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Kakurasu Too-Big Squares: Cross Them Out First

Too big to fit is the simplest Kakurasu technique: a square worth more than what’s left of its line’s target can’t be shaded, so cross it out. A row needing 5 can’t use squares 6 or 7. A row that needs 9 and already has square 6 shaded only has 3 left, so squares 4, 5 and 7 are out.

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This is the second of the Kakurasu techniques.

The rule

For each line, work out what’s left: the target minus the squares already shaded. Every open square worth more than that is out.

Too big to fit: a 7-square row with target 5 A row of seven squares with target 5. Squares 6 and 7 are each worth more than 5, so both are crossed out. 1 2 3 4 5 6 7 5
Target 5 with nothing shaded yet: squares 6 and 7 are too big.

It’s at its most useful partway through a puzzle, once a line has a square or two shaded and only a little is left.

Too big for what is left: a 7-square row with target 9 and square 6 shaded A row of seven squares with target 9 and square 6 already shaded, leaving 3. Squares 4, 5 and 7 are each worth more than 3, so they are crossed out. 1 2 3 4 5 6 7 9
Target 9 with square 6 already shaded leaves 3. Squares 4, 5 and 7 are too big for that.

In a real puzzle

On the 7×7 used on every technique page, two rows have small targets: row 2 needs 4 and row 7 needs 2.

Too big to fit at the start of a 7 by 7 puzzle Row 2 needs 4, so squares 5, 6 and 7 are crossed out. Row 7 needs 2, so squares 3 to 7 are crossed out. 1 2 3 4 5 6 7 1 2 3 4 5 6 7 12 4 11 23 25 17 2 9 25 13 7 19 10 15
Row 2 (4) loses squares 5, 6 and 7. Row 7 (2) loses squares 3 to 7. Eight squares crossed out before any adding.

Applied to every row and column at the start of a puzzle, this is the opening sweep: a quick pass that crosses out every square too big for its row or its column.

Its mirror

Too big to fit only ever crosses squares out. Its partner, counting the empty squares, works the same way from the other side: a square worth more than the empty squares can add up to must be shaded. Between them they cover both ends of every line: small targets cross squares out, big targets shade them in.

Watch out for

  • Using the full target instead of what’s left. The rule is only as good as your subtraction. See losing track of what’s already shaded.
  • Reading the wrong numbers in a column. Down a column, compare against row numbers, not column numbers.

Next steps

Questions

Can too big to fit ever shade a square?

No, it only crosses squares out. Even a row needing 1 only gets squares 2 and up crossed out this way; knowing square 1 is shaded comes from the one-way targets. Its mirror, counting the empty squares, is the one that shades.

Does it work on columns too?

Yes. In a column, a square is worth its row number, so a column needing 3 can’t use rows 4 and below.