### vici's blog

By vici, 14 years ago,

All right I come back. Now we’ll analyze the problem.

According to the sentence the stranger said, “At least one is red”, we can infer three cases:

(1)1  red, 2 black

(2)2 red, 1 black

(3)3 red

Case 1: One red, two black

So after the stranger left the island, the red man would see two black, and then he can infer that he is the red, so he should kill himself in the first dusk. The other two noticed his suicide in the second morning, inferred it is “Case 1”, and went to the Pandora in the second dusk.

Case 2: Two red, one black

In the first day, the red saw one red and one black, he would consider that if he is black, then it is “Case 1”, the red he see will kill himself in the first dusk, and if he is red, it is “Case 2”, the red won’t go. The black saw 2 red, he excluded “Case 1” directly, and would consider that if he is black, then it is “Case 2”, otherwise it is “Case 3”. The next day, no one died. The two red confirmed it is “Case 2”, and did what they should do in the dusk. The third day, the black noticed it is “Case 2”, and found he is the black, so he killed himself in the third dusk.

Case 3: Three red

In the first day, three people saw two red, then they would consider, if he is black, then it is ”Case 2”, two people will die in the second dusk, and if he is red, the other two will wait for the result till the third morning, no one will die in the first two days. As they considered, no one ran a risk before the third day, so in the third morning they all judged it is “Case 3”, and went to the Heaven in the dusk.

The Conclusion:

Case 1: The red went to Heaven in the first day, the two black did it in the second day.

Case 2: The two red went to Heaven in the second day, and the black did it in the third day.

Case 3: The three men went to Heaven synchronously in the third day.

And in the story, it is "Case 2".

All right, is it interesting? But it’s just the beginning! I will take some more interesting stories in my next blogs, coming soon!

• 0

| Write comment?
 14 years ago, # |   0 One can notice that this problem could be generalized by induction to an arbitrary number of people living on the island.
•  14 years ago, # ^ |   0 Yes, good idea!