Anagram is needed, and it will answer: What Masyu do with the antique clock?
$\begingroup$ I think there might be an error in the rot13(guveq znflh, nf gur gjb juvgr naq gjb oynpx pvepyrf va gur gbc yrsg 3k5 nern sbez na hafbyinoyr flfgrz). That, or my approach given the rot13(frpbaq cuenfr, j gb juvgr, o gb oynpx) is incorrect $\endgroup$– StephenTGJun 26, 2020 at 13:25
$\begingroup$ I get the same as Stephen. If we rot13(znxr jung frrzf gur boivbhf thrff nobhg jung zvfgnxr unf orra znqr) then rot13(gur hahfrq fdhnerf' yrggref nantenz gb "bvy gur pybpx" juvpu vf fheryl gur vagraqrq nafjre). $\endgroup$– Gareth McCaughan ♦Jun 26, 2020 at 13:43
1$\begingroup$ @GarethMcCaughan That seems pretty answer-worthy to me. $\endgroup$– Deusovi ♦Jun 26, 2020 at 14:29
$\begingroup$ Yeah, but I thought (1) maybe Rand had already got as far as finding the error and then wrongly given up because he thought he must have made a mistake, and (2) for sure Stephen had already got as far as finding the error, so I don't really feel I've contributed much that others hadn't done earlier :-). $\endgroup$– Gareth McCaughan ♦Jun 26, 2020 at 18:45
$\begingroup$ @Gareth In fact, I went AFK and didn't even have time to make the initial board setup for the third one. Wouldn't grudge you if you want to make that an answer. $\endgroup$– Rand al'ThorJun 26, 2020 at 18:48
Partial answer: solved the Masyu puzzle. (My first time solving one of these!)
The letters not covered by the path spell:
NOW LETS FLIP THE CIRCLES COLOR
Argh! It seems this puzzle just got bigger. Here's the new version:
Solution to that one:
This time the unused letters spell out
W TO WHITE B TO BLACK.
7$\begingroup$ Watching this answer develop is like watching an excellent TV series... Full of cliffhangers! Waiting on the edge of my seat to see how this one pans out. Huge kudos to @athin for creating this - incredible...! $\endgroup$– StivJun 26, 2020 at 12:20
$\begingroup$ Solution for the next step. Just can't figure out what the anagram could be. I'll probably be kicking myself when I see the solution... $\endgroup$– JafeJun 26, 2020 at 16:58
$\begingroup$ @jafe Maybe we're supposed to, not only replace the B and W by black and white circles, but also vice versa? That would mean a couple of extra Bs and Ws in the grid, which might help for the anagram. $\endgroup$ Jun 26, 2020 at 17:09
$\begingroup$ @jafe You missed a B. $\endgroup$– Gareth McCaughan ♦Jun 26, 2020 at 18:47
$\begingroup$ @GarethMcCaughan Augh, that's it! $\endgroup$– JafeJun 26, 2020 at 18:50
I feel a bit guilty posting this as an answer since I know that at least StephenTG had done most of it before
running into an unfortunate error in the puzzle, and giving up.
and also because frankly Rand did most of the work. But here we go. After Rand's solving we have
the message W TO WHITE B TO BLACK which means that we should interpret letters W and B as white and black circles and solve the third Masyu that @athin has somehow managed to pack into this grid. Unfortunately there is a small error: there's a cluster of circles at top left that can't all be made to work. But if we make what seems to me the obvious guess about what's gone wrong and allow the white circle on the top row not to have a 90-degree turn in either of its adjoining cells, we get a unique solution thus:
which when overlaid on the original letters (and, unfortunately, also the original circles, so the following diagram looks annoyingly Wrong...) yields:
the letters that aren't on the path anagram to OIL THE CLOCK which is presumably the intended solution.
Besides StephenTG, at least one other person has done essentially the same as I have, but (see my comment on the original puzzle) I'm pretty sure I did it first, so there :-).
$\begingroup$ Sorry for causing some messes ><, this is indeed the intended final answer, well done! Now I'm pretty clueless on which should I tick the answer to... Welp $\endgroup$– athinJun 26, 2020 at 22:34
2$\begingroup$ Neither of us is exactly starving for Meaningless Internet Points, so no hard feelings either way :-). $\endgroup$– Gareth McCaughan ♦Jun 27, 2020 at 15:44