Akagram Strategy: Solving Tips and Forced Moves

Start with row and column totals

Subtract the bulbs already placed from the line’s clue. Compare the number still needed with the undecided cells that can legally hold a bulb. If none are needed, mark the rest ×. If every remaining candidate is needed, each is a bulb. Apply the same check to columns after each row deduction.

Example: a row with a clue of 3 already has two bulbs and only one remaining candidate. That cell must be a bulb. If it sees an existing bulb or breaks a wall clue, the position is inconsistent: revisit an earlier move instead of forcing it. A wall stops light, but it does not split the outside row total.

Count the open sides of numbered walls

A 0 wall excludes bulbs on all its open sides. For any other numbered wall, subtract adjacent bulbs from the clue and count the undecided side-neighbors still available. If two bulbs are still needed and only two candidates remain, both are forced. When the clue is satisfied, mark every other side-neighbor ×. Diagonal cells never contribute.

A wall numbered 2 on an edge may have only two usable open neighbors. Both must contain bulbs. Do not assume every 2 has this property: inspect walls and empty marks around that particular clue.

Use visibility to exclude bulbs and force illumination

After placing a bulb, trace each straight path to the next wall or board edge. No other cell on those paths can hold a bulb. Mark those cells ×, then revisit the row, column and wall counts affected by those exclusions.

Now examine an unlit cell. A bulb must be in that cell or in an open cell with a clear horizontal or vertical path to it. If exactly one legal candidate can light it, that candidate is forced. A × rules out a bulb at that position; it does not block light passing through.

Distinguish a Legal Candidate from a Forced Move

A candidate may fit its nearby clues and still prevent some distant cell from receiving light. Do not call it forced just because no immediate conflict appears. A forced move is required by the remaining constraints: for example, it is the only legal light source for a dark cell, or the only candidate left for a missing row total.

Suppose an unlit cell has two possible light sources, A and B. A row total elsewhere rules out A, leaving B as the only source. B is now forced. If you merely prefer B while both sources remain possible, that is a choice to investigate rather than a completed deduction. Marking unsupported choices as certain can hide the move that caused a later contradiction.

Akagram Tips: Choose Your Next Deduction

Scan zero and completed line totals, then numbered walls, then the paths from newly placed bulbs. Look for an unlit cell with only one remaining light source. Repeat after each new mark: a deduction in one row can finish a column or a wall clue elsewhere.

When the board stops yielding moves

First check whether you have confused a wall clue with a whole-line total, counted a diagonal, or treated × as a wall. If you guessed earlier, use Undo and reconsider that placement. Check can test whether the position is still completable; Hint can supply one forced move. Neither promises a written explanation, and these techniques are not a guarantee that every puzzle will feel easy.