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At the "Oilympic" Games (Posted on 2004-03-01) Difficulty: 3 of 5
The three oil-producing countries Qatar, Romania, and Saudi Arabia were the finalists in long jump. Walking around, I heard three comments from three different persons, one from each country:

"Saudi Arabia got the Gold."
"Qatar ended in a higher place than Saudi Arabia".
"Romania was the worst."

A judge commented that whenever a person said anything mentioning his own country, he was right in his beliefs, but if he only spoke about other countries, he was wrong. I didn't know which person was from which country, but I could recognize the Romanian because of his occidental clothes. With help of the judge's comment, I could reason out the final standings. What were they?

See The Solution Submitted by Federico Kereki    
Rating: 3.7500 (8 votes)

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Solution Solution | Comment 3 of 16 |
Answer: The Romanian said "Romania was the worst" (true). The Qatari said "Saudi Arabia got the Gold" (false).  The Saudi said "Qatar ended in a higher place than Saudi Arabia" (true). The final standings: Qatar: Gold; Saudi Arabia: Silver; Romania: Bronze.    
 
Explanation:
 
You knew which one was Romanian. The Romanian made one of the three statements.
 
Case 1: The Romanian said "Qatar ended in a higher place than Saudi Arabia". Then you knew that this statement was false, and either Saudi Arabia got Gold and Qatar got Silver or Bronze, or Saudi Arabia got Silver and Qatar got Bronze. You knew that a non-Romanian said  "Romania was the worst," so that statement was false, and Romania got Gold or Silver. If the Saudi said "Saudi Arabia got the Gold", then Saudi Arabia got Gold. If the Qatari said "Saudi Arabia got the Gold", then Saudi Arabia got Silver or Bronze. There are two different medal standings that fit these possibilities: (1) Saudi Arabia got the Gold, Romania the Silver, Qatar the Bronze; (2) Romania got the Gold, Saudi Arabia got the Silver, Qatar the Bronze. Therefore, Case 1 would have given you  insufficient evidence to deduce the final standings. Case 1 is ruled out.   
 
Case 2: The Romanian said "Saudi Arabia got the Gold." . Then you knew this statement was false, and that Saudi Arabia got Silver or Bronze. You also knew that whoever said "Romania was the worst" was a non-Romanian, and so that statement was false, and Romania got Gold or Silver. Since you knew that either the Qatari or the Saudi said "Qatar ended in a higher place than Saudi Arabia", you knew this  statement was true, and either Qatar got Gold and Saudi Arabia Silver or Bronze, or Qatar got Silver and Saudi Arabia got Bronze.  Each of the following two medal results fits the possibilities of Case 2:  (1) Qatar got Gold, Romania got Silver, Saudi Arabia got Bronze; (2) Romania got Gold, Qatar got Silver and Saudi Arabia got Bronze.  So in Case 2 you would have had insufficient evidence to deduce the results. Case 2 is ruled out.
 
Case 3: The Romanian said "Romania was the worst." Then you knew that this statement was true, and Romania got Bronze. If the Saudi said "Saudi Arabia got the Gold", then Saudi Arabia got Gold; this means that the Qatari must have said "Qatar ended in a higher place than Saudi Arabia", and the Qatari would have been lying about his own country, which would contradict the judge. So the Qatari must have been the one who said "Saudi Arabia got the Gold" , and that statement was therefore false, and so Saudi Arabia got Silver. Thus Qatar got the Gold. Only Case 3 would have allowed you to deduce the final standings.   

 

Edited on March 1, 2004, 6:52 pm
  Posted by Penny on 2004-03-01 16:15:13

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