Sam was playing on the \(3\times 3\) lights out board, and starting from all lights off, he pressed every single button on the board. What light pattern did he get in the end?
Find a quiet plan for the \(1\times 5\) “Lights Out" board.
There are \(57\) buttons placed evenly around a circle, each with a light underneath it. Pressing a button changes the state of its own light and also the lights under its two neighbouring buttons. Changing state means that a light which is on becomes off, and a light which is off becomes on. If all the lights start off, what is the smallest number of presses that need to be done so that the entire circle lights up?