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... ?
Suppose the Nepalese won gold. In that case, it must have been the Nepalese making the third statement, the Omani making the first, and the Pakistani making the second. But, in that case, neither the Nepalese won bronze nor the Omani won gold, so we can determine nothing further (and, since learning which country won allowed the author to determine the winner, that cannot be the case).
So, suppose the Omani won gold. He, then, must have made the third statement, with the Paki making the first statement and the Nepalese making the second. By the Nepalese runner's statement, he got silver, and the Pakistani would have gotten bronze. Since this scenario allows us to determine the complete standing, it is a solution to the problem.
For completeness, let's consider the case where the Pakistani won gold. Then, either the Nepalese or the Omani could have made the third statement, and we can determine nothing further here either.
So, the unique solution is that the Omani won gold, Nepal won silver, and the Pakistani runner earned a bronze medal.
Posted by DJ
on 2004-07-21 15:09:02