Brain Teasers

[Emil]

No, I don't have the slighest clue. Care to enlighten me?

[anileve]

I'll let others guess before I reveal my answer.

[Sip]

*Sigh* Looks like someone paid a visit to the Google fairy. Oh well. Personally I don't understand the point of looking up the answer online and then posting it. What does that prove exactly? That you can do research online? Well woopty doo, I sense a smelly kangaroo.

Anna jan, I told you so. My forehead was a bit on the reddish side, I looked like I got out of a trailer home.

Nope sorry, I solved this one on my own. I've seen like a gazillion of them in the past few years and they are all usually variations on the same limited number of themes.

Other forms might be:

MTWTFS_
JFMAMJJAS_

This is one below of the hardest ones I've seen (I couldn't figure it out but I know the answer now ... so before spending time on it, be warned that it is not trivial to figure out):

1 3 4 9 10 12 13 27 28 30 31 36 37 39 40 ...

If you want an easier one, try this:

1, 1 1, 2 1, 1 2 1 1, 1 1 1 2 2 1, 3 1 2 2 1 1, ...

[Anonymouse]

There is a certain island where all of the inhabitants have either brown or blue eyes. It's a small island, and everybody knows everyone else, so everybody knows everyone else's eye color. However, nobody knows his own eye color, because there are no mirrors on the island. And nobody will tell anyone else his own eye color, because all of the inhabitants adhere to a strict religion which holds that if you learn your own eye color, you must commit suicide within 24 hours. The island being small and news travelling fast, all of the inhabitants will immediately learn of any suicides. All of the inhabitants are perfect logicians, meaning they will immediately make any deductions that can be made, and all of them are aware of all of these facts, including this one.

Once every 1000 years, a mystical green-eyed goddess appears on the hill outside town, and she always speaks the truth. All of the islanders gather around to hear her speak. On one occasion, she appeared, surveyed the crowd before her, and announced, "I see someone with blue eyes."

What happens?

[sSsflamesSs]

This is one below of the hardest ones I've seen (I couldn't figure it out but I know the answer now ... so before spending time on it, be warned that it is not trivial to figure out):

1 3 4 9 10 12 13 27 28 30 31 36 37 39 40 ...

Is the next number 54?

[Sip]

I see your logic It is not "the" answer but from the given pattern, I think that's a valid answer.

Now try the other one! It's much more fun.

[Sip]

Anon, a very interesting problem. So let me take a crack at it:

Since the goddess speaks the truth, then there must be at least 1 person with blue eyes. If there is only one person, that person will immediately know it is him or her and will instantly commit suicide. Everyone else will see this and realize there must only have been 1 person with blue eyes and kill themselves. Everyone dies.

If there are 2 people with blue eyes, they will both commit suicide on the 24th hour. Those that see 2 people with blue eyes will not kill themselves while the two that only see one other person with blue eyes will kill themselves on the 24th hour knowing they have waited long enough to find out. At this point, everyone else will know they have brown eyes and kill themselves.

With 3 blues, it's going to take 24 hours for them to realize there is a 3rd person with blue eyes after which (another 24 hours), all 3 will kill themselves. They will each know they have blue eyes if they only see 2 other people with blue eyes.

So I think by induction, if there are n people with blue eyes, after 24*(n-1) hours, those with blue eyes will kill themselves. After this, those with brown eyes will be left over and they will kill themselves. So everyone dies.

[nairi]

1 3 4 9 10 12 13 27 28 30 31 36 37 39 40 ...

43 or 44 or 41

If you want an easier one, try this:

1, 1 1, 2 1, 1 2 1 1, 1 1 1 2 2 1, 3 1 2 2 1 1, ...

13112221

[anileve]

If you want an easier one, try this:

1, 1 1, 2 1, 1 2 1 1, 1 1 1 2 2 1, 3 1 2 2 1 1, ...

OMG, I am such a goat! I was trying to solve it in terms of Decimals and Binaries. I was looking for a pattern in binaries and then converting. Little did I know how easy this one is. That's simply ridiculous.

so the next after nairi's is 1113213211? Unless I counted wrong....

[anileve]

Anon, a very interesting problem. So let me take a crack at it:

Since the goddess speaks the truth, then there must be at least 1 person with blue eyes. If there is only one person, that person will immediately know it is him or her and will instantly commit suicide. Everyone else will see this and realize there must only have been 1 person with blue eyes and kill themselves. Everyone dies.

If there are 2 people with blue eyes, they will both commit suicide on the 24th hour. Those that see 2 people with blue eyes will not kill themselves while the two that only see one other person with blue eyes will kill themselves on the 24th hour knowing they have waited long enough to find out. At this point, everyone else will know they have brown eyes and kill themselves.

With 3 blues, it's going to take 24 hours for them to realize there is a 3rd person with blue eyes after which (another 24 hours), all 3 will kill themselves. They will each know they have blue eyes if they only see 2 other people with blue eyes.

So I think by induction, if there are n people with blue eyes, after 24*(n-1) hours, those with blue eyes will kill themselves. After this, those with brown eyes will be left over and they will kill themselves. So everyone dies.

How will that one person immediately know that it's him if he has never seen his own eye color nor was he told by others? Where did you get the 24th hour from? The problem doesn't mention a time frame. In addition, unless the goddess actually points out the person with blue eyes, there is no way that anything would be different than it was before her appearance. The people knew of each others eye color but not of their own and they would not reveal it, unless they wanted the other person to commit a suicide, so the information does not shed new light on the situation. The problem doesn't make sense, nor does it give enough information. Seap your solution confuses things even more.