Cyclists have an aversion to the number zero (because it is oval) and the number eight (because that's how the wheels look after accidents). How many members can register in a cycling club if each must have a three-digit identification number, without using the digit zero or the digit eight?

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Solution

Since the cyclists do not use the digit 0 or 8, the remaining digits are $1,2,3,4,5,6,7$ and 9. Thus, there are 8 possibilities for the choice of each digit. We need to choose three-digit numbers. Therefore, we have 8 options for the first digit, 8 options for the second digit, and 8 options for the third digit. Hence, as

$$
8 \times 8 \times 8=512
$$

we conclude that a maximum of 512 members can register.