Here's a quick Monday morning puzzle.
You have a 14x14 rectangular game board except that the last 7 fields of the last row are missing. Each field has a lamp, and a button that toggles the lamps on that field and each of its neighbours in a cardinal direction, altogether at most five lamps. At the start, all lights are lit. Find out which buttons to push to unlight all lights.
Why I like this puzzle is:
Update: here's an example. Suppose we have a 3x4 board with the last 1 field of the last row missing. At the start, it looks like this, all lamps lit:
Now we press the button on the bottom left field so three lights go off:
then press the button above that so two lights turn back on but two lights go off:
now press the second button in the bottom row:
now the button above that one:
finally press the top right button:
and all the lights are off, so we've solved this small board.