Q:
9 coins,one of them is fake. Use a balance to weigh them not more than 3 times and find the fake.
A fake coin is not necessarily lighter.

hint:
split coins into 3 groups.

Max:
Initially after taking 3 groups of 3 coins each, in the
first attempt to weigh 2 groups,
we can find in which group
that coin exists. In 2nd attempt we can weigh two coins out
of 3,
in this attempt itself we will be able to find out
which coin it is. i.e., in two attempts we should
be able to
find out.