6. In $\{1000,1001, \cdots, 2000\}$, how many pairs of consecutive integers can be added without carrying over a digit?
6 . Let $n$ have the decimal representation $1 a b c$. If one of $a, b$, $c$ is $5, 6, 7$ or 8, then adding $n$ and $n+1$ requires carrying 3. If $b=9, c \neq 9$ or $a=9, b$ and $c$ are not 9, then adding $n$ and $n+1$ requires carrying.

If $n$ is not as described above, then it must be of one of the following forms:
$1 a b c, 1 a b 9,1 a 99,1999$,

where $a, b, c \in\{0,1,2, 3, 4\}$. For such $n$, adding $n$ and $n+1$ does not require carrying. Therefore, there are $5^{3}+5^{2}+5+1=156$ such $n$.