Walkthrough: Puzzle 20, Masyu

Here’s a walkthrough for puzzle 20, a small but tricky Masyu that hinges on an obscure technique that I’ve recently failed to explain well. Of course, I encourage everyone to try to figure it out on their own, maybe using the hints from the comments on the original post. Here’s the puzzle, spoilers after the break. masyu-corners-start To start, there’s some standard deductions to be made.masyu-corners-aThe observation that can be exploited now is that if you have a diagonal of white clues, the loop crosses that diagonal exactly once for each clue. In particular, look at the diagonal of three whites in the top right corner. masyu-corners-b-diag With this, we can cut off an area in the top right corner, the border of which is crossed once so far. The diagonal gives us three extra crossings. That’s an even number in total, so the loop can’t cross the border in the rightmost column, yielding the X below. masyu-corners-b-follow The green loop parts are again standard Masyu deductions. We’re ready for the next diagonal:masyu-corners-c-diag Here, we have a diagonal of two cells which must be crossed an even number of times, and there’s one white clue. So we also have to cross in the unclued cell. (We could also view this one as a one- or a three-cell diagonal.) masyu-corners-c-follow The next step requires applying the technique in both the top and bottom left corner. (We could have made these deductions a bit earlier.) masyu-corners-d-diagIn the top left corner, the number of crossings is odd, so we mark a segment. In the bottom left corner, it’s even, so we mark an X. masyu-corners-d-follow Here, we need a slight bit of “what if”-logic: It’s clear that the black in R5C3 can’t open to the top left or bottom right. With our new deductions, it also can’t open to the bottom left. The rest should be straightforward. masyu-corners-done

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