2. (8 points) One day, Xiao Ming was chatting with his brother. Xiao Ming said to his brother: "I am particularly looking forward to the year 2013, because 2, 0, 1, and 3 are four different digits. I have never experienced such a year before." His brother smiled and said: "Yes, we can call such years 'lucky years'. If we count this way, next year will be the 2nd 'lucky year' I have experienced." So, the brother was born in the year $\qquad$.
【Answer】Solution: Tracing back from 2013, the years are:
2012, has 2 twos;
2011, has 2 ones;
2010 has 2 zeros;
2009 2000, all have at least 2 zeros;
1999 1989, all have at least 2 nines;
1988, has 2 eights;
1987 all four digits are different;
So the brother was born in 1987.
The answer is: 1987.