Before the last race, I heard the runners from Nepal, Oman and Pakistan make predictions about the final standings:

"I hope the Nepalese gets bronze, for then I'm certain to get silver."

"The Omani could get gold, but in that case I'd get silver."

"The gold medal will go to the Pakistani or to me."

I didn't know which runner said what, but as I learned later, they were all right. Furthermore, knowing which country won the race allowed me to calculate the final standings, which were... ?

(In reply to Solution by DJ)

I'm in agreement. I didn't post for a number of reasons.

First, the problem's wording makes me think that if you know who won the race, you can calculate the final standings. By my analysis - and apparently yours as well - you don't need to know who won before determining the standings. There is only one unambiguous order given that the three statements are correct. This solution (Oman - S3, Nepal - S2, Pakistan - S1) does not require you to previously know that Oman won. Given the three true statements, there is only one way to determine without doubt the absolute order.

Second, I wasn't sure about what the statements meant. I took them as follows:

1) If Nepal gets third, the speaker MUST get second, and not first or second. If Nepal doesn't get third, the position of the speaker is undefined.

2) Similar to the first - if Oman doesn't win, the position of the speaker is undefined.

3) No further explanation or interpretation required.

Last, I assumed that each person made one and exactly one statement, and they didn't speak about themselves. So, S1 was made by either the Pakistani or the Omani, S2 by the Nepalese or Pakistani, and S3 by either the Nepalese or Omani.

Posted by Eric on 2004-07-21 15:18:44