Lights Out is an electronic logic puzzle consisting of a 5x5 square array of buttons. At any given time, some of the buttons will be lit and others won't. The aim is, as the name suggests, to have none of the buttons lit.

The way the puzzle works is as follows: pressing a button toggles it and all of its horizontal and vertical neighbours between on and off. In other words, buttons which are dark become lit and vice versa.

The interesting thing about Lights Out is that for any solvable state, the solution never requires more than 25 buttons to be pressed. The overall effect of pushing any button is completely independent of the state of the puzzle when it is pressed because it merely toggles between two states, therefore if a button is pushed twice it merely undoes the first push. This means that all solvable states are solved by a specific button combination, and the order the buttons are pressed is irrelevant.

Because there are 25 buttons, each of which is either on or off, the number of possible states is 225, which is 33,554,432. The number of distinct states is considerably fewer, since most of them are rotations and/or reflections of each other. The number of solvable states is also 225, because each button is either pressed or not during solving. However, just because these number are the same does not mean that all states are soluble. One example of an insoluble Lights Out puzzle is shown to the right.

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Lights Out in popular cultureEdit

  • In the PlayStation game Alundra, one dungeon contains a puzzle that works in the same way as Lights Out, but with a 4x4 array of switches instead of 5x5. Its starting state is that all sixteen switches are off, and all of them have to be turned on to proceed.

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