(1) 2011 is such a four-digit number, the sum of its digits is 4; there are $\qquad$ such four-digit numbers whose digits sum to 4.
(1) 20 Hint: The number of such four-digit numbers $\overline{x_{1} x_{2} x_{3} x_{4}}$ is the number of integer solutions to the equation $x_{1}+$ $x_{2}+x_{3}+x_{4}=4$ that satisfy the conditions $x_{1} \geqslant 1, x_{2}, x_{3}, x_{4} \geqslant 0$; that is, the number of non-negative integer solutions to $y_{1}+x_{2}+x_{3}+x_{4}=3$, where $y_{1}=x_{1}-1$. It is easy to see that there are $\mathrm{C}_{344-1}^{4-1}=\mathrm{C}_{6}^{3}=20$ (solutions), meaning there are a total of 20 such four-digit numbers. (Note: They can also be listed directly.)