Shared squares is the general Kakurasu technique: list every way a line’s target can be made, then shade the squares every way uses and cross out the squares no way uses. A 5-square row needing 11 can only be 1 + 2 + 3 + 5 or 2 + 4 + 5, and both use squares 2 and 5, so those are shaded. Every other technique is a shortcut to part of what this one finds.
This is the fourth of the Kakurasu techniques.
The rule
- List the combinations that make the line’s target, using only open and shaded squares.
- Shade any square that appears in every combination.
- Cross out any square that appears in none of them.
Sometimes the combinations between them use almost everything, and only one square drops out.
What it adds over the quick techniques
Too big to fit and counting the empty squares only look at how big each square is. Listing combinations also catches squares that are the right size but still don’t fit. In the row needing 11, square 5 falls to counting the empty squares (the empty squares add up to 4, too little for square 5), but square 2 only shows up here.
In a real puzzle
On the 7×7 used on every technique page, every square the quick techniques find at the start is also found here. Exactly one square is found only by listing combinations: square 2 of row 2.
One square sounds small, but it’s a crossed-out square in column 2, and every cross cuts the combinations of the line running through it. That’s the next technique.
When to use it
- On short lists. Targets near either end, and any line with a few squares already settled, have only one to three combinations. List those.
- After the quick techniques. Use one-way targets, too big to fit and counting the empty squares first. They’re faster, and they shrink the lists you’ll need to write here.
- Never as a guess. Only act on squares that every combination agrees on. Picking one combination early is the biggest Kakurasu mistake.