Find the cells every placement shares.

You can know where part of a black group belongs before you know where the group starts.

Fill the shared part. Leave everything else unknown, then check the crossing lines.

Start with a long run in a short line

Imagine seven empty cells with a single clue of 5. The group may start at cell 1, 2 or 3. You cannot choose a starting position yet, but the middle three cells are covered in every arrangement. Those three cells are safe to fill.

Try sliding the complete group from its earliest position to its latest. The shared part is the overlap. You are not drawing the most likely answer: you are keeping only the cells that cannot change.

Clues: 5

Arrangement1234567
Earliestblackblackblackblackblackemptyempty
Middleemptyblackblackblackblackblackempty
Latestemptyemptyblackblackblackblackblack
Certainunknownunknownblackblackblackunknownunknown
In seven cells, every placement of a run of 5 covers cells 3, 4 and 5. Dots in the Certain row stay unknown; × in the other rows describes that particular possibility only.

Count the room that is left

For one group in an otherwise unknown line, subtract the group length from the line length. That difference is the amount of room the group can slide. In this example it is 7 minus 5, or 2 cells. The first two and last two cells remain undecided.

A clue of 3 in seven cells has no immediate overlap. That does not make the line useless; it means you need information from its crossing columns before this technique can help.

Return to the crossing lines

Each newly filled cell also belongs to a column. Inspect those columns next. A known black cell can rule out placements that were possible before and create another overlap elsewhere.

When a line has several groups, keep their order and the mandatory separator between groups. Comparing two imagined placements while ignoring a smaller group can give a false deduction. The reliable principle stays the same: a black cell must be black in every arrangement still compatible with all clues and known marks.

A common mistake to avoid

Do not mark the cells outside the overlap as empty. They are uncertain, not white. A later crossing-line deduction may show that the group extends into them. Use Erase to return a guessed mark to unknown and continue from facts.

Try three small deductions

These are practice lines, not a saved game. Fill only what is certain; leave anything uncertain unknown.

Find the overlap

Fill only the cells that must be black. Leave every uncertain cell unknown.

Clues: 3

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