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?

Assuming that an "either...or..." statement precludes both events from being true, then the announcer's statement leaves the following possibilities:

GIH (Greece won gold; Italy won Silver; Holland won bronze)
HGI (Holland won gold; Greece won Silver; Italy won bronze)
HIG (Holland won gold; Italy won Silver; Greece won bronze)

We are told that the Italian reporter cannot deduce the other teams' places despite knowing Italy's position. This means that either GIH or HIG must be true, since HGI cannot be true.

Similarly, we are told that the Dutch reporter cannot deduce the other teams' places despite knowing Holland's position. This means that either HGI or HIG must be true, since GIH cannot be true.

Therefore it must be HIG that is true.

So Holland won gold, Italy won Silver and Greece won bronze.

If my original assumption regarding "either...or..." statements is invalid, then the announcer's statement permits that GHI is true. However, it is then the only one of the four possibilities where Holland win silver, therefore the Dutch reporter could deduce the other positions if he knew Holland finished second. ie the Dutch reporter's remark prevents GHI from being true and therefore the answer is unchanged.

Posted by fwaff on 2003-10-13 08:44:15