3. (5 points) If $\overline{\mathrm{abc}}$ and $\overline{\operatorname{def}}$ are two three-digit numbers, and $a=b+1, b=c+2, \overline{\mathrm{abc}} \times 3+4=\overline{\operatorname{def}}$, then $\overline{\mathrm{def}}$ $=$ $\qquad$
【Analysis】Obviously, $a$ is 3 more than $c, a$ is at least $3, b$ is at least $2, c$ is at least 0, and $\overline{a b c} \times 3+4=\overline{\operatorname{def}}, d$ is at most 9, only when $a=3$ does it satisfy the condition, so we can find $\overline{\operatorname{def}}$.

【Solution】According to the analysis, $a=b+1=c+2+1=c+3$, and since $a, b, c$ are all single digits, the minimum value of $a$ is $3, b$ is at least $2, c$ is at least 0,
and $\because \overline{\mathrm{abc}} \times 3+4=\overline{\operatorname{def}}$,
$\therefore d$ is at most 9, at this point $a=3, b=2, c=0$ which means $\overline{\mathrm{abc}}=320$,
then $\overline{\operatorname{def}}=\overline{\mathrm{abc}} \times 3+4=320 \times 3+4=964$;
Therefore, the answer is: 964.