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chinese emperor -- solution

There are 3 cases.

case 1> B, B, W
There are only 2 black balls, so the one with a white ball would know his color;

case 2>B, W, W
Thee 1st white one would say 'I don't know' (he could be black, as in case 1, or white), after hearing
this, the 2nd white one knows he is white (otherwise, the 1st white one would have said 'I am white', see case 1);

case 3>W, W, W
The 1st would say 'I don't know',
the 2nd still have to say 'I don't know', because he could be black as in case 2, or white.
At this moment, the 3rd knows he is white (because if he
were black, the 2nd would have said 'I am white', see case 2).

Pan, Wenyu
Sunday, September 22, 2002

Not quite fullly explained.

Case 1: W B B

The fiirst person sees two blacks and knows he must be white; the second person knows that he must be black or the first person would have remained silent; the third person knows he must be black for the same reason.

Case 2: B W B

The first person cannot tell the answer and remains silent; the second person knows he must be white becaise the other two are black; the third person knows he must be black because otherwise the second one would have remained silent.

Case 3:  B B W

The first person remains siilent; the second also; the third knows he must be white because the other two are black.

Case 4: W W B

The first person remains silent. The second person knows he must be white because otherwise the first person would have said he was white, since there would have been two blacks; the third person knows he must be black since the second person would have remained silent had he been white.

Case 5: B W W

The first and second must remain silent. The third person knows he must be white since otherwise the second person would have see the two blacks and announced he was white.

Case 6:  W B W

The first person remiains silent; the second person remains siilent. The third person know he must  be white since otherwise the first person would have known the answer

Case 7:W W W

The first and second must remain silent; the third person knows he must be white since if he were black we would have Case 4 and the second person would have been able to announce he was white.

I think this covers all the cases. In every one the last person in the first round will come out safe.

Now all we need is a more elegant solution.

Incidentally I am using "he" as the generic singular pronoun, not presuming all the sages are men (though historically that would be likely). I could have used "they" as the generic singular but that would merely have left me open to the fury of the deluded grammarian for that of the demented feminist.

Stephen Jones
Thursday, October 24, 2002

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