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?
Brazil won gold, Argentina the silver, and Chile the bronze.
Since there are only three teams and three positions, there are six possible outcomes. If ABC means Argentina won gold, Brazil won silver and Chile the bronze, then these are:
ABC
ACB
BAC
BCA
CAB
CBA
From the first reporter's statement we can eliminate ABC, CAB and CBA (neither Brazil won gold nor Chile won silver) and BCA (both Brazil won gold and Chile won silver). This leaves ACB and BAC.
We don't know how the second reporter's sentence ended... it might have been "Chile won silver, but not both" or "Chile won gold, but not both." Had it been the former, the third reporter would have been unable to distinguish between options ACB and BAC. Since we were told he could reason the final order, the sentence must have ended "Chile won gold, but not both". This eliminates ACB (neither Argentina won silver nor Chile won gold) so the only possible answer is BAC.
Solution
