This tool looks pretty sophisticated! I think each red circle might have slightly different reasons for not containing a
2 hint, but as an example, let's look at the red circle on Row 1, Column 2.
Suppose we did write a
2 there. Then:
- To complete Column 2, we must write a
4 in Row 3 (it can't go in Row 8 because of the box) and a
3 in Row 8.
- From there, we know Row 8, Column 5 must be
6 (all other numbers are already aligned with the cell in at least one direction).
- Which solves Row 7: Column 4 contains a
3 and Column 7 contains a
- This in turn solves Row 5: Column 7 contains a
3 and Column 9 contains a
- And it finishes off Column 9 because we know to write a
3 on Row 3.
- But now we are in trouble: where, on Row 1, can we write a
It can't go in Column 2 because we started by writing a
2 there. It can't go in Column 4 because we added a
3 to Column 4 on Row 7. It can't go in Column 6 or Column 7 either, and that's all the open columns. Since we arrived at this point by following the only possible logical path beginning with a
2 at Row 1, Column 2, we've "proven" that writing a
2 there would be a mistake.
I haven't tried the other cells you circled in red in the image, but I imagine following a similar algorithm leads each choice into a contradiction or error of some kind.
Edit: Importantly, each of the other choices along this path are valid on their own (which is why the numbers indicated in these steps also tend to show up in those hints); for example, we might be able to put a
3 on Row 8, Column 2, without making it impossible to solve Row 1, as long as the cell on Row 1, Column 2 remains open. It's the combination of all these steps, beginning with writing a
2 on Row 1, Column 2, which leads to the unsolvable scenario at the end.