Question 80
A panel contains 100 light bulbs, arranged to form a square of 10 rows and 10 columns. Some of them are on, the others are off.
The electrical system is such that when you press the button corresponding to any of the light bulbs, all the light bulbs found on its column and all those found on its row change state (that is, they turn on or off) (including the light bulb corresponding to the pressed switch).
a) Starting from which configurations, by operating appropriately, is it possible to ensure that all the bulbs are switched on in the end?
b) What is the answer to the previous question if there are 81 light bulbs, arranged to form a panel of 9 rows and 9 columns?
The electrical system is such that when you press the button corresponding to any of the light bulbs, all the light bulbs found on its column and all those found on its row change state (that is, they turn on or off) (including the light bulb corresponding to the pressed switch).
a) Starting from which configurations, by operating appropriately, is it possible to ensure that all the bulbs are switched on in the end?
b) What is the answer to the previous question if there are 81 light bulbs, arranged to form a panel of 9 rows and 9 columns?