1. 182 For 1 to 1000000000, find the sum of the digits of each number; then for the resulting 1 billion numbers, find the sum of the digits of each number, $\cdots$, until obtaining 1 billion single-digit numbers. Question: Among the resulting numbers, are there more 1s or 2s?
[Solution] 1 is 1 more than 2.
In fact, any number and the sum of its digits have the same remainder when divided by 9. Therefore, in this problem, 1 is obtained from those numbers that give a remainder of 1 when divided by 9: 1, 10, 19, 28, ..., 999999991, 1000000000, while 2 is obtained from those numbers that give a remainder of 2 when divided by 9: 2, 11, 20, 29, ..., 999999992. Since the numbers that give a remainder of 1 are 1 more than those that give a remainder of 2, the result is that 1 is 1 more than 2.