After the weight lifting event, the announcer said “Either Holland was better than Italy, or Greece won gold.”

An Italian reporter heard that, and commented that even knowing his own country’s final place, he wasn’t able to deduce the other places.

Curiously, a Dutch reporter who knew Holland’s final place, and who hadn’t heard the other reporter, made exactly the same remark.

Which were the final places?

In this riddle, I decided to make two assumptons:

(1) Holland, Greece and Italy, in some order, won gold, silver and bronze.
(2) The "either/or" part of the announcer's statement is exclusive. Both statements "Holland was better than Italy" and "Greece won gold" cannot be true. One of them is true and one is false.

Everyone, including the Dutch and Italian reporters, knew that Italy did not win gold, since if Italy had won gold, both statements "Holland was better than Italy" and "Greece won gold" would be false.

If Greece had won gold, "Greece won gold" is true, so "Holland was better than Italy" must be false. Greece would have won the gold, Italy the silver and Holland the bronze. The Dutch reporter would have known that, since he knew Holland's standing, and would have known that "Holland was better than Italy" is false, and "Greece won gold" is therefore true. Then he would have known that Greece won gold, Italy silver and Holland bronze. Therefore Greece did not win the gold, since the Dutch reporter could not figure out the standings.

So Holland must have won gold. Both reporters knew their own countries' standings, and they knew that "Holland was better than Italy" and "Greece won gold" are mutually exclusive. If Italy had won bronze, the Italian reporter would have known that "Holland was better than Italy" is true, and that therefore "Greece won gold" is false. So he would have known that Greece must have won silver and Holland gold and Italy bronze - he would have known the final standings. Since he didn't, Italy must have won silver and Greece bronze.

The final standings:
Holland - gold
Italy - silver
Greece - bronze

Posted by Dan on 2003-10-14 21:08:38