IT-CESENATICO 2001 Problem 6
A panel contains light bulbs, arranged in a by square array. Some of them are on, the others are off. The electrical system is such that when the switch corresponding to a light bulb is pressed, all the light bulbs that are on the same row or column of it (including the bulb linked to the pressed switch) change their state (that is they are turned on or off).
- From which starting configurations, pressing the right sequence of switches, is it possible to achieve that all bulbs are on at the same time?
- What is the answer to the previous question if the bulbs are , arranged in a by panel?
Dataset text AI-MO AoPS. Quoted with source.
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