B says: "Suppose I have red-red. A would have said on her second turn:
'I see that B has red-red. If I also have red-red, then all four reds
would be used, and C would have realized that she had green-green. But C
didn't, so I don't have red-red. Suppose I have green-green. In that
case, C would have realized that if she had red-red, I would have seen
four reds and I would have answered that I had green-green on my first
turn. On the other hand, if she also has green-green [we assume that A
can see C; this line is only for completeness], then B would have seen
four greens and she would have answered that she had two reds. So C
would have realized that, if I have green-green and B has red-red, and
if neither of us answered on our first turn, then she must have
green-red.
"'But she didn't. So I can't have green-green either, and if I can't have green-green or red-red, then I must have green-red.'
So B continues:
"But she (A) didn't say that she had green-red, so the supposition that I have red-red must be wrong. And as my logic applies to green-green as well, then I must have green-red."
So B had green-red, and we don't know the distribution of the others certainly.
(Actually, it is possible to take the last step first, and deduce that the person who answered YES must have a solution which would work if the greens and reds were switched -- red-green.)
"'But she didn't. So I can't have green-green either, and if I can't have green-green or red-red, then I must have green-red.'
So B continues:
"But she (A) didn't say that she had green-red, so the supposition that I have red-red must be wrong. And as my logic applies to green-green as well, then I must have green-red."
So B had green-red, and we don't know the distribution of the others certainly.
(Actually, it is possible to take the last step first, and deduce that the person who answered YES must have a solution which would work if the greens and reds were switched -- red-green.)
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