Question

There is an island inhabited by monks who are very intelligent but have some very rigid rules that they live by. For one, they believe that blue eyes are evil and if a monk finds out he has blue eyes he must kill himself *that very day.* Another rule is that, despite everyone seeing each other every day, they cannot communicate in any way whatsoever. That, combined with the fact that there are no reflective surfaces on the island, means that blue-eyed monks never find out their eye color and so all is good for years and years. One day a visitor come to the island and before he leaves, rema

Answer 1

There is an island inhabited by monks who are very intelligent but have some very rigid rules that they live by. For one, they believe that blue eyes are evil and if a monk finds out he has blue eyes he must kill himself *that very day.* Another rule is that, despite everyone seeing each other every day, they cannot communicate in any way whatsoever. That, combined with the fact that there are no reflective surfaces on the island, means that blue-eyed monks never find out their eye color and so all is good for years and years. One day a visitor come to the island and before he leaves, remarks for all to hear that he's never seen such beautiful blue eyes as on this island.

Assumptions: -every monk sees every other monk each evening at communal dinner. -it is common knowledge on the island that all monks are rational and obey all monk protocols perfectly. -monks reason instantly and if one concludes that he has blue eyes he will commit suicide at midnight of that day. -the visitor's announcement is made publicly at the dinner. -the visitor adds nothing but that observation (that there exist blue eyes on the island).

What happens to the monks?

Answer 2

can we assume the visitor is telling the truth and the monks believe him?

Answer 3

:) good question! It's not listed in the assumptions.

Suppose the visitor has no reason to lie.

Answer 4

What if a monk knows that he's never seen blue eyes?

Answer 5

thats it ! right ?

Answer 6

Not quite.

Suppose monk A has never seen blue eyes. Then he will assume that he is the one with blue eyes, and kill himself at midnight.

Answer 7

But what if he knows that monk B has blue eyes?

Answer 8

more than two monks can have blue eyes is it oh

Answer 9

i mean, more than one monk

Answer 10

you're right in both ways... Could be one, two, or more have blue eyes.

Answer 11

one would commit suicide for sure

Answer 12

but no monk can resolve if he has blue eyes or not

Answer 13

Maybe.
Suppose you are monk A and you have blue eyes, but you don't know. You do know that monk B has blue eyes. So you don't commit suicide at midnight. However, neither will monk B, because he knows you have blue eyes. So you both show up to dinner the next night.

Answer 14

oh yes

Answer 15

if im monk A, and if i see nobody has blue eyes then only i would commit suicide,

other monks would knw they dont have blue eyes by my disappearance.

Answer 16

if im monk A, and if i see >=1 other monks have blue eyes, then therez ambiguity

Answer 17

So the second night after the announcement: monk A and monk B show up to dinner. Monk A looks at B and wonders "why has he not killed himself", monk B looks at monk A wondering the same. They will figure out that they both have blue eyes, and kill themselves at midnight.

All the other monks (who have only seen two pair or blue eyes) are now safe, for on the third night, A and B will be absent.

Answer 18

and so it goes...