Every square in Kakurasu belongs to a row and a column, so each square you settle cuts the combinations of the line crossing it. A shaded square rules out every combination that leaves it out; a crossed-out square rules out every combination that uses it. This is what moves a puzzle forward once the obvious lines are done: middle targets that told you nothing at the start fall to one or two crosses.
This is the fifth of the Kakurasu techniques.
The rule
When a square in a line is settled from outside (by the line crossing it):
- Shaded: keep only the combinations that use it.
- Crossed out: keep only the combinations that don’t use it.
Then apply shared squares to what’s left.
In a real puzzle
On the 7×7 used on every technique page, read every row and column on its own first. Column 4 needs 7, which has five combinations: 7, 1 + 6, 2 + 5, 3 + 4 and 1 + 2 + 4. On its own it gives nothing away.
But two crossing rows have reached it. Row 5 needs 25, and counting its empty squares shaded its square 4, which is row 5 of column 4. Row 7 needs 2, which crossed out its square 4. So column 4 must use row 5 and can’t use row 7. Of the five combinations, only 2 + 5 fits.
Five combinations to one, from two squares settled somewhere else.
Making it a habit
- Look both ways after every move. When you settle a square, check the line running the other way through it before going on.
- Cross out finished lines. When a line meets its target, cross out its other squares. Those crosses are what the crossing lines need (see leaving a finished line open).
- Come back to middle targets. A line that gave nothing at the start is worth another look every time a square in it changes.