$100$ perfect logicians have been gathered on an island. It is common knowledge that logicians always have blue or brown eyes, though on this island, all eyes are blue. However, there are no reflective surfaces, and talking about eye color is forbidden; in short, each logician knows everyone else's eye color, but not their own.

One Sunday afternoon, a green-eyed oracle visits the island, and makes the following decree, loud enough for all to hear:

> 
> The number of blue eyed logicians on this island is **not** a multiple of $17$.
> 
> 
> 

(The multiples of $17$ up to $100$ are $0,17,34,51,68,85$).

It is common knowledge that the oracle knows all, and never lies. Starting that on that Sunday midnight, and every midnight thereafter, a ferry comes to take away anyone who knows their own eye color. The question is:

> 
> Will the logicians ever leave, and if so, on what day?
> 
> 
> 

*Please hide any guesses/solutions with spoilers, for the benefit of other solvers.*

**Remarks:** It seems like the oracle has said nothing new, since everyone already knew the number of blue-eyed logicians was either $99$ or $100$, and $17$ divides neither of these. Anyone familiar with [these sorts of puzzles](https://puzzling.stackexchange.com/questions/236/in-the-100-blue-eyes-problem-why-is-the-green-eyed-oracle-necessary) will confirm that, counterintuitively, statements like this have some content, which can be enough do allow the logicians to deduce their freedom.

**Edit** I changed the number the oracle says, since I think it was originally too easy.