Gonna Make Your Brown Eyes Blue
1,000 mathematicians live on an island. 600 have brown eyes, and 400 have blue eyes. According to an ancient tradition which is honored by all, if a person ever discovers that he has blue eyes, he will promptly commit suicide the following morning.
There are no mirrors on the island, and it is considered to be in very poor taste to discuss the subject of eye color. Of course, everyone knows what everyone else’s eye color is.
One day, a soothsayer passes through the island, and in the presence of the assembled inhabitants solemnly announces: “At least one of you on this island has blue eyes.”
- What happens?
- What information was divulged by the soothsayer that wasn’t common knowledge before?
- Extra credit: suppose each of the blue-eyed inhabitants had resolved not to commit suicide if they ever discovered their eye color. What happens now?
Submitted by Steven Phelps.
That would be another fine way to phrase it.
You should say the mathematicians are perfect logicians. Who can deduce from any info or lack of info.
Yes, they know
Do the mathematicians know their eyes are either blue or brown? Or are they under the assumption their eyes could be a different color?
Yes, these are standard riddles. I know the answers and am happy to provide hints (email sjm1 AT williams.edu). I want people to have the fun of solving it themselves; if you don’t wish that fun, feel free to search the web.
the truth is you does’nt really KNOW the ANSWER .. your questions is just PIRATED and COPIED from other sites about math riddles .. if you really know the right answer then post it , do not make the people wait for the answer .. we need the answer .. IKR .
nope.
does the inhabitants know that in total there are 400 blue eyed man and 600 brown ones
Jake: emial me at sjm1 AT williams.edu
something was revealed — I sent you a hint (email me at sjm1 AT williams.edu to chat more).
1. No one dies since people will not talk about their eye color. There are not any mirrors. So they could not know for sure that they have blue eyes. -OR- This will make people want to check if they have blue eyes; so they would look into calm pool of water and see their reflection. At least one person will die if not all four hundred of the blue eyed people.
2. She revealed nothing. Everybody knew that at least one person has blue eyes because they can see each other’s eye colors. Everyone can see at least one person with blue eyes.
3. The wording on this one is a bit tricky. How would a person know ahead of time that their eye color was blue? It said that each blue eyed person had decided not to commit suicide if they found out their eye color. To make that decision, each of them must of known their eye color making them commit suicide the next morning. So the blue eyed people would die.
No, some info was imparted — I’ll send you a hint
nope — email me for a hint. [email protected]
The problem involves evaluating two cases: 1) one where there is one person with blue eyes and 2) another where there are two or more people with blue eyes.
Case 1)
What happens? The person w/ blue eyes kills himself (this person will know he has blue eyes as the question stem states that ‘every person knows the color of everyone else’s eyes’, therefore the person with blue eyes will see that everyone else has brown, and thus know that he’s the one with blue eyes).
What information was divulged by the soothsayer that wasn’t common knowledge before? That someone actually has blue eyes.
Case 2)
What happens? Nothing. Since the soothsayer stated that at least one of you has blue eyes (and this was already common knowledge), there will be no way for any one person with blue eyes to know with certainty that he has blue eyes, therefore, no one will kill themselves.
What information was divulged by the soothsayer that wasn’t common knowledge before? Nothing. This was already common knowledge.
I’ll send a hint first //s
Can I have the answer at [email protected] please?
your email didn’t work: email me at [email protected] to chat about this riddle. //s
sure //s
I think I am on the right track. Please send me a hint.
hint sent
send me solution please
glad you’re enjoying — sjm1 AT williams.edu
This is by far the best puzzle I’ve ever encountered. It is so deep! Thank you for posting.
let me send a hint first //s
Can you send me the solution
more than 1 dies….
1 blues will die
2 the tradition is if you figure it out so now they know
3 they will have to leave the island because they will be dishonoring the tradition.
ok, will send
plz send soln. wouldnt the brown eyed ppl always be wary o teh blue eyed ppl they see everyday and wonder why they are still alive? the soothsayer should have warned them that someone who has blue eyes is alive, were they separted? were they born there and do not know what blue looks like?
monkey68pl: correct, not posting as it’s the soln == you can email solns to me at sjm1 AT williams.edu
no — email me at sjm1 AT williams.edu if you want to chat more about this //s
does 1 random blue eyed guy kill himself and then the rest just get on with their day?
could you please send me the answer…
not a big fan of the extra credit, but the friend who passed it along was….
extra credit: that seems a bit contradictory! how come they can sit down and decide not to commit suicide when they don’t know their own eye colors on the first place…. its either all the inhabitants should resolve or no one I think
Yes. Their resolution violates the earlier assumptions, so this is NOT something they should do — this lacks honor!
The 3rd part of the problem says to suppose that the blue-eyed people resolved NOT to commit suicide (I understand that this is not a part of the first 2 parts of the problem). My question was whether it is safe to assume ONLY the blue-eyed people resolved not to commit suicide if they found out.
Everyone is honorable (think Worf like Klingon). They will kill themselves if they are blue eyed and they know it, but not otherwise. //s
For the “extra credit,” did it just happen to be that ONLY the blue-eyed people resolved not to commit suicide, or did everyone resolve not to if they discovered they had blue eyes?
sure ..s
Could you please send me the answer?
try doing smaller cases — imagine there are just two people, or three people, or four….
Perhaps you can help me. I’ve got a problem with the Common Knowledge solution. It seems to me that everyone on the island knows “Hundreds of people have blue eyes.” It also seems apparent that all the mathematicians know everyone else knows that, too (assuming everyone has access to everyone and nobody is sight-impared).
So, if everyone knows the statement “Hundreds of people have blue eyes” to be true, then how is anyone drawing conclusions about the first night having no suicides? I’m aware this works in the smallest case of blue-eyed islanders, but the common knowledge solution seems to think the islanders would ignore this and continue to only draw conclusions from suicides and guests to the village.
Jim: correct,not posting as it’s the soln
Start small. Imagine first there are just 2 people, and see what happens. Then try 3 people, then 4….
But do they know everyone on the island? I.e., while they don’t know the exact numbers they know that there are a bunch of each type, and there are more brown eyed people than blue-eyed people, etc etc.
no
Do they know that 600 of them have brown eyes and 400 of them have blue eyes?
imagine there is just one person on the island. then imagine there are just 2, then 3. do special cases first….
Cant think of nything! Please give me hint!
imagine there were just 1 or 2 or 3 people on the island, and try to generalize
ah, but these are honorable klingons, and if it is a good day to die, then die they shall.
ahahaha, I can think of a dull idea
no one will commit suicide if they wear brown contact lens, ahahahaha
i can’t think of ANY bright ideas…
sorry
no. try special cases. image there are 4 people, 5 people, ….
1. they will not talk about it because they dont want anyone of them die
2 there are more brown eyed people that blue eyed
fortunately no — only the blue eyed people die.
Wouldn’t All Of Them Commit Suicide?
Not quite following, but I think you’re close.
1. nothing
2. none
the logic is as everyone on the island can see either 399 or 400 blue eyed people, the already knew “at least 1” has blue eyes
I prefer not to post the solns online, as that ruins the fun for some people as they might accidentally see the answer before they’re ready to see it. Email me at [email protected] for the soln. .s
whats the soln
Cute, but not the soln. If you want a hint, email me at sjm1 AT williams.edu.
1. Nothing
2. None, 4 out of ever 10 people they know has blue eyes.
3. The subject of eye color would lose its “taboo” status and become the #1 topic of discussion.