by Prasanna Seshadri

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(Note: This puzzle is at a Saturday+ difficulty, and is being posted today to mark the occasion of Prasanna’s birthday. Our regular “easy” puzzles will run on Tuesday and Wednesday this week.)

Birthday Loop by Prasanna Seshadri

(View image directly for larger form.)


or solve online (using our beta test of Penpa-Edit tools in yajilin mode where left click shades squares, left click+drag draws lines and right click marks X’s; note that the default puzzle info is too long — even for an url shortener — so copy and paste all the text in this file into the “Load” option in the upper-right of the penpa-edit interface to access.)

Theme: 24 on 03/02/15

Author/Opus: This is the 73rd puzzle from our contributing puzzlemaster Prasanna Seshadri.

Rules: This puzzle combines four loop varieties commonly featured at GMPuzzles: Balance Loop (upper left), Yajilin (upper right), Castle Wall (lower left), and Masyu (lower right).

Draw a single, non-intersecting loop throughout all four quadrants. The loop may enter and exit the different quadrants as many times as needed.

The standard rules for each puzzle type are true for each quadrant, with these additional considerations:

Balance Loop: Use the entire length of segments (including parts of the segments that extend into an adjacent quadrant) when determining the balanced/unbalanced status of a circle clue.

Yajilin: The arrow clues refer only to shaded cells within the Yajilin quadrant. The loop must occupy all cells adjacent to a shaded cell, even in an adjacent quadrant.

Castle Wall: Number clues can see beyond the CW quadrant ONLY IF the line segment begins from a cell within the CW quadrant. (For example, if a segment starts in the rightmost column of the CW quadrant and goes three cells further to the right into the Masyu quadrant before turning, this segment would contribute 3 to the count of segments for that row.)

Masyu: Normal rules apply for white and black circles, but the path satisfying these rules can extend into an adjacent quadrant. (For example, a white circle can be passed through crossing a quadrant edge, provided it turns immediately on one side of the circle whether the turn is in the Masyu quadrant or in another quadrant.)

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 Standards (highlight to view): Grandmaster = 30:00, Master = 55:00, Expert = 1:50:00

Solution: PDF

  • Aaron Chan says:

    This was very hard. The Yajilin side was especially unforgiving. Beautiful puzzle, though.

    • Andrew Brecher says:

      Yeah, after an hour, I gave up on deducing the yajilin path and just made a few good guesses. I think I see the logical approach now, but it’s still fairly heavy on the bifurcation. Anyone find a more elegant approach on that quadrant?

  • Allen Kong says:

    A beast of a puzzle. Thanks for the challenge. And happy birthday.

  • Rob says:

    Took me longer than it should have to figure out the full theme. Congratulations!

  • Francis says:

    This shizz was cray-cray (in a good way).

  • Neelix says:

    I got about 3 quarters of this done fairly quickly… The yajilin was giving me trouble though, and I wasted a lot of time exploring a lot of dead ends. After a while I noticed that the middle of the puzzle seemed to have multiple possible solutions, and I started to think I must have made a mistake somewhere along the line. So I reviewed the rest of the puzzle, and suddenly realised that I’d missed a clue in the otherwise fully resolved Castle Wall that resolved the middle of the puzzle. After that it all fell into place fairly easily.

    Thanks for the puzzle, and a belated Happy Birthday Prasanna. 🙂

    – SC

    • Funnily enough, I too stared a while when I first re-solved this puzzle. Two testers also had a similar experience with the single Castle Wall clue.

      Thanks! 🙂

      • Francis says:

        After making an early (stupid) mistake on the border between the yajilin and masyu, I was watching that corner of the castle wall like a hawk, so happily didn’t have that problem.

  • Gavriel Hirsch says:

    Wow, that was very tough but a lot of fun. I broke it a few times after getting more than halfway through, but after 3 sittings and a total of about 4 hours, I finally finished it. Great job on making this puzzle, and also happy belated birthday Prasanna!

  • Carl W says:

    Happy birthday, Prasanna! This puzzle is remarkably impressive.

    The Masyu went smoothly for me, then the Castle Wall and Balance Loop were a fair amount more work. But then I totally got shut down on the Yajilin. I think that might be just a weak spot of mine, (though the comments above sugested others also had trouble finding the logical path there).

    I broke the whole puzzle, (all clues satisfied but two loops), and backed up to around where I thought my mistake was (undo is much easier on a computer than with pencil-and-paper). My wife was kind enough to consult the solution for me to find the errant square I had shaded, (much nicer than starting an hours-long puzzle over). Even after that, I still ended up making two guesses before I completed it.

    I’m glad to have this beast behind me. Thankfully, I didn’t keep careful track to know how many total hours I spent on this.

  • aclayton says:

    Like some others here, I got stuck in the Yajilin quadrant for a very long time. In case it helps anyone, here are the two logical steps that broke the final stretch for me: (rot13)

    With the lower left cell of the Yajilin quadrant named a1, and columns a-l to the right, and rows 1-12 upwards:

    – Gur 3 pyhr ng r10 erdhverf gjb oynpxrarq pryyf cynprq ba rvgure gur yrsg be evtug fvqr bs gur pyhr ng v10. Jung unccraf gb gur cngu vs gur gjb oynpxrarq pryyf ner cynprq gb v10’f evtug?

    – Ybbxvat ng gur 3k5 ertvba FR bs gur 3 pyhr ng r7, jung unccraf gb gur ahzore bs rkvgf vs gjb bs r7’f oynpxrarq pryyf ner cynprq pybfrfg gb vg (juvpu qrsvarf gur cynprzrag bs v9’f oynpxrarq pryyf)?

  • P says:

    Delightful puzzle, thank you for this.

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