1. (8 points) Three people, A, B, and C, participated in a competition, and they placed in the top 3 (no ties).
A says: “I am first”
B says: “I am not first”
C says: “I am not third”
Only one of the three is telling the truth.
If the ranks of A, B, and C are $A$, $B$, and $C$ respectively, then the three-digit number $\overline{\mathrm{ABC}}=$ $\qquad$
【Solution】Solution: Assume A is telling the truth, that is, A is the first place, and B saying "I am not the first" would also be true, which means 2 people are telling the truth, contradicting the problem statement, so A telling the truth is incorrect;

Assume B is telling the truth, then C is lying, C can only be third, B can only be second, and A can only be first, this way A also tells the truth, contradicting the problem statement, so B is lying;

Therefore, it can only be that C is telling the truth, A and B are lying, B is the first place, and not third, can only be second, A is third;

That is, $A=3, B=1, C=2$.
The three-digit number $\overline{\mathrm{ABC}}=312$.
Therefore, the answer is: 312.