We say that a number is ascending if each of its digits is greater than the digit to its left. For example, 2568 is ascending and 175 is not. How many ascending numbers are there between 400 and 600?
The numbers we are looking for are greater than 400 and less than 600, so the hundreds digit can only be 4 or 5. Since they are ascending numbers, the tens digit is less than the units digit. Let's see how to choose the tens and units digits.

$$
\begin{gathered}
4\left\{\begin{array}{l}
56 \\
57 \\
58 \\
59
\end{array} \quad ; 4\left\{\begin{array}{l}
67 \\
68 \\
69
\end{array} \quad ; 4\left\{\begin{array}{l}
78 \\
79
\end{array} ; 4\{89\right.\right.\right. \\
5\left\{\begin{array}{l}
67 \\
68 \\
69
\end{array} \quad ; \quad 5\left\{\begin{array}{l}
78 \\
79
\end{array} ; 5\{89\right.\right.
\end{gathered}
$$

Therefore, we have 10 ascending numbers with the hundreds digit equal to 4 and six ascending numbers with the hundreds digit equal to 5. Thus, we have 16 ascending numbers between 400 and 600.