There live 201 people on an island. 100 of them are blue-eyed, 100 of them are
brown-eyed and one of them is the Guru, old and wise.
None of them can speak and none of them know the colour of their eyes, or even
which colours there can possibly be, but everyone possesses infallible logic,
and everyone knows this. They do not know that they are divided into two equal
groups, that is just a coincidence.

Every day at noon a boat comes and everyone who knows the colour of their eyes
can leave. There is no trying. They really have to know it.

One day the Guru speaks. "I see someone with blue eyes".

Can everyone leave the island?
How long does it take for them to leave?

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It is logically possible to answer the questions without any workarounds like
"I try with blue on the first day". The guru will never speak again or
interact in any way, nor will he ever leave (lets say he has fiery red eyes
for arguments sake).