Linear Algebra in Room Escape

Last weekend I went to play a reality room escape game with some friends. It’s a lot of fun and we finally escape on time!

The only thing make it less perfect is that we skip a “very hard” puzzle according to the staff in the room. We spend 1O minutes on it and we could not found an effective way to solve it.

The game is consisted of a board with 5 rows * 5 columns = 25 lights. Each light is either on or off. Player could switch any light on/off, but switching any light will also switch it’s neighbour on up/down/left/right position at the same time. The goal of this game is for a given status, try to switch some of the lights to make all the lights on.

You could also refer to this graph for the “switch logic”.

Light out example

To win the game, For example, if the initial status looks like the following board (O mean an enlighted light and X mean an off light), then we could switch 2 lights on (2,1) and (4,3) to make all the light on. But is there an systematic way to get a solution?

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