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(5):solution by Charlie)
Agreed,
The "but not both" is necessary in the case of (2), because otherwise it is incorrect for Federico to have written "similarly" in the problem. He would have just written "the radio reporter started to say...".
Given that the "but not both" is in the statement,
"Argentina won silver, or Chile won silver" does not need to be addressed. If one wishes to address it ANYWAY, then your logic holds, and it doesn't uniquely identify the outcome.
STILL... as Charlie also contends... the solution must still address bronze.
In any case, the English statements above have an implied "exclusive or" in it. And the "but not both" (provided you don't say the non-sensical silver/silver) is exclusive or. Either/OR *is* exclusive or.
Therefore, logically, we do know, that the second announcer said Gold. (The statement of the problem implies that he continues with "but not both" at the end... but it is redundant.)
re(6):solution
