Three reporters were discussing the hockey results. The TV reporter said "Either Brazil won gold, or Chile won silver, but not both." The radio reporter similarly started to say "Either Argentine won silver, or Chile won …", but a sudden noise cut him off.

The press reporter, who was lucky enough to hear the complete sentence, could reason out the final order of the three countries. What was it?

(In reply to re(4):solution by SilverKnight)

The second reporter could have said:

1) "Either Argentina won silver, or Chile won Gold" (possibly, but not necessarily, adding "but not both").

2) "Either Argentina won silver, or Chile won Silver" (making any reference to "but not both" unnecessary and redundant).

or

3) "Either Argentina won silver, or Chile won Bronze" (possibly, but not necessarily, adding "but not both").

Since we already know that Chile did not win gold, either version of (1) implies the order BAC for Gold, Silver and Bronze.

If the statement had been (2), then the more-hearing listener would still not have been able to determine the outcome, but in fact he did, so we know that statement (2) was not made, not because it is a ridiculous thing to say, but because it wouldn't have determined the order.

If statement (3) had been the case, then the version with "but not both" would have left an impossible situation, that is, inconsistent with what we already know, so that didn't happen. The version without the "but not both" is consistent and again points to the order being BAC.

So we know the order is BAC, but don't know how the second announcer continued what he was saying.

Posted by Charlie on 2003-10-07 13:36:17