## 51. Math Puzzle $8 / 69$

A very superstitious boy received a bicycle as a gift and wanted to learn how to ride it. When he heard about a bicycle malfunction that we usually refer to as "eight," he feared that it would bring bad luck if the six-digit number stamped on the frame contained one or even several digits 8. Before he looked at the bicycle number, he made the following consideration: When writing any number, 10 digits can be involved, namely $0,1, \ldots, 9$.

Among them, only the digit 8 appears as "unlucky." Therefore, there is only one case out of ten that can be called "unlucky."

Is our young cyclist right?
Our young friend was indeed mistaken.

In total, there are 999999 numbers, ranging from 000001 to 999999. For the "lucky" numbers:

The first position can be any of the 9 digits, namely $0,1,2,3,4,5,6,7,9$; the second position can also be any of these 9 digits. Therefore, there are $9 \cdot 9=9^{2}$ "lucky" two-digit numbers.

For the subsequent digits, there are 9 possible digits each, so the number of "lucky" six-digit numbers is $9^{6}$. Since the bicycle number 000000 is not valid, the number of "lucky" numbers is $9^{6}-1=531440$, which is slightly more than $53\%$ of all numbers, not $90\%$ as our racer assumed.