Compare every legal placement of a group. A square shared by all those placements can be filled before you know the group’s exact endpoints.
| 5 | 1 1 | 1 1 1 | 1 1 | 5 | |
|---|---|---|---|---|---|
| 5 | |||||
| 1 1 | |||||
| 1 1 1 | |||||
| 1 1 | |||||
| 5 |
The game is paused.
Fill cells to match each row and column’s clue groups in order. Leave at least one empty cell between separate groups. A 0 means the whole line is empty. Select Fill or Mark empty, then select a cell. Select it again with the same tool to clear the mark. Arrow keys move through the board; Enter or Space applies the tool. These three 5 × 5 puzzles do not save progress when you leave.
An overlap identifies squares that must belong to a filled group wherever that group can legally fit. It does not require recognizing the final picture or selecting a favorite placement. Start with the line length and its clue, consider the legal positions, and keep only the squares common to all of them. The resulting information can be smaller than the complete group.
The playable classic board above has five rows and five columns. That compact size makes the following examples easy to count, but a particular example is not a claim about the clue currently displayed on your chosen puzzle. Use the numbers from your own line before transferring any result. Different lengths and multiple groups need their own calculation.
Number a row’s positions one through five. With a single clue 3, the group can occupy one to three, two to four, or three to five. Position three appears in every placement. It is therefore safe to fill that middle square. Positions one, two, four, and five remain uncertain at this stage; none becomes an empty square merely because it was outside one placement.
This distinction is the point of the technique. Filling the central square does not decide whether the group starts at one, two, or three. If you immediately put empty marks at both ends, you would be choosing the middle placement without evidence. Keep the uncertain squares available until a crossing clue or another constraint removes a possibility.
With a clue 4, there are only two placements: one through four, or two through five. Their intersection contains positions two, three, and four. All three can be filled. The first and fifth squares are still undecided, because each belongs to one legal placement and not the other. You have proved three squares without pretending to know all four.
More generally, compare the group pushed as far left and as far right as the available segment allows. Squares present in both extremes are present in the placements between them for a single uninterrupted group. Be careful about the available segment: known empty squares can split a line, and other groups can reserve some of the room.
A clue such as 2,2 describes two groups, not one group of four. In five positions, the mandatory gap means the whole arrangement is fixed: filled, filled, empty, filled, filled. Applying the single-group overlap to an imaginary four-square group would erase that required separator and produce the wrong shape.
For a clue 2,1 in five positions, the groups and one mandatory gap use four spaces. The remaining space may occur at an end or increase the gap. You must account for the order and for the positions both groups could use. If you are unsure which group a filled square belongs to, postpone a conclusion rather than assigning it to whichever group is convenient.
Once you have an overlap, inspect the columns that cross its newly filled squares. A column may now have only one possible location for a group. That information can return to a different row. Alternating between directions is often more useful than trying to complete every horizontal line before using any vertical clue.
Suppose a column of five requires a group of four and its first square is already proved empty. Only positions two through five remain available, so the whole group is located. This deduction is stronger than the original overlap because it uses an additional restriction. The restriction must itself be proved; an earlier guess should not silently become a fact.
Use Fill and Mark empty to distinguish your conclusions. Selecting the same tool on a mark clears it, and Undo steps back. Unknown squares are a third state. The game does not certify every entry when you make it, so a mark should be supported by a sentence such as “this position belongs to every legal placement.”
If a later line becomes impossible, check whether an uncertain endpoint was marked too early or a separator was forgotten. You may be able to correct one decision without replacing the puzzle. The classic game does not save marks when the page is reloaded or closed; Pause only hides the board while it remains open. The guide expands these ideas with other worked line decisions.
Not necessarily. It proves only squares shared by all legal placements.
Only the third position is common to all three placements.
Positions two, three, and four are common to both placements.
No. Different groups require at least one empty square between them.
No. They remain unknown until another restriction decides them.