Signal Grid: understand what overlapping switches cancel
Reason about a press as a set of changes. A worked two-by-two example explains why pressing an unlit square can be the right move.
A press changes a neighbourhood
Signal Grid uses a five-by-five board. Each press flips its selected square and the squares directly above, below, left and right of it. A lit lamp becomes unlit; an unlit lamp becomes lit. A corner press changes three squares, an edge press usually changes four, and an interior press changes five.
This means pressing a lit square is not automatically progress. Its neighbours may change in ways you do not want. Equally, an unlit square can be a useful place to press because its neighbourhood includes a lamp you need to clear. Plan the group of changes, not just the square under your pointer.
Two changes restore the original state
Press any square twice. Every lamp in its neighbourhood changes once and then changes back. The board returns to the state it had before those two presses. For the final result, each square therefore only needs a yes-or-no decision: press it once, or do not press it.
The order of a fixed collection of presses does not change the final lamp pattern. Each lamp only cares whether it is flipped an odd or even number of times. Order still matters to how understandable the intermediate boards feel, but it does not create a different final answer for the same set of presses.
Follow a smaller teaching example
To make the overlap easier to inspect, imagine a separate two-by-two board. This is a teaching example, not the size of Signal Grid’s playing board. Label its top squares A and B and its bottom squares C and D. Begin with A and B lit, while C and D are unlit.
Press C. It flips A, C and D, leaving B, C and D lit. Now press D. It flips B, C and D, clearing the board. Both chosen squares were unlit at the start. Pressing them worked because their effects on the bottom lamps cancelled, while each top lamp changed exactly once.
Count effects on one lamp at a time
For any lamp, list the presses that can affect it: its own square and its existing orthogonal neighbours. If the lamp starts lit, your complete plan needs an odd number of those presses. If it starts unlit, it needs an even number, including the possibility of zero.
Use that test to check a proposed small sequence. It is more reliable than judging whether each intermediate board contains fewer lights. A useful press may briefly increase the number of lit squares while setting up a later cancellation. A temporarily darker board may instead leave awkward lights along the bottom edge.
Use cancellation as a check, not a guess
Recognising cancellation does not tell you the correct set of presses immediately. It gives you a way to explain and verify a set once you have proposed it. If an experiment is unhelpful, Undo can restore the previous board without requiring you to remember every changed lamp individually.
The generated game boards have a solution because they start from an unlit board and are changed through legal presses. Repeating those generating presses would reverse their effect. You are not shown that history, so finding your own solution remains the puzzle; a low move count alone does not demonstrate that it is the shortest one.
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