4. $\overline{a b c}$ represents a three-digit number in decimal. If $\overline{a b c}$ is equal to the sum of all two-digit numbers formed by the digits $a, b, c$, write down all the three-digit numbers that satisfy the above condition.
4.【Solution】Find $a$, $b$, and $c$ that satisfy $\mathrm{a} \times 100+\mathrm{b} \times 10+\mathrm{c}=(\mathrm{a}+\mathrm{b}+\mathrm{c}) \times 10 \times 2+(\mathrm{a}+\mathrm{b}+\mathrm{c}) \times 2=22 \times(a+b+c)$.
The equation is: $100 a+10 b+c=22 a+22 b+22 c$, which simplifies to: $78 a-12 b-21 c=0$.
Since $12 \times 9+21 \times 9=297, 297 \div 78<4$, $a$ can only be $1, 2, 3$.
If $a=1$, then $78=12 b+21 c$, and $c=\frac{78-12 b}{21}$. Testing $1, 2, 3$ for $c$, we find that $b=3, c=2$ satisfies the condition.
If $a=2$, then $156=12 b+21 c$, and $c=\frac{156-12 b}{21}$. Testing $1, 2, 3$ for $c$, we find that $b=6, c=4$ satisfies the condition.
If $a=3$, then $234=12 b+21 c$, and $c=\frac{234-12 b}{21}$. Testing $1, 2, 3$ for $c$, we find that $b=9, c=6$ satisfies the condition.
Therefore, there are three three-digit numbers that satisfy the condition: $132, 264, 396$.