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Puzzle

There used to be a certain village in which, all the people had either a red or a black mark on back of their neck. They could see other person's mark but not their own. In fact, they had a rule that, if anyone ever got to know color of his/her own mark, he/she would have to commit suicide. They didn't have a single mirror in the village and they never discussed colors of anyone's marks. They were all logical and intelligent people. One fine day a tourist landed in their village. And after a pleasant stay went off saying that "atleast one of you has a red mark".

What do you think happened to the people of this village in some time?

This puzzle is coursey some website. But it is posted along with its answer. So I will not reveal the name of that website for a while.

Comments

Chintan said…
This is a classic M$ interview question (google "microsoft interview question" and you'll get some more really interesting questions).

The logic is very deep (multi-layered). But the final outcome is that everyone in the village will know the colour on their forehead and hence mass suicide entails.

Lets wait some more until we can give away the logic.
Also, a good question will be: how many days until everyone is dead?
2:35 PM
Bobby said…
lets say there is exactly one person who has a red spot...then its easy to see why they will all commit suicide...coz the one with the red mark will know that he has a red spot and then others will know after he commits suicide. If there are two people who have red spots....then each will know that if the other is not commiting suicide its because he also has a red spot...and then the others know that they commited suiced coz they were the only people who had red spots....for three people with red spots,each one can argue as follows: if i have a black spot and only the other two have red spots, then they would have commited suicide but the fact that they didnot implies that he also has red..and so on....from this one can also find the time taken for all to commit suicide.
6:23 AM
Perseus said…
if all but one is red then everyone dies
or else no one dies.
because the unique red one will first figure out his colour and then other black ones will figure out their colours and then there is no point in living ...

btw what happened to the tourist ?
just kidding :)
9:21 AM
Anonymous said…
:-) And there is something much deeper than just the mass suicide.
(and you need to specify that he/she has to commit suicide at a particular time in the day. that is essential for the argument to go through.)

Assuming that there were at least two red marks in the village. Then each person would see at least one red mark.
Hence, each person already knew that 'atleast one of us has a red mark' which is what the peasant said.
So was the peasant's statement really necessary? Didn't he just say something that they already knew?
8:55 AM
Nutan said…
@bobby,@raghav, bobby's answer is correct.... everybody will commit suicide

@ramprasad you argument abt time of the day is correct....but one can say eventually they will know someone committed suicide and that would be enough, i guess...

and about whether the info provided additional info, well yes!! indeed, had turist not said anything, none would commit suicide... so this info was crucial!!

@raghav, tourist later returned to village and became king of the whole empty village...:)
10:42 AM
Anonymous said…
suppose that there were only two persons with the red mark. Now suppose nothing happens and nobody commits suicide. Let the two persons with the red mark be x and y. Now since x is intelligent, he thinks "had i been black-marked, x would have seen all black marks and known immediately that he is the one with the red mark, hence commited suicide by now. But since he hasn't, that means I am red-marked." This way, x figures out his mark and hence should commit suicide. But since both x an y are equally intelligent, who's the one to think of this logic first..????
2:07 PM
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