|The enlightened frogs
There are 100 lights initially all turned on in a line,
numbered from 1 to 100. If you press a lightbulb it will
turn on if it's currently off, or it will turn off if it's
There are also 100 frogs. The first frog jumps over all the
lights so turning them off. When it's arrived the second frog
starts from the second light and jumps on every other light (i.e.
on the lights 2, 4, ..., 98, 100) turning back on all the lights
with an even number. When the second frog it's arrived the third
frog starts from the third light and jumps on a light every three
(so on the lights 3, 6, 9, ..., 96, 99 - see figure above) turning
on the lights it finds off and turning off the lights it finds on.
The 100 frogs all follow this pattern (e.g. the 18th frog starts
from the 18th light and jumps on one light every 18); the last
(100th) frog jumps only on the last light (number 100).
When all frogs ended their dance, which lights are on and which
ones are off ?
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