113. How many two-digit natural numbers are there in which the first digit is greater than the second?
$\triangle$ If the first digit of a two-digit number is 1, then there is only one such number - 10. If the first digit of the number is 2, then there are two such numbers - 20 and 21. If the first digit is 3, then there are already three such numbers - 30, 31, and 32. And so on. Finally, if the first digit is 9, then there are nine such two-digit numbers - from 90 to 98. Therefore, the total number of numbers is $1+2+3+\ldots+9=45$.

Answer: 45.

![](https://cdn.mathpix.com/cropped/2024_05_21_0aa0e6ac168e80891953g-049.jpg?height=603&width=1336&top_left_y=1777&top_left_x=360)

48