Lantern Grid strategy: reserve the wall candidates before chasing light.
Compare a brightening move that blocks a numbered wall with a forced seven-bulb solution. A fixed board, candidate table and straight-line source checks make each deduction reproducible.
A bulb that brightens many cells can still destroy a solution. Before chasing a dark area, ask which cells must stay available to a numbered wall. This lesson uses a different layout from the beginner board to connect two checks: remaining bulb positions beside a wall, and remaining light sources for a dark cell. You will compare a tempting wrong move with a forced seven-bulb route.
Load the wall-reservations board
Choose Practice this example beside this article, or Load strategy board in the game. Confirm Toggles 0 and the layout below. This is the second board in the existing five-puzzle collection, now available directly for repeatable study; it is not an expanded collection. Dots are white cells and digits are fixed walls. Coordinates count rows from the top and columns from the left.
0 1 · 1 1 · · · 2 · · · 3 · 2 · · · · 1 · 1 · 1 ·
Use paper to note exclusions. The game currently records bulbs only: an empty cell is not an automatic pencil mark or a promise that the cell can hold a bulb. A + shows light, not a second bulb. Undo reverses one toggle; Retry clears bulbs on unchanged clues. Neither command changes the reasoning printed here.
Count available neighbours, not just empty neighbours
For a numbered wall, let r be its target minus the bulbs already beside it. Let c count the remaining adjacent white cells that have not been ruled out. Rule out a candidate if it would exceed another wall number or see an existing bulb. Keep exclusions supported by a stated deduction; an unexplored cell must not be crossed out simply because it looks inconvenient.
- If r = 0, none of the other adjacent cells can contain a bulb.
- If r = c and r is positive, all c remaining candidates need bulbs.
- If r > c, the current assumptions cannot be completed. Trace the assumptions back instead of adding a bulb elsewhere.
These tests are necessary, not a complete solver. Two candidates might conflict with each other, or a distant white cell might have no possible light source. Passing r ≤ c at every wall does not prove that a partial pattern has a solution.
Use a forced bulb to reduce another wall's choices
The 1 at R1C4 has only one adjacent white cell, R1C3. Put a bulb there. It illuminates R2C3 directly below, so a bulb at R2C3 would see the existing bulb and is excluded. The same placement satisfies the 1 at R1C2, excluding its other white neighbour R2C2. The zero at R1C1 separately excludes R2C1.
The 1 at R1C5 likewise forces a bulb at R2C5. That cell is enclosed by walls and the grid edge, so it lights only itself. After these two placements, just 3 of 15 white cells are lit. A small lighting gain can still be a forced and useful move.
| Neighbour | Can it contain a bulb? | Reason |
|---|---|---|
| R2C3 | No | It sees the bulb at R1C3. |
| R3C2 | Yes; now forced | One of exactly three remaining candidates. |
| R3C4 | Yes; now forced | One of exactly three remaining candidates. |
| R4C3 | Yes; now forced | One of exactly three remaining candidates. |
The central wall still needs three bulbs, and precisely three of its four geometric neighbours remain available: r = c = 3. Reserve all three. None sees either existing bulb or another of these three forced bulbs; the central wall blocks the relevant straight paths. A 3 with four white neighbours did not start as an immediate all-neighbours deduction. The earlier exclusion made it one.
Compare a brightening move that loses the reservation
Before placing the central three bulbs, keep only R1C3 and R2C5. Try R3C1 because it reaches much of the left column. Predict the lighting gain, then ask what happens to the central wall's candidates. An accepted click is not the game's endorsement of your choice.
Reveal the wrong branch, capacity contradiction and exact recovery
At Toggles 3, bulbs at R1C3, R2C5 and R3C1 light 8 of 15 cells, up from 3. Check lighting reports 7 dark cells, 6 mismatched wall counts and 0 visible bulb pairs. No wall is overfilled: the mismatches are still underfilled walls. The current three bulbs do not see each other, yet the branch is impossible.
R3C1 illuminates R3C2 across row 3, excluding a bulb at R3C2. R2C3 remains excluded by the earlier R1C3 bulb. The central 3 now has only R3C4 and R4C3 available: r = 3, c = 2. Adding either or both cannot supply the third bulb. The display reports current counts, not this future-capacity contradiction.
Undo once removes R3C1 and returns to Toggles 2, 3 lit cells and the original two-bulb checkpoint. It restores the missing central candidate. Check adds no toggle. Continue with R3C2, R3C4 and R4C3, or Retry before following the complete route below.
Check sources for the dark cells that remain
After the central three bulbs, the five bulbs light 12 of 15 cells. The dark cells are R2C1, R5C1 and R5C5. For any dark white cell, list every white cell in its uninterrupted row and column segments, including itself. Those are the only positions whose bulb could illuminate it. Remove positions already ruled out; if only one remains, that source is forced.
R2C1's geometric source set is R2C1, R2C2, R2C3, R3C1, R4C1 and R5C1. The zero excludes R2C1. The satisfied 1 at R1C2 excludes R2C2. R1C3's beam excludes R2C3. R3C2's beam excludes R3C1, and R4C3's beam excludes R4C1. Only R5C1 remains, so place that bulb. It lights both R5C1 and R2C1 through R4C1 and R3C1; it does not turn into column 2.
R5C5 is isolated: above it is a numbered wall, to its left is another numbered wall, and its other two sides are grid edges. Its only light source is itself. Place its bulb last. The relevant wall counts also become exact, but the source argument explains why that particular cell needs a bulb.
Replay the complete route and verify every checkpoint
Retry to start at Toggles 0. Activate the following cells once each. Every row below has 0 visible bulb pairs. The mismatch count includes underfilled walls during the attempt; it is not a count of irrecoverable errors.
- R1C3: the only neighbour of the top 1 at R1C4. Toggles 1; 2 cells lit; 7 wall counts mismatched.
- R2C5: the only neighbour of the top-right 1. Toggles 2; 3 cells lit; 6 mismatches.
- R3C2: preserve the first central reservation. Toggles 3; 7 cells lit; 6 mismatches.
- R3C4: supply another central neighbour and the two right-hand 2 walls. Toggles 4; 9 cells lit; 4 mismatches.
- R4C3: complete the central 3. Toggles 5; 12 cells lit; 3 mismatches.
- R5C1: the sole remaining source for R2C1. Toggles 6; 14 cells lit; 2 mismatches.
- R5C5: light the isolated corner. Toggles 7; 15 cells lit; all wall numbers exact.
Now use Check lighting. Only that successful check records the finish and locks the white-cell buttons. Undo remains available; undoing the final bulb reopens the board at Toggles 6, with R5C5 dark and two wall counts mismatched.
Reveal the finished map and a source-set self-check
0 1 B 1 1 + + + 2 B + B 3 B 2 + + B + 1 B 1 + 1 B
There are seven bulbs, all fifteen white cells are lit, all ten numbered walls match and no bulb sees another. Independent enumeration finds exactly one valid bulb pattern for this clue set.
Could R4C2 replace R5C1 as a source for R2C1? No. They share neither a row nor a column, and light cannot turn a corner at R4C1. R4C2 is also already illuminated by the bulb at R4C3, so adding a bulb there would create a visible pair. A source set contains straight sight lines, not every connected white cell.
Keep deductions separate from guesses
Repeat the cycle: update exclusions, count a wall's remaining candidates, then examine dark cells' possible sources. A zero-source dark cell or a wall with too few candidates disproves the assumptions that caused it. If no forced move appears, these local checks may be insufficient; do not declare a guess proven or assume every larger puzzle resolves this way. In this fixed board the full route follows forced placements, without a minimum-toggle claim.
Load strategy board restores this layout. Load beginner board selects lesson 1. Refreshing either practice address restores its clues with no saved bulbs or history; New puzzle clears the practice address and advances through the same five prepared rounds. Keyboard arrows skip walls, while Enter or Space toggles the focused white cell.