Monday, October 01, 2007

Rethinking the Riddle

I'm gettin reports that everyone is stumped on this one so maybe I'll just tell you the answer and pose a secondary question.

Take the case of 1 person with blue eyes and 199 people with brown eyes. The statement "I see blue eyes" would clearly refer to that 1 person and that 1 person would see no other blues eyes and understand this fact. 1 person with blue eyes will leave that first night.

Take the case of 2 people with blue eyes and 198 people with brown eyes. Each person with blue eyes would see exactly 1 other person with blue eyes. Blue #1 sees Blue #2 and thinks, "If he is the only one with blue eyes then he'll leave tonight." (Btw, blue #2 thinks exactly the same thing) Blue #2 won't leave that night however because he see's Blue #1. Therefore, Blue #1 can now deduce that Blue #2 sees a pair of blue eyes and since Blue #1 only see's one pair of blue eyes, then the second pair must belong to him. Both of them will leave on night 2.

Take the case of 3 people. The third person with blue eyes sees 2 people with blue eyes. Knowing what we just talked about, he expects them to both leave on night 2 if they see no third set of blue eyes. Since they DO see another set of blue eyes they don't leave on night 2 and thefore the third guy can now deduce they were looking at him. 3 people leave on night 3.

And so on...

100 people will leave on the 100th night. People with brown eyes would expect to leave on night 101 if they also had blue eyes. Since everyone left a day earlier, they know they do not have blue eyes.

Confused? Good - just mull this over and answer the next part of the riddle. Keep in mind that part of the key here is that blue eyed people see one less set of blue eyes than brown eyed people.

What piece of information is introduced by the statement "I see a person with blue eyes" that was missing before it was said? In other words, everyone knew that other people on the island had blue eyes so why was it important that a third party introduces the sentence?

Ross

6 comments:

CYNTHIA said...

i don't know, but i can barely remember people's names so I'm pretty certain that there's no way that i could remember whose eye color i had counted and whose i hadn't, much less how many days had passed. and where would i write this information down, being on an island and all...

Anonymous said...

Why, you'd etch it on a coconut of course.

Ross

Unknown said...

i would have to go drown myself!

Anonymous said...

Someone has to be blind in this scenario - right?! Of course, I'm with Cynthia and I think that thinking about this riddle just shoved each one of my 100 student's names slide out of my brain...you owe me big Ross, BIG!

lvabgr to you!

Unknown said...

I'm not sure why someone has to be blind but someone always has to be left out. The reason it's important someone outside of the scenario raises this question is b/c if a blue eyed person said, "I see someone with blues eyes.", there would be no way for him to deduce his own eye color.

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