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?

1. Let's assume that the first statement was made by the Saudi Arabian. Then the statement is true. So Saudi Arabia gets the Gold.
Assuming the first statement is true, the second statement must have been made by the Romanian, because the Qatarian cannot be talking about his own country while the first statement is true. Therefore the statement is false. So Qatar gets either Silver or Bronze and Saudi Arabia gets either Gold or Silver.
Assuming the first statement is true and the second false, let's also assume that the third statement was made by the Qatarian. The statement is false as he is not talking about his own country, so Romania gets Silver.
The final places are as follows:
Saudi Arabia - Gold
Romania - Silver
Qatar - Bronze

2. Let's assume that the first statement was made by the Romanian. The statement is false, so Saudi Arabia gets either Silver or Bronze.
Assuming that the first statement is false, let's also assume that the second statement was made by the Qatarian. This statement is true, so Qatar gets either Gold or Silver
Assuming that the first statement is true and the second one is false, let's say that the third statement was made by the Saudi Arabian. It is a false statement, so Romania gets Silver.
Based on this situation, the results are as follows:
Qatar - Gold
Romania - Silver
Saudi Arabia - Bronze

3. Let's assume that the first statement was made by the Qatarian. It is false, so Saudi Arabia either gets Silver or Bronze.
Assuming that the first statement is false, let's say that the second statement was made by the Saudi Arabian. It is a true statement, so Qatar gets either Silver or Bronze.
Assuming that the first statement and second statements are true, let's say the third one was made by the Romanian. It is true, so Romania gets the Bronze.
So,
Qatar - Gold
Saudi Arabia - Silver
Romania - Bronze

4. Now let's assume that the first statement was made by the Qatarian. It is false, so Saudi Arabia gets either Silver or Bronze.
With the first statement assumed true, let's say the second statement was made by the Romanian. It is false, so Saudi Arabia gets either Gold or Silver.
With the first and second statement being true, let's say that the third statement was made by the Saudi Arabian. It is false, so:
Romania - Gold
Saudi Arabia - Silver
Qatar - Bronze

5. Let's say that the first statement was made by the Romanian. It is false, so Saudi Arabia gets etiher Silver or Gold.
With the first statement assumed true, let's say the second statement was made by the Saudi Arabian or the Qatarian; it is true so Qatar gets Gold and Saudi Arabia gets Silver.
The Qatarian or the Saudi Arabian could not have made the last statement, because Romania could not have gotten the Gold or Silver based on the first two assumptions. Therefore, the final places are:
Qatar - Gold
Saudi Arabia - Silver
Romania - Bronze.

Now, based on all the different situations, the following statements were made:

The first statement was made by the Qatarian, the second statement was made by the Saudi Arabian, and the third statement was made by the Romanian.

..and the final places should be:

Gold - Qatar
Silver - Saudi Arabia
Bronze - Romania

Posted by Jane Doe on 2004-03-01 15:38:22