I had an iPod back when iPods were slowly not becoming a thing anymore running Rockbox, which has a 4x5 Lights Out called FlipIt which I’d play between or durin

I had an iPod back when iPods were slowly not becoming a thing anymore running Rockbox, which has a 4x5 Lights Out called FlipIt which I’d play between or during university lectures: https://download.rockbox.org/daily/manual/rockbox-fiiom3k/rockbox-buildch12.html#x15-21000012.1.13 https://download.rockbox.org/daily/manual/rockbox-fiiom3k/ro... With a bit of work I discovered that the 4x5 version could be solved mentally, although perhaps not in minimal moves, but definitely without pushing the same button twice. Here's how I thought through it: Define R-propagation as the process of pressing in the 2nd column to turn off the lights in the 1st column, pressing in the 3rd column to turn off the lights in the 2nd column, and so on until the only lights on are in the 5th column. Then define L-propagation as the mirror image process. I was very surprised to find that for 4x5, R-prop followed by L-prop solves the Lights Out; L-prop of these two cases is (stopping before the last step otherwise it's boring), . . . . o o . . . . . . . . . --> . o . . . . . . . . o o . . . . . . . . . o . . . . . . . . . o . . . . . . . o --> . o . . . . . . . . . . . . . . . . . . o o . . . This means that all you have to do to mentally solve 4x5 is to figure out, “if I did R-prop, what buttons would I end up pressing in the 5th column,” press those buttons first, and then L-prop will solve the rest. Fun times!