Bright idea, or "good idea," or "seeing the light" is a 
colloquial expression describing a sudden advance towards
the solution; see 
PROGRESS AND ACHIEVEMENT,
6. The coming of a bright idea is an experience familiar to everybody
but difficult to describe and so it may be interesting
to notice that a very suggestive description of it has been 
incidentally given by an authority as old as Aristotle.
Most people will agree that conceiving a bright idea is 
an "act of sagacity." Aristotle defines "sagacity" as follows:
"Sagacity is a hitting by guess upon the essential
connection in an inappreciable time. As for example, if 
you see a person talking with a rich man in a certain
 way, you may instantly guess that the person is trying to
borrow money. Or observing that the bright side of the
moon is always toward the sun, you may suddenly
perceive why this is; namely, because the moon shines by the 
light of the sun."1
     The first example is not bad but rather trivial; not 
much sagacity is needed to guess things of this sort about 
rich men and money, and the idea is not very bright.
The second example, however, is quite impressive if we
make a little effort of imagination to see it in its proper 
setting.
    We should realize that a contemporary of Aristotle had
to watch the sun and the stars if he wished to know the
time since there were no wrist watches, and had to observe
the phases of the moon if he planned travelling by
night since there were no street lights. He was much
better acquainted with the sky than the modern city
dweller, and his natural intelligence was not dimmed by 
undigested fragments of journalistic presentations of
astronomical theories. He saw the full moon as a flat disc,
similar to the discs of the sun but much less bright. He
just have wondered at the incessant changes in shape
and position of the moon. He observed the moon 
occasionally also at daytime, about sunrise or sunset,  and
found out "that the bright side of the moon is always
towards the sun" which was in itself a respectable 
achievement. And now he perceives that the varying aspects of
the moon are like various aspects of a ball which is
illuminated from one side so that one half of it is shinny
and the other half dark. He conceives the sun and the
moon not as flat discs but as round bodies, one giving
and the other receiving this light. He understands the 
essential connection, he rearranges his former conceptions
instantly, "in an inappreciably time"; there is a 
sudden leap of the imagination, a bright ideal a flash of
genius.