The case notes
Reject an arrow bulb that empties its box
This arrow sits almost entirely inside one Sudoku box. The two threes outside the box clear its upper rows, leaving three only in these arrow cells. Watch a worked example, then try the idea in a puzzle.
Put it into practice
Box 4 needs a 3 on the arrow
This arrow sits almost entirely inside one Sudoku box. The two threes outside the box clear its upper rows, leaving three only in these arrow cells.
Suppose the bulb is 7
Try seven in the arrow circle. Then its three-cell shaft must add to seven. Because all three cells share a box, their digits cannot repeat.
Shaft would be {1, 2, 4}
The only three different positive digits that add to seven are one, two and four. So the shaft cannot contain three. The circle is seven, not three, either.
No 3 in the box? Impossible.
But the box still needs a three, and every other place for it is gone. Seven in the circle would leave no three in the box. Cross out seven.
Read the transcript
This arrow sits almost entirely inside one Sudoku box. The two threes outside the box clear its upper rows, leaving three only in these arrow cells. Try seven in the arrow circle. Then its three-cell shaft must add to seven. Because all three cells share a box, their digits cannot repeat. The only three different positive digits that add to seven are one, two and four. So the shaft cannot contain three. The circle is seven, not three, either. But the box still needs a three, and every other place for it is gone. Seven in the circle would leave no three in the box. Cross out seven.
