After the fencing competitions, the radio reporter commented “Denmark won silver, and/or Spain won gold.”

The TV reporter said “Denmark won bronze, and/or France won ...” but an ovation from the public drowned his comment.

The press reporter, showing again his good sense of hearing, managed to hear the whole sentence, and was able to deduce the final standings. What where they?

Combinatorially, there are six possibilities (listing gold first and bronze last):

(1) DSF
(2) DFS
(3) SFD
(4) SDF
(5) FDS
(6) FSD

The first, fully heard sentence rules out (1), (2), and (6). The second sentence must be one of:

Demark won bronze, and/or France won gold.

Denmark won bronze, and/or France won silver.

Denmark won bronze, and/or France won bronze.

The first of these does not allow us to distinguish between (3) and (5), the third does not allow us to distinguish between (3) and (4), so it follows that the press reporter must have heard the third sentence, which can only be true if the order is as in (3), i.e. Spain wins Gold, France Silver, and Denmark Bronze.

Posted by RoyCook on 2003-10-09 10:17:24