In this Sunday 5-star of June 13, 2021, two 4-fills are resolved before the bypass value march begins. Follow-up continues in box marking, leaving little line marking to be done. Coloring is demanded and it responds, with an unexpected discovery.
The two 4-fill traces show exactly what happens.
In r1, 4 is missing and can’t fill in NE. In r9, 9 is missing and can’t fill in SW. With 9 placed, 457 are missing, and r1c1 can’t be 4 or 5.
The most important take away is, what signaled these moves?
Then if you follow this bypass trace,
and pass this grid to box marking,
an ordinary box marking turns into something else.
Coloring the almost filled grid, notice how the removal of 1r8c8 allows the blue/green cluster to be completed.
That means there are at least two solutions. Something that isn’t supposed to happen, but when it does, it can be discovered by coloring. In this case, we don’t really know. I might have gotten a given in the wrong place when I dragged them into my template grid.
I meant it when I said “at least”. For the correct answer, use one of the many backtracking solvers that cover the whole tree of possible solutions. I consulted Andrew Stuart’s on his Sudokuwiki site to learn my possibly mistaken version of the Dave Green puzzle has 5 solutions.
Next time, we look at a Sunday 5-star with four 4-fills on the opening grid. Ordinarily, 4-fills are passed over if they don’t resolve immediately, but in this case, let’s fully process each one and see how we like that experience. It appeared in my paper 1/23/22.