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07 August 2009 @ 12:42 am
Friday Puzzle #9 - White Pearl, Black Pearl, ...  
I can't remember how old I was, but I have a vague recollection that the first time I ever saw the puzzle now called Masyu it was labeled White Pearl, Black Pearl in GAMES magazine. I know it later went by just the name "Pearl" but at some point I could swear the two colors were separated out in the name like that. Wikipedia suggests that the name "White Pearls and Black Pearls" (in Japanese of course) was used for several years until an early misreading of the name by Maki Kaji eventually became Masyu, even if that name, meaning "evil influence", doesn't make a lot of sense. Today, I'd like to share another of my "Thomasyu" variations (the first being Total Masyu) that fits the name "White Pearl, Black Pearl, ..." pretty well.

In these puzzles, you will have to solve a Masyu by forming a single closed loop using the normal black/white circle rules. However, as in a well-patterned pearl necklace, you must also alternate between black and white circles when forming this loop. In other words, the loop cannot pass through two black circles or two white circles in a row. As you might expect, this introduces a lot more "avoid-self"-type loop constraints, but now between different loop segments.

While that twist might be fun enough, it seems reasonable to add in some gray circles (which must be a part of the loop and can serve the role of either black or white circles) with the same alternating color constraint. The loop can pass through two gray circles in a row, obviously, but it must alternate between the behavior of a black and a white circle in doing so.

But why use white and black at all? The rules of this variation should allow for a unicolor version. I can't reveal the true difficulty below, but it suffices to say, if I wasn't so bent on having a big ? symbol in the grid, it might not have ended up as hard.

Until the next Thomasyu puzzles, enjoy....
zundevil zundevil on August 7th, 2009 05:53 am (UTC)
I liked the first one, and think the alternating-pearl idea is a good one. I would wait to comment after the next two...if I felt confident I'd get it right. :)

Anyhow -- R910C45 appears to have a spot of non-uniqueness. I've been wrong many times before. Your thoughts?
motris motris on August 7th, 2009 01:48 pm (UTC)
I've fixed the problem you uncovered which was staring me in the face when I checked my solution. I spent a lot more time getting 2 and 3 to work out right, though, so please give them a try eventually.
zundevil zundevil on August 7th, 2009 04:47 pm (UTC)
I did, and they were terrific. Given their relative difficulties, I actually struggled with 2 more than 3. Both were well done. And speaking of staring me in the face -- not sure how I'd never even considered this as a variation!
motris motris on August 8th, 2009 02:58 am (UTC)
Even having solved tons of puzzles and woken up with dozens of weird puzzle dreams, I would never begin to think I could consider all variations of a puzzle (even the "obvious" ones that involve a very simple change). This one's been percolating for several years though (and is even vaguely referenced in that Total Masyu post). The addition of gray stones though was more recent, and really pushed the idea over the top as worth exploring.
thedan on August 8th, 2009 02:42 pm (UTC)
Agreed that 2 was a bit harder than 3. Enjoyed all of them though.
(Anonymous) on August 7th, 2009 04:25 pm (UTC)
I enjoyed these puzzles. #3 wasn't as bad as I was afraid it would be (not any harder than #2 imho). I ended up using the total count of B/W for both #2 and #3. As far as I could tell they have unique solutions.
(Anonymous) on August 7th, 2009 05:13 pm (UTC)
I've also got them all unique, with 2 a bit harder than 3 (thought it was going to be nasty when you claimed that it was harder than you wanted). Very nice!
motris motris on August 8th, 2009 02:51 am (UTC)
Earlier versions of that puzzle were indeed harder (and had fewer circles near the ?) but after thinking a particular version amazingly had only one answer because of global loop constraints, it turned out to have two very different answers so more stones were added. Since most of my time was spent with a different version, my four gray rating may not match your four gray rating. I'm also obviously not the best test-solver for my own ideas, but its a small operation here for these free Friday puzzles :).
(Anonymous) on August 8th, 2009 05:34 pm (UTC)
I just figured the gray pearls in the ratings were for us to determine. The gray in puzzle number 2 is a black one, and only the first two out of four in puzzle #3 are black.
lardarsegreg on August 8th, 2009 12:55 am (UTC)
You could always call the puzzles "Knit one, Pearl one"...
Robert Hutchinson ertchin on August 8th, 2009 08:33 pm (UTC)
Mark me down as another who found both 2 and 3 challenging, but has solved 3 and is still staring at 2 . . .
thesubro on September 16th, 2009 02:35 am (UTC)
Not a fan of Masyu, but a fan of Thomayu
As with many of Nikoli's puzzles (e.g., Heyawake and Nurikabe), in order to rank Masyu harder, they simply make the grids bigger and the boxes smaller... and the challenge is not thinking and logic as much as it becomes endurance. With these gray variations, it was fun and challenging despite their smaller size. I went and did a few Masyu afterwards, as these piqued my interest, and I found them pretty boring.

Tom, you spoil us - like sex with a gorgeous cheerleader. When you then go and have relations with your wife again, it is just never the same.

Loved the "?" theme buried into the all gray #3. Nice touch. I think that #3 was easier than #2 because in order to force singularity and an answer with all grays, you may need to limit options too much and insert too many "pearls" I say that the best bet is sticking with the mixed bag when revisiting the variation. Also curious to see if the puzzle is as enjoyable when you eliminate the black/white alternating rule and keep the grays. Surprise us, oh master puzzle producer.

Thanks for these great puzzles.


"How many could have created it? ... how many could have solved it? How wonderful for both."