"Petals around the Roses" - Can you figure it out?

LordShaithis · Post by **LordShaithis** » 2004-05-30 01:31am

I took a look at it, didn't see any roses or petals, and decided not to waste any more time. If you can't be bothered to state the question, I can't be bothered to pull an answer out of my ass.

EDIT: Finished reading the thread. LOL. You have to be fucking kidding me. I thought logic puzzles had something to do with... you know... logic, not someone going "These dots are a rose! Whee!"

Cyborg Stan · Post by **Cyborg Stan** » 2004-05-30 01:53am

Dannyalcatraz wrote:There are 10 islanders with blue eyes-and only 10 islanders. Each knows that the 9 other Islanders have blue eyes. The sailor never mentions any other eye color besides blue. His not mentioning that there was someone with another eye color implies that there is no other eye color to mention-it is logical that someone's uniqueness would be mentioned. It took them 10 days to starve themselves to death.

Errr..... no. This works for any number of islanders (As long as it's at least ten, of course.) To clarify on the eariler hint :

What is the minimum requirement for the sailor's saying to be true? What is the only way you could know, if it's the case? What about the next-to-minimum requirements?

Or, another one is, if the sailor was lying, everyone would have killed themselves right away.

EDIT : Added another hint.

InnerBrat · Post by **InnerBrat** » 2004-05-30 08:06am

Was this supposed to be hard?

If there had been islander with blue eyes, he wouldn' have known it must have been him, as no one else had blue eyes. He would have killed himself on the first day.
If there had been two, they each would have noticed at the second meeting that the one other islander hadn't killed himself and realised they were waiting for each other to kill themselves. They would then have killed themselves.

And so on. As there were ten islanders with blue eyes, they each saw nine blue-eyed islanders, and would have expected a mass suicide on the ninth night. There wasn't one, so they each deducted they had blue eyes.

next?

Post by **Dalton** » 2004-05-30 10:01am

GrandAdmiralPrawn wrote:I took a look at it, didn't see any roses or petals, and decided not to waste any more time. If you can't be bothered to state the question, I can't be bothered to pull an answer out of my ass.

EDIT: Finished reading the thread. LOL. You have to be fucking kidding me. I thought logic puzzles had something to do with... you know... logic, not someone going "These dots are a rose! Whee!"

Well, it's not stated to be a logic puzzle. It's a mind game, the sort that requires imagination.

Mad · Post by **Mad** » 2004-05-30 12:09pm

On the blue-eyed: yeah, same as InnerBrat's conclusion. Well, it'd be odd to see it done another way...

All the other islanders see 10, so they're relieved to see the mass suicide on the 10th day because if there wasn't, everybody would be forced to conclude that they were blue-eyed (each thinking they're the 11th).

Dannyalcatraz · Post by **Dannyalcatraz** » 2004-05-30 05:32pm

Cyborg Stan, I think you misunderstand my answer.

Each islander knows the eye color of all the other islanders-he sees them every night at the campfire. However, he cannot know his own eye color since the island has no reflective surfaces and there is no communication between islanders.

When the sailor arrives, he doesn't mention any eye color other than blue. He comments that he's not the only blue-eye around, a state he is used to, by implication. Logically, any oddball eye color would have been noted by the sailor as being analogous to his own ususal condition of oddity.

Furthermore, given that there were 10 blue-eyes who killed themselves, there could only be 10 islanders. If there were more, the sailor would have commented about the ratio in some way, and each islander would have been aware that there were some islanders whose eyes were not blue, and thus, could always infer that their own eyes were not blue.

Thus, all of the Islanders must have blue eyes. 10 dead = 10 islanders.

As to why it took 10 days- starvation was my only answer. No one is going to help kill the blue-eyes by the conditions of the island's taboos and no mention of dangerous predators, cliffs, and the like. If that's incorrect, I'm stumped there.

Cyborg Stan · Post by **Cyborg Stan** » 2004-05-30 06:10pm

Considering InnerBrat already posted the answer, I'm not too sure why this is still a problem. All the information was in the original statement of the problem. Your answer requires adding in a bunch of stuff that was never there, such as the implication the sailor is used to having only blue eyes around (Huh?), the sailor would have definately commented on the ratio if there were more than ten (Huh?), not to mention the fact the blue-eyed natives were supposed to kill themselves right away, not do nothing for ten days which contradicts the premise.

Dannyalcatraz · Post by **Dannyalcatraz** » 2004-05-30 06:31pm

InnerBrat already posted the answer

It doesn't adequately explain the 10 days.

If the islanders waited 1 day after the sailor's announcement, they would all have realized that no one had comitted suicide because they were each waiting for the guy who couldn't see his own eyes.

Day 2 everyone commits suicide.

They would have to be exceptionally slow to take 10 days to realize this, and that is counter to the problem as stated.

Cyborg Stan · Post by **Cyborg Stan** » 2004-05-30 08:12pm

Let's try this again...

Meeting 1 : Sailor makes his revelation.

a) At this point, if there was only one native with blue eyes, he/she would've killed themselves as they would've realized that none of the others could've been it, leaving themselves.

b) If one perceives at least one other blue-eye, that person does not kill themself, because they are not sure what color their own eyes are.

Meeting 2 : All the natives count the others. If it were a) : There is one less blue eyed, then that means that that one realized what was going on and killed himself, and everyone is happy except for the now-dead blue eyes.

If it were b) : If he is still here, then that means that he percieved at least one other blue eyes and thus wasn't sure of his own eye color. This leads or C or D.

c) In this case, if you're a native that notices that there is only one other blue eye, that means that the other blue eye would be yourself. You and the other kill yourselves.

d) If on the other hand, you perceive two or more, then you're still unsure of your eye color - the blue eyes could've been pausing for someone else.

Meeting 3 : Again, the natives count the others. If there are two less, then that means all the blue eyes killed themselves. (Scenario C)

If on the other hand, the blue-eyes are still here, then scenario D occured - there's more than two blue eyes. This leads to scenario E or F.

e) If at this point, someone notices only two other blue eyes, they would have killed themselves because it meant they were the third blue eyed.

f) If there are more than two noticed, then the blue eyes could be pausing for someone else again....

And so on and so forth.

Dannyalcatraz · Post by **Dannyalcatraz** » 2004-05-31 12:11am

We all agree that the Islanders follow this thought process:

1)The sailor said he's not the only blue-eye.
2)I can see everyone else on this island has blue eyes.
3)No one comitted suicide overnight.
4)They are all waiting for someone else to do so

You propose that each evening, someone kills themselves, until all are dead.

Except that it was not a case of gradual suicides diminishing the population to two, then none. As the problem states:

Counting the night after the sailor's revelation as the first night, all ten blue-eyes kill themselves on the 10th night. Not the 9th or 11th. The tenth.

Note, that is not BY the tenth night, but ON the tenth night.

They ALL kill themselves/die in one single night of revelation.

The "process of elimination" doesn't explain that.

Each islander could assume at any time that since the others can perceive equally well the eyes of the other 9 islanders, and he sees that the others all have blue eyes, "They are waiting for somebody else, but not me."

Yet after 10 days without deaths the conclusion to becomes "They are all waiting for me, EVEN THOUGH they all have blue eyes themselves."

As long as there are multiple blue-eyes for islanders to percieve, there is no logical requirement that forces someone to look around and think that their eyes are blue.

What breaks that logical impasse?

As far as I can tell, only the inference that the sailor didn't mention any other eye color among the islanders breaks that impasse, although, as I have admitted, I don't see how that then initiates a mass suicide on the 10th night and none other.

This is like a variant of "Indian Poker" in which everyone holds a card to his head without looking at it-high card wins. If everyone folds- you probably have an ace.

To make this empirical- change the conditions to have 10 people with cards to their foreheads (dealing each a spade), and all people with spades must fold. Deal yourself a spade, "accidentally" drop it and say "at least I'm not the only one with a spade." Watch.

Edited to add example.

Cyborg Stan · Post by **Cyborg Stan** » 2004-05-31 12:20am

READ WHAT I WROTE : Everyone kills themself at the same time.

Gil Hamilton · Post by **Gil Hamilton** » 2004-05-31 12:29am

Got it after a minute or so. The trick was not trying to look for a mathematical pattern, because those things never work that way.

Knife · Post by **Knife** » 2004-05-31 12:38am

Meh, took me about 10 or so tries before I caught on. I'd like to think I would have gotten it quicker but I statistacly got a couple right and that put me off on a tangent that was incorrect.

Dannyalcatraz · Post by **Dannyalcatraz** » 2004-05-31 12:54am

I reread what you wrote as I was editing, and admit I misread it initially.

However, as I said in my edit, at no point is it a logical necessity that everyone waiting means they are waiting for "you" when multiple blue-eyes are percievable.

Despite uncertainty in your own eye color, you know that there are other blue-eyes on the island that someone could be waiting for to kill himself.

With 2 islanders, the game is up after the 1st night, as each realizes the other is waiting on him. Binary problem, only 1 answer.

With 3 or more, though, each knows that there are others blue-eyes each could reasonably think that, although uncertain about his own eye color, each other islander can be waiting for any/all of the ones plainly visible.

While it is POSSIBLE that the other islanders are waiting on him to kill himself, it is not neccessary- each could still be waiting on the other blue-eye that he can definitely perceive.

1, 2 and 3 are all blue-eyed islanders, conforming to the original problem.

1 thinks 2 is waiting on 3 and 3 is waiting on 2.
2 thinks 3 is waiting on 1 and 1 is waiting on 3.
3 thinks 2 is waiting on 1 and 1 is waiting on 2.

1 day passes, all 3 are still alive.

1 thinks 2 is waiting on 3 and 3 is waiting on 2.
2 thinks 3 is waiting on 1 and 1 is waiting on 3.
3 thinks 2 is waiting on 1 and 1 is waiting on 2.

Day 2 passes, all 3 are alive.

1 thinks 2 is waiting on 3 and 3 is waiting on 2.
2 thinks 3 is waiting on 1 and 1 is waiting on 3.
3 thinks 2 is waiting on 1 and 1 is waiting on 2.

ad infinitum.

There is no necessary reason for 1 to think that both 2 and 3 are waiting for 1 to kill himself, since he knows that 2 can plainly see 3 is a blue eye, and 3 can plainly see that 2 is a blue eye. It is possible, but not a logical neccesity. 1 may not know his own eye color, but he knows the eye colors of 2 and 3 with 100% certainty, and knows with 100% certainty both that 2 knows with 100% certainty that 3 has blue eyes and that 3 knows with 100% certainty that 2 has blue eyes. There is no reason to think that they are waiting for him, since they are so obviously waiting for each other.

Cyborg Stan · Post by **Cyborg Stan** » 2004-05-31 02:25am

No, it works. I even wrote a jury-rigged simulation of this problem, along with access to the source to check.

Dannyalcatraz · Post by **Dannyalcatraz** » 2004-05-31 04:33am

It took me a little mulling over before I spotted my logical flaw.

You're 100% correct on this'n, Cyborg Stan.

Bob the Gunslinger · Post by **Bob the Gunslinger** » 2004-06-01 06:11pm

Innerbrat got it earlier, and so did Zaia.

Here's a new one:

Stan lives on the tenth floor of his apartment building.
Every day when he leaves, he takes the elevator to the ground floor.

When he comes home, he takes the elevator to the 5th floor and walks the rest of the way up, unless it is raining or there is another person in the elevator. Then he takes it to the tenth floor.

Why?

(And yes, this is an old one)

Post by **Dalton** » 2004-06-02 01:17am

Bob the Gunslinger wrote:Why?

I got it.

Stan's a midget. He can only reach the 5 button, but if it's raining, he can use his umbrella to hit the 10 button, and if there's another person there, they can hit 10 for him. Since he can reach the ground button, he'll take it down every time.

Bob the Gunslinger · Post by **Bob the Gunslinger** » 2004-06-02 05:09pm

Good. You got it.

Here's another one.

A terrorist has kidnapped 4 people.
He is a crazy terrorist, so he ties up one person in a room by himself and the other three in a hallway.
The three people are all single file, facing forward, so thet the first cannot see anyone, the second can see the back of the first and the third can see the back of the second and first people. None of them can see the guy in the room.

Then he takes 2 black strips of paper and 2 white strips. He attaches one strip to the back of each person, and tells them that if anyone can guess what color is on his or her back, he will let them all go.

But if they communicate at all, he will kill them all.

So who figures out which color is on his or her own back?

Just to specify, 1. White, 2. Black, 3. Black, other room guy White.

3. can see the backs of 1 and 2. 2 can see the back of 1.

I think I give you guys too many hints in my puzzles.

Mad · Post by **Mad** » 2004-06-02 05:34pm

Bob the Gunslinger wrote:Here's another one.

A terrorist has kidnapped 4 people.
He is a crazy terrorist, so he ties up one person in a room by himself and the other three in a hallway.
The three people are all single file, facing forward, so thet the first cannot see anyone, the second can see the back of the first and the third can see the back of the second and first people. None of them can see the guy in the room.

Then he takes 2 black strips of paper and 2 white strips. He attaches one strip to the back of each person, and tells them that if anyone can guess what color is on his or her back, he will let them all go.

But if they communicate at all, he will kill them all.

So who figures out which color is on his or her own back?

Just to specify, 1. White, 2. Black, 3. Black, other room guy White.

3. can see the backs of 1 and 2. 2 can see the back of 1.

I think I give you guys too many hints in my puzzles.

My answer:

#2 notices that the person in front of him (#1) has white. He also notices that #3 does not immediately come to a conclusion about the color, which would be possible if #1 and #2 were both white (#3 would have to be black). Therefore, #1 and #2 must have different colors. So #2 knows he has black, and can say so.

(Edited to shrink answer.)

The lost Prophet · Post by **The lost Prophet** » 2004-06-02 06:35pm

i have a head for mathematics like no other, literary is a bane of my existence

ergo.....took me for ever till i read the fucking answer, and thank goodness for that or i would never have gotten it.

Bob the Gunslinger · Post by **Bob the Gunslinger** » 2004-06-02 09:22pm

Yeah thet's it.

Let me think for a while and maybe I'll have some more.