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Not really, these things are designed to be pretty counter-intuitive. Think about it a bit and perhaps it will make more sense later.

So this is the answer I was looking for: By telling the monks "at least one of you has blue eyes", the stranger is actually telling the monks a sequence of facts, at least one of which is new knowledge to them. S1) At least one monk on the island has blue eyes. S2) Every monk on the island...

Nope, starting date is irrelevant. Even if they were all "put on the island initially in a single day", this chain reaction would not occur without the strangers words...

Inherent in genes, carved on a stone tablet, whatever...it is not the issue of the question. And the guy has given them an extra piece of information...the process would not occur without his words. By what means would any monk deduce the colour of his/her eyes otherwise?

Bingo. The first pirate does NOT receive all the money, but the solution is significantly > 202 pirates for the reason you mentioned. Survival plays a major role in the higher ranked pirates decisions. I will post a soln later tonight if no-one else does.

So you can think about the problem more, it ISN'T 202 :). (Although that was the first thing I thought it was.)

No worries. Yep, the logic is definitely more important than the answer.

I won't confirm whether 202 is the correct answer until tomorrow to give more people a chance to do it :).

So this explains why the inductive argument from before wouldn't work if the stranger was not there...but the 'paradox' is more on the logical side: what additional piece of information has the stranger provided to the monks if there were say 50 brown 50 blue?

DAFUQ has been the closest logically, but neither 198 or 200 are correct. Though as a hint, if it gets down to 200 pirates, it will go no further!

Bent my mind when I first heard a form of this problem.

Yep, happy with Realise's explanation. It is essentially an inductive proof of the statement: If there are n blue-eyed monks, they will chill until the n-th night, when they will all commit suicide. (0<n<101) As the monks are all intelligent, they are aware of this fact, so if a bunch of...

Yep, can you please explain this "chain-reaction" a little more clearly though?

Shotgun not being starting pirate king.

(I might leave this one up for a day or so before I answer it, as I stress: it IS quite hard/counter-intuitive.) Try the monk riddle just below this one in the extracurricular section for something that is easier to solve quickly.

Not quite, but I feel it might take quite a while to explain why. Try playing with toy situations where there are a small number of gold pieces and a small number of pirates to get a feel for things. The answer is definitely larger than 100.

Not quite.

Alas, despite their mathematical inclinations, these pirates are not particularly thrifty...and they prefer cold hard gold.

Getting from the case where 1 monk has blue eyes to the case where 2 monks have blue eyes is probably the most crucial step. Try to base an inductive argument on this.

Integers.