20. (6 points) Five people, A, B, C, D, and E, are guessing the top five individual subject total scores in the class:
A: “The first place is $D$, the fifth place is $E$. ”
B: “The second place is $A$, the fourth place is $C$.”
C: “The third place is $D$, the fourth place is $A$ ”,
D: “The first place is $C$, the third place is $B$. ”
E: “The second place is $C$, the fourth place is $B . ”$
If each person only guesses one person's ranking correctly, and each ranking is only guessed correctly by one person, then the first, second, third, fourth, and fifth places are . $\qquad$
【Analysis】This problem can be solved using the assumption method in two steps:
Step one: Assume the first half of what Jia said is true, then $D$ is the 1st place. In this case, the first half of what Bing said is false, and the second half is true. Therefore, $A$ is the 4th place. Similarly, the second half of what Yi said is true, making $C$ the 4th place. This is a contradiction. Therefore, the second half of what Jia said must be true. Step two: Knowing that $E$ is the 5th place and $D$ is not the 1st place, the only statement left regarding the 1st place is what Ding said. Assume $C$ is the 1st place. Then, Wu: “The 2nd place is $c$, and the 4th place is $B$.” This means the first half is false and the second half is true, so $B$ is the 4th place. And from Yi: “The 2nd place is $A$, and the 4th place is $c$.” This means $A$ is the 2nd place. $D$ is the 3rd place.

【Solution】Step one: Assume the first half of what Jia said is true, then $D$ is the 1st place. In this case, the first half of what Bing said is false, and the second half is true. Therefore, $A$ is the 4th place. Similarly, the second half of what Yi said is true, making $C$ the 4th place. This is a contradiction. Therefore, the second half of what Jia said must be true. That is, the 5th place is $E$; Step two: Knowing that $E$ is the 5th place and $D$ is not the 1st place, the only statement left regarding the 1st place is what Ding said. Assume $C$ is the 1st place.

Then, Wu: “The 2nd place is $c$, and the 4th place is $B$.” This means the first half is false and the second half is true, so $B$ is the 4th place. And from Yi: “The 2nd place is $A$, and the 4th place is $c$.”

This means $A$ is the 2nd place. $D$ is the 3rd place.
In summary, the 1st, 2nd, 3rd, 4th, and 5th places are $C A D B E$.