Take the 2-minute tour ×  Hy all! My problem is as follows:
There's a board of 10 by 10 light bulbs. (So it's a square with
10 columns and 10 rows.) Every single bulb has got its own
switch. However, something went wrong and when you use a switch
not only does it change the state of the proper light bulb but
states of all other 18 bulbs in its column (9) and row (9). (a
state change obviously means: off lights turn on, on lights turn
off) So one click changes the required bulb's state AND all the
bulbs in its row and column. How many clicks (switches used)
will be needed at least to turn off all the bulbs if they are
all on?  I've literally spent hours thinking it over and over.
It's kinda straight-forward that the order of the clicks are
irrelevant and using the same switch more than once is
meaningless. (I mean using the same switch twice is like not
using it at all, and using it three times is like only once
{only parity (even/odd) matters}.) Consequently, there are 2^100
possibilities, so unfortunately mo