Clue Grid strategy: keep every possible run until the crossings decide.
Use overlap and complete line candidates on a new fixed board, then follow eight justified steps to a checked solution without choosing an unproved endpoint.
A run of four fits in a five-square line in two places. Filling either entire placement immediately commits you to an endpoint that the clue has not established. A safer move is to keep both placements, fill only their overlap, and let crossing clues decide which endpoint survives.
This lesson turns that habit into a repeatable method: list complete legal patterns for one line, remove those that disagree with known marks, and record only what every surviving pattern shares. A new five-by-five example can be completed with eight such line checks. None of its starting clues fills an entire line by itself.
Separate possible, forced, and ruled out
A candidate is a complete pattern that fits one line's ordered run lengths and mandatory gaps. A filled square in one candidate is merely possible. It becomes forced for that line only if every remaining candidate fills it. The same rule identifies empty squares when every candidate leaves a position empty.
Use ■ for a fill, × for an established empty square, and ? for undecided. Unknown does not mean empty. When comparing a candidate with existing marks, it must retain every established fill and every established ×. Do not reject a candidate because it differs at an undecided position.
A single surviving candidate settles that line. Several surviving candidates may still share useful marks. No surviving candidate means the current marks contradict the line's clue; look for an earlier mistake rather than inventing another placement. These are paper reasoning steps. The live game's Check lines button does not enumerate candidates or identify incorrect cells.
Load the candidate example
Choose Practice this example in the side panel or Load strategy example below Clue Grid. Both load this fixed board with all marks unknown and Edits at zero. Rows are R1–R5 from top to bottom, columns C1–C5 from left to right. Verify the clues before following the walkthrough:
Rows Columns R1: 2 C1: 2 R2: 2 1 C2: 2 1 R3: 1 C3: 2 R4: 3 C4: 4 R5: 4 C5: 2
This is neither the beginner's frame nor the game's original teaching board. It has thirteen filled squares in its unique solution. New puzzle gives different clues; use Retry this board when comparing attempts on this example.
Begin with an overlap, without choosing an end
Column 4 has clue 4. Its only two legal placements are shown below, reading each line from row 1 to row 5. The last line records only what they share:
Top run: ■ ■ ■ ■ × Bottom run: × ■ ■ ■ ■ Shared: ? ■ ■ ■ ?
Fill R2C4, R3C4, and R4C4. Leave R1C4 and R5C4 undecided. Both possible runs contain rows 2–4, so those three fills are justified without guessing. The clue has not yet told you whether the run starts at row 1 or row 2.
The temptation to pack the run against the top would produce a valid column pattern, but validity in one column is not validity for the whole puzzle. We will settle the ends after information comes back from other lines.
Use a crossing fill to remove whole candidates
Row 2 has clue 2 1. In five squares, there are exactly three legal complete patterns. The two-square run comes first; the separate single square comes later:
A: ■ ■ × ■ × B: ■ ■ × × ■ C: × ■ ■ × ■
R2C4 is already filled by the column overlap. Pattern A retains that fill. Patterns B and C put an empty square at C4, so both are ruled out. You are not choosing A because it looks promising: the other complete possibilities contradict an established mark.
Fill R2C1 and R2C2, and mark R2C3 and R2C5 empty. R2C4 was filled already, so do not activate it again with Fill square selected; that would clear it. For the replay below, make the two new empty notes before the two new fills.
Notice how an empty note becomes useful evidence. Row 2's new × at C3 can restrict column 3 later, even though no new fill was made there. Candidate elimination works with both kinds of established marks.
Alternate directions instead of staring at one line
Row 3 has clue 1 and already contains the fill at C4. It must leave C1, C2, C3, and C5 empty. At this point the board should look like this:
? ? ? ? ? ■ ■ × ■ × × × × ■ × ? ? ? ■ ? ? ? ? ? ?
Now inspect column 1. Its run of two must include R2C1, while R3C1 is empty. The run cannot extend downward through row 3, so it has to occupy rows 1–2. Fill R1C1 and mark R4C1 and R5C1 empty.
That new R1C1 fill settles row 1's run of two at C1–C2. Row 1's C4 is therefore empty, finally rejecting the top-run candidate for column 4. This is information returning to the line that started the process; it is not evidence that the column's overlap was wrong.
Replay the full eight-check ledger
Start with Retry so every square is unknown and Fill square is selected. Follow the steps below. Within each step, write the listed empty notes first, then change back to Fill square for any listed fills. Activate only new marks; leave earlier ones untouched. The running counts include cell edits, not action-choice changes or Check lines.
- Column 4: fill R2C4, R3C4, R4C4. The two length-four placements share these positions. Edits: 3.
- Row 2: mark R2C3 and R2C5 empty; fill R2C1 and R2C2. Only candidate A retains the known C4 fill. Edits: 7.
- Row 3: mark R3C1, R3C2, R3C3, and R3C5 empty. Its single fill is already at C4. Edits: 11.
- Column 1: mark R4C1 and R5C1 empty; fill R1C1. Its run of two ends at row 2, above the known gap. Edits: 14.
- Row 1: mark R1C3, R1C4, and R1C5 empty; fill R1C2. Its run of two starts at the already filled C1. Edits: 18.
- Row 5: fill R5C2, R5C3, R5C4, and R5C5. C1 is empty, so the run of four has only one place left. Edits: 22.
- Column 2: mark R4C2 empty. Its clue 2 1 is already satisfied by rows 1–2 and row 5, with row 3 empty; row 4 must separate the final single fill. Edits: 23.
- Row 4: fill R4C3 and R4C5. With C1 and C2 empty, the run of three must occupy C3–C5, including the existing C4 fill. Edits: 25, and the board is complete.
This exact order reaches the first win on its last edit. It places thirteen fills and twelve empty notes, each once. Twenty-five is the cost of this documented replay, not a claim about the fewest actions the game permits. Empty notes are optional for the win condition, but writing them makes the reasoning and the candidate checks visible.
Reveal the final pattern and check all crossings
■ ■ × × × ■ ■ × ■ × × × × ■ × × × ■ ■ ■ × ■ ■ ■ ■
Read column 3 as empty, empty, empty, filled, filled: one run of two. Column 5 has that same pattern. Column 4 is empty, filled, filled, filled, filled, selecting the lower length-four placement. All row and column run lists match the printed clues.
Two useful stopping checks
What if row 2 has both C4 and C5 filled?
None of A, B, or C has fills in both positions. The current marks contradict clue 2 1. This does not prove the puzzle is impossible: an earlier fill may be wrong. In the worked route, C4 was established by the overlap and C5 was ruled empty. Check your reasoning or undo the unsupported edit. The live line check reports matching lines; it does not supply this candidate diagnosis for you.
When may you fill an undecided endpoint?
When the remaining evidence forces it. Column 4's overlap initially left both endpoints undecided. After row 1 makes its top endpoint empty, only the lower placement remains and its bottom endpoint is filled. Choosing an endpoint earlier would be a guess even if it happened to match the eventual answer.
Know when this method has run out of evidence
Repeat the process with a line that received a new mark: list its complete allowed patterns, remove contradictions, and keep shared fills and gaps. Recheck crossings after each change. Use Retry to restore the same starting clues, or Undo to inspect one earlier cell state; neither stores a separate record of your reasoning.
Some other boards may stall with several candidates left in every line and no shared undecided mark. This line-by-line method alone has then found no next deduction. That is not permission to promote one possible placement into a forced one, and a unique global solution does not guarantee that local overlap checks will finish it. The present example is verified to finish by the eight checks above; it does not establish a universal solving algorithm.