A (written in the decimal system) four-digit number is divided into two groups according to whether it can be written as the product of two two-digit numbers or not. Which group is larger?
From a four-digit number, there are 9000, and from a two-digit number, there are $90$ instances. Let's calculate the maximum number of different products that can be formed from the $90$ two-digit numbers. For products with identical factors (square numbers), there are 90, and for products with different factors, there are at most $\frac{90 \cdot 89}{2}$ instances, so in total, there are no more than $4095$ instances. (Among these, there are some that are not four-digit numbers, and there are duplicate products.)

Therefore, the number of four-digit numbers that can be expressed as the product of two two-digit numbers is at most 4095. Thus, the number of numbers that cannot be expressed in this way, which is at least $9000-4095=4905$, is greater than the number of those that can be expressed in this way.

Borsi Zsolt (Szentendre, Ferences Gimn., III. o.t.)