A repeatable deduction sequence
Remove direct conflicts.
For each placed character, eliminate its row, column, colored region and eight neighboring cells. These eliminations are justified only if the existing placement is correct.
Look for a single remaining candidate.
If an unfinished row, column or region has one legal candidate, it must hold that unit’s character. If it has zero candidates, revisit a placement or exclusion: the current assumptions cannot all be right.
Use a region’s reserved line.
If every remaining candidate of a region lies in one row, that region must use that row. Eliminate candidates in the same row belonging to other regions. The same reasoning works for a column. You do not yet know which square inside the region is correct.
Repeat after each justified placement.
A new piece affects several units at once. Rescan from the most restricted area instead of guessing in the largest open region.
Worked example: Level 4
| 1 | 2 | 3 | 4 | |
|---|---|---|---|---|
| 1 | G | V | Y | Y |
| 2 | G | G | Y | Y |
| 3 | G | G | Y | Y |
| 4 | G | G | P | P |
G = Mint · V = Violet · Y = Yellow · P = Pink
- R1C2: the violet region has only this square.
- R2C4: row 2 loses C2 to the occupied column, and C1/C3 to neighboring diagonals.
- R4C3: pink can use C3 or C4; C4 is occupied by row 2.
- R3C1: columns 2, 3 and 4 are now occupied. The remaining mint square completes the board.
Compare the solution with the recorded completion →
When a hypothetical move creates a contradiction
Suppose you temporarily consider one candidate. If it leaves any required row, column or region with no possible character, that candidate cannot belong to a complete solution under your current valid premises. Remove the assumption and return to the original board.
A failed assumption does not automatically prove a different square. A remaining alternative becomes forced only when it is the sole surviving candidate for a required unit. An assumption that does not immediately fail is also not proof that it is correct.
Two regions can reserve two rows
If two distinct unfinished regions can use only the same two rows, together they occupy those rows. Other regions cannot use either row. This concerns two rows, not two cells shared by different regions: each cell belongs to one colored region. Check that both regions really are restricted to that pair before applying the rule.
Reasoning is derived from the official uniqueness constraints and the visible no-touch rule and Level 4 example ↗.