T Nation

Riddle me this

There is an isolated village. Everyone in this village has a dot on the back of his/her head. Each dot is either red or blue. If a villager finds out the color of the dot on the back of their head, they have to kill themselves. Villagers do not talk about the color of the dots on anyone’s head. So one day this stranger arrives in the village. He has NO dot on his head. He tells the entire village exactly one thing during his visit, “At least one of you has a red dot on the back of your head.” After the stranger leaves, villagers start killing themselves, and eventually, all of the villagers are dead.

The question is this: What new information did the stranger give the villagers?

And I really don’t know the answer.

He tells them that they all have red dots on the backs of their heads.

Well…
The only answer I can come up with is that only one of the villagers had a red dot on the back of his head. So when that person saw only blue dots on the heads of others, he came to the conclusion that his dot was red, and then went on to perform a local version of seppuku. Then when the rest of the village realized that the red-dotted one had seen only blue dots and hence committed suicide, they follow down the same road. I think.

I think that there is only one person with a red dot on their head and they suddenly know by a process of elimination. The first death proves to all the others that they can not have a red dot, therefore they must be blue.

If there is more than one villager with the red dot then the stranger didn’t introduce any new information to the group.

Feel free to argue the point if you have another solution.

Bilt

I agree with doberman but I think the villagers should get their assses kicked right before they die for not asking what color thier dots are.

Maybe instead of killing themselves they should kill the fuckers that paint the dots in the first place. And anyone who advocates dot based suicide.

Just a though.

OK, here’s the solution:
Let’s assume we have two villagers only(A & B), both having red dots. So, when A hears that stranger’s words, he figures: “Hey, I know B has a red dot, so if I had a blue dot, he’d shoot imself immediately. As B didn’t shoot himself immediately, this means I have a red dot.”. Then A shoots himself. When B figures this out, he also understands that (or from coming to the same conclusion as A), and shoots himself as well.
Now extend this to a 3 villagers riddle (all having red dots): The logic is a bit more complicated, but finally at least one of the 3 villagers will come to the conclusion that he doesn’t have a blue dot, because if he did, it would have been the same A & B situation for the other two villagers (meaning they’d be dead soon enough). So this villager shoots himself as well (leaving the other two in the previously described situation).
Now one can extend this to any number of villagers, but at the end, they’ll all shoot themselves.

(Got a Math degree what can I say).

D.

Let me guess the strange gave them a mirror. Before they had no mirrors becuase it was a backwards villiage. Once they had the mirror they could all see their own dots.

Still think the villagers are sheep for going along with the whole thing.

Bluey,

Wouldn’t he have to give them two mirrors so they could see their own dot?

What if he told them all:

“you do not have a dot on the back of your head, so what’s the big deal?”

The only way to verify, is to check

Two mirrors and some clippers to shave their hair so they could even see the backs of their heads. Unless the populations has some sort of genetic baldness.

Or you could break the mirror in two.

This sounds like the sneeches not knowing which ones were star-bellied and which ones weren’t.

Digdis, would you mind working out your three-villager case in detail? I don’t think the logic quite carries over from the two-villager case.

Ah–made a mistake there. Digdis’s solution is correct for the situation where three villagers have red dots, and it does carry over to the more general case.

ok, here’s another one…

3 guys go on a road trip, they get half way to wherever they are going and are really tired, so decide to stop at a hotel. They find this shitty hotel run by an old woman and her daughter. They ask for 1 triple room (3 single beds…). They next morning they go down to pay, and the old woman says, “that’s $30 please…” So they all pay $10 each. They walk out of the door to their car, and the old woman realises that she has over charged the guys, the room was only meant to be $25. She calls her grandaughter over and gives her 5 x $1 bills and tell her to go and give it back to the guys before the drive off. On the way over the grandaughter realises that she cant split $5 between 3 guys evenly, so she pockets $2 and gives them back $1 each.

Here’s the riddle: Each guy initially paid $10 each, (3 x 10 = $30), but they all got $1 back, so they actually paid $9 each, (3 x 9 = $27), the girl kept $2 dollars, but $27 + $2 = $29… where is the missing dollar?

In response to Merlin’s riddle. It says the villagers have “either a red or a blue dot…” it doesnt say that they cant all have blue dots. If they all have blue dots, they’s all see each other and assume that they are the one with the red dot…

daughter has 2, each of the guys gets a dollar back. 2+1,1,1=5.

5+25 for room equals the original 30.

he said that “at least one of you has red dot” but they all have red dots.

so they look around, see a red dot on someone elses head and then assumes they have a blue dot so they start offing themselves.

Takman got it. He lied to them.

They all had blue dots. When somebody realized he saw blue dots on EVERYBODY else, he erroneously determined he must have a red one, and he killed himself. The process repeated itself.