Friday night Brain teaser

Pundit · Mar 23, 2002

<< What threw me off was that the people on the island know how many people of each color eye there is on the island... >>

They don't.

Xesh · Mar 25, 2002

Calbear, read this whole response before replying...

OK.... here's the gist of your solution: there are 10 blue-eyed people. After 9 nights, each of these 10 blue-eyed people realizes that since the other 9 are still alive, he must himself have blue eyes, and each by this logic kills himself. But why does each blue-eyed person assume that the other 9 will kill themselves after 9 nights? Here's why....

He assumes that there are only 9 blue-eyed people (because he sees them). After 8 nights, each of these 9 blue-eyed people realizes that since the other 8 are still alive, he must himself have blue eyes, and each by this logic kills himself. But why does any blue-eyed person assume that the other 8 will kill themselves after 8 nights? Here's why....

He assumes that there are only 8 blue-eyed people (because he sees them). After 7 nights...

You see, there are actually 10 people, but the solution is based on the idea that each one of them will work out a similar solution in his mind for only 9 blue-eyed people. He will then see that his prediction based on this solution is wrong and realize that he must therefore be blue-eyed.

The proof of the solution is an inductive one. If you can prove that in a situation with n blue-eyed people, they will all kill themselves after n nights, then you can prove that in a situation with n+1 blue-eyed people, they will all kill themselves after n+1 nights. However, you can't prove the basis step of the prove, or that in a situation with 1 blue-eyed person, he will kill himself after 1 night.

calbear2000 · Mar 25, 2002

Take 2 blues as the base case and think recrusively from there.

CalamitousSoul · Mar 25, 2002

Is the answer to your riddle 99 of the people kill themselves while 1 survives?

SociallyChallenged · Mar 25, 2002

lol, I'm too tired for riddles. So the blue-eyed people all die? Am I right?

calbear2000 · Mar 25, 2002

Its been answered several times, and challenged several times. But yes the 10 blues die on the 10th night.

Pundit · Mar 25, 2002

<< Take 2 blues as the base case and think recrusively from there. >>

As I stated above, I think you must begin with 3, not 2.

calbear2000 · Mar 25, 2002

2 can be used as the base case...

alrocky · Mar 25, 2002

If for some reason the original 10-Blue-Eyes don't die on the 10th night, what happens on the 11th night?

If someone correctly answers the question above, I'll try to give a clear answer to Calbear2000 riddle. Calbear2000 you're having fun aren't you?

calbear2000 · Mar 25, 2002

<<

<< So can someone answer the question I posted last?: If for some reason the original 10 Blues did not die on the 10th night what would happen on the 11th night? >>

Well, if we assume that there actually is an ultimate being, and it is not just a contrivance of the Browns to justify the elimination of the Blues because they are 'different', then the answer is simple.

The ultimate being will see their actions as seditious and will systematically expunge the lot of them. >>

Yep having a blast... I don't think I should post any more riddles here

Pundit · Mar 25, 2002

<< 2 can be used as the base case... >>

Are you inferring from your question that the people know there is at least one blue-eyed? The ultimate being says "when each blue-eyed finds out...", but this doesn't imply that there must be at least 1 of them. Hence, when we consider the case with only 2 blues on the island, each looks at the other thinking "Damn, he thinks everybody is brown-eyed. If he only knew he was the only blue."

Ender · Mar 25, 2002

Since they're on an island couldn't they see their reflection in the water and check if they have blue or brown eyes??

Pundit · Mar 25, 2002

<< Since they're on an island couldn't they see their reflection in the water and check if they have blue or brown eyes?? >>

callbear says no.

hzl eyed grl · Mar 25, 2002

<< Since they're on an island couldn't they see their reflection in the water and check if they have blue or brown eyes?? >>

That's what I was thinking.

calbear2000 · Mar 25, 2002

<<

<< 2 can be used as the base case... >>

Are you inferring from your question that the people know there is at least one blue-eyed? The ultimate being says "when each blue-eyed finds out...", but this doesn't imply that there must be at least 1 of them. Hence, when we consider the case with only 2 blues on the island, each looks at the other thinking "Damn, he thinks everybody is brown-eyed. If he only knew he was the only blue." >>

Oops. You're right... 3 is the base case.

Pundit · Mar 25, 2002

<<

<<

<< 2 can be used as the base case... >>

Are you inferring from your question that the people know there is at least one blue-eyed? The ultimate being says "when each blue-eyed finds out...", but this doesn't imply that there must be at least 1 of them. Hence, when we consider the case with only 2 blues on the island, each looks at the other thinking "Damn, he thinks everybody is brown-eyed. If he only knew he was the only blue." >>

Oops. You're right... 3 is the base case. >>

dude, 1 more post and your a senior member! Please post another problem. Please, please, please!!!

alrocky · Apr 1, 2002

10 Blue Eyed Islanders. Each Blue sees 9 Blues and knows that every other Blues sees at least ONE Blue. Thus we can say:

1) Blue => 1; or
2) This is the equivelent to the Ultimate Being saying, "There is amongst you at least ONE Blue."

Item 2) can be deduced from the original riddle even though it was specifically stated in said riddle. Apply Item 1) or assume Item 2) is stated for the following Island populations:

1 Blue. Blue sees no other Blue and concludes he is Blue. He dies that night.
2 Blues. Each Blue sees ONE Blue and waits for that other Blue to die that night. No Blue dies that night and both conclude that the other Blue didn't die because that Blue had seen another Blue; ie, they see each other. Both Blues die on night 2.
...etc.

This is essentially Shooters's (albeit he omitted part of the rationale) as well as MisterNi solutions - the latter provided a clearer answer. The nth night here can equal 1 or 2. MereMortal and Calbear2000 missed the question: If for whatever reason the original 10 Blues do not die on the 10th night, what happens on the 11th night?

edit: #$@# typo ... "die on the 10th night" not 19th. sorry 'bout that. Fatalbert in the next post has provided the correct answer! Good work!
Happy April Fools all!!!

fatalbert · Apr 1, 2002

<<
This is essentially Shooters's (albeit he omitted part of the rationale) as well as MisterNi solutions - the latter provided a clearer answer. The nth night here can equal 1 or 2. MereMortal and Calbear2000 missed the question: If for whatever reason the original 10 Blues do not die on the 19th night, what happens on the 11th night?
 >>

the answer to that bolded question is that it is an impossiblity. They have to kill themselves due to the thought process. however, assuming by a fluke that it went through everyone on the island would kill themselves because they would all assume they were blue eyed

LongCoolMother · Apr 1, 2002

this has become an issue of debate...hmmm

AzNmAnJLH · Apr 1, 2002

when i read the question if the fact that the ultimate being said that there are 10 blue eyes then you solution would be correct but the ultimate being didn't so therefore all your solutions are incorrect

question was poorly written you will have to include that the 100 islanders knew that 10 among them have blue eyes otherwise it is impossible for anyone to die

AzNmAnJLH · Apr 1, 2002

it is like trying to find a solution with all variables without a solid fact

ndee · Apr 1, 2002

<< when i read the question if the fact that the ultimate being said that there are 10 blue eyes then you solution would be correct but the ultimate being didn't so therefore all your solutions are incorrect

question was poorly written you will have to include that the 100 islanders knew that 10 among them have blue eyes otherwise it is impossible for anyone to die >>

Jup, the Islanders HAVE TO know that there are 10 blue-eyed hippies.

LikeLinus · Apr 1, 2002

This is one stupid riddle.

All they have to do is look at their reflection in the ocean/river water on the island and see what color eyes they have.

Problem solved.

Pundit · Apr 1, 2002

People, look at some of the solutions we have posted and you'll realize that there is enough information. They don't need to know that there are 10 blues. Just try and work it out with 3 blues and 97 browns and work it out from there.

Murphyrulez · Apr 1, 2002

AAAAAAAAAAHHHHHH

I can't believe people are STILL saying that the riddle is unsolvable.

READ THE ANSWER. COMPREHEND THE ANSWER.

Follow the logic, it makes sense. There are 10 people going to die. Until the 10th night they all think the other 9 are the only blues.

A Brown might think he is blue up until the 11th night when all the blues kill themselves! They all kill themselves because they can see 90 browns! The browns know that the blues can see how many browns there are! They can count! It's pretty simple!!! Every blue says, "hey there are 9 blues, and either 91 browns or I'm a blue. Therefore, when the 11th day rolls around and the other 9 are still kickin, I must be blue! AHHHH SUICIDE!!!". Every brown says, "Hey there are 10 blues, and either 90 browns, or I'm a blue. therefore when the 11th day rolls around and the 10 blues kill themselves, I must be brown!!! YEAAAHH!!!"

get it?

Friday night Brain teaser

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