13. Five people are in a competition, each pair competing once. Winning a game earns 2 points, a draw earns 1 point, and losing earns 0 points; the first place has no draws, the second place has no losses, and all five people have different scores. What are the scores for each person? $\qquad$
【Answer】6, 5, 4, 3, 2
【Analysis】Exam Point: Logical Reasoning in Sports Competitions
5 people are competing, with a single round-robin system, so there are a total of $5 \times 4 \div 2=10$ matches. The scoring system is 2 points per match, so the total score is $10 \times 2=20$ points. The first place has no draws, so the score of the first place must be an even number. Each person plays 4 matches, so the maximum score is 8 points. If the first place gets 8 points, then they must have won all their matches, which means they should have beaten the second place. However, the second place has not lost any matches, which is a contradiction. Therefore, the first place cannot have 8 points. If the first place gets 4 points, since the five people have different scores, the remaining four people's scores can only be $3, 2, 1, 0$. The total score of the five people would then be 10 points, which contradicts the total score of 20 points. Therefore, the first place can only have three wins and one loss, totaling 6 points, with the one loss being to the second place. Since the five people have different scores, the remaining four people's scores can be at most $5, 4, 3, 2$. At this point, the total score of the five people is exactly 20 points, which is the highest total score. In other cases, the total score of the five people would be lower than 20 points. Combining the total score of 20 points, the scores of the five people are $6, 5, 4, 3, 2$.