Simple boxes: fill the overlap of a long clue

How to do it by hand

Take a clue such as 4 3 in a row of ten squares. Pack the runs hard against the left edge, with exactly one empty square between them. Then pack them against the right edge. Compare the two layouts block by block. The first run, the 4, covers squares 1 to 4 in the first layout and squares 3 to 6 in the second, so squares 3 and 4 are covered both times. The 3 covers 6 to 8 and then 8 to 10, so square 8 is shared.

Only overlaps of the same run count. Square 6 is covered by the 4 in one layout and by the 3 in the other, so the shared colour tells you nothing yet. Keep track of which run you are following.

A shortcut for the overlap

You do not have to draw both layouts. Total the clue plus its gaps (4 + 1 + 3 = 8) and subtract from the line length (10 - 8 = 2). That leftover is the slack. A run longer than the slack always has squares in the middle that it cannot avoid: its length minus the slack. The 4 leaves 2 squares, the 3 leaves 1.

Do this to every row and column before you try anything cleverer. On a fresh grid it is usually the only productive move.

The move in three steps

1. Pack left. Place every run as far left as it can go, with one empty square between runs.
2. Pack right. Place every run as far right as it can go.
3. Keep the overlap. For each run, fill the squares it covers in both layouts.

Worked example: two clues

Take eleven squares with the single clue 7. It uses seven, leaving a slack of four, so the run can start anywhere from square 1 to square 5. Whatever it does, it covers squares 5, 6 and 7.

Now a row of eight with the clue 3 3. The clues and their gap use seven squares, slack one. Each 3 is longer than one, so each fills two squares: squares 2 and 3 for the first run, and squares 6 and 7 for the second.

Common slip. Filling squares that two different runs reach. Follow one run at a time through both layouts.