TECHNIQUE 4 OF 4
Chase lights downward without undoing finished rows
Row chasing replaces scattered experiments with a repeatable test. First choose which buttons, if any, to press in the top row. The remaining rows can then be processed systematically.
The rule
After the first-row choice, press directly below each lit square in row 1. Those presses clear row 1. Next press below each lit square in row 2, and continue downward. A press affects only its own row and the rows immediately above and below, so working farther down cannot disturb rows already left behind. The bottom row determines whether the chosen first-row pattern succeeded.
A common mistake
An uncleared bottom row does not mean random extra presses will preserve the work above. Reset to the same starting board and test a different first-row pattern. A complete chase is a solution only if the final row is also dark; it is not automatically a minimum-move solution.
TRY IT 1 · lights-chasing-1
| C1 | C2 | C3 | C4 | C5 | |
|---|---|---|---|---|---|
| R1 | |||||
| R2 | |||||
| R3 | |||||
| R4 | |||||
| R5 |
What can you justify?
Choose no first-row presses. The first lit square in row 1 is R1C1. Which row-2 button clears it as the next row-chasing step?
Written explanation
Press R2C1, directly below R1C1. This is a row-chasing step for the zero first-row choice, not a promise that the final row will be dark. Reset and test another first-row pattern if the full chase leaves lights on.
TRY IT 2 · lights-chasing-2
| C1 | C2 | C3 | C4 | C5 | |
|---|---|---|---|---|---|
| R1 | |||||
| R2 | |||||
| R3 | |||||
| R4 | |||||
| R5 |
What can you justify?
Choose no first-row presses. The first lit square in row 1 is R1C1. Which row-2 button clears it as the next row-chasing step?
Written explanation
Press R2C1, directly below R1C1. This is a row-chasing step for the zero first-row choice, not a promise that the final row will be dark. Reset and test another first-row pattern if the full chase leaves lights on.
Correcting the bottom directly can undo the row above
During row chasing on a five-by-five board, rows 1–4 have been cleared, but R5C3 remains lit. The other bottom-row cells are not specified.
The tempting move
Press R5C3 and assume the four completed rows will stay clear.
Why it fails
Pressing R5C3 also toggles R4C3, turning a light back on in the cleared row above. There is no row 6 from which to clear the bottom while leaving row 4 untouched.
What is actually justified
The chosen first-row pattern has failed the row-chasing test. Return to the same starting board and try another first-row pattern. A lit bottom row does not by itself prove the original board unsolvable.
Transfer the idea
You have finished choosing top-row presses, and only R1C2 and R1C5 are lit in row 1. Which row-2 buttons clear them? Can later presses in row 3 change row 1?
Check your reasoning
Press R2C2 and R2C5. Each affects the square directly above it, so those two top-row lights turn off. Row-3 presses reach rows 2–4, not row 1, so they cannot change that finished top row. Continue by inspecting the new state of row 2.