6. (10 points) An exam has 3 questions. After the exam, four friends check their answers and find that they got $3, 2, 1,$ and $0$ questions right, respectively. At this moment, the teacher asks: How did you do on the exam? Each of them says 3 sentences (as follows):
甲: I got two questions right, and I did better than 乙, 丙 did worse than 丁.
乙: I got all questions right, 丙 got none right, 甲 did worse than 丁.
丙: I got one question right, 丁 got two questions right, 乙 did worse than 甲.
丁: I got all questions right, 丙 did worse than me, 甲 did worse than 乙.
If each person tells as many true statements as the number of questions they got right, and let 甲, 乙, 丙, 丁 get $A, B, C, D$ questions right, respectively, then the four-digit number $\overline{\mathrm{ABCD}}=$
【Solution】Solution: According to the analysis, no one in the team would say they got fewer than 3 questions correct, so only Yi and Ding could possibly get all questions right. If Yi got all questions right, then the ranking would be Yi, Ding, Jia, and Bing, which contradicts Bing's statement: “Ding got two questions right” being a lie; If Ding got all questions right, then Bing's last two statements are lies, so Bing cannot be in 2nd place, and from Ding's “Jia did worse than Yi,” we can know that the 2nd place is Yi,

So Bing got all questions wrong, and Jia only has “Bing did worse than Ding” as a true statement, the ranking is Ding, Yi, Jia, and Bing, and after verification, there are no contradictions in the statements of the four people.

Therefore, Jia, Yi, Bing, and Ding got $1, 2, 0, 3$ questions correct respectively.
The answer is: 1203.