A firm wants to assign its employees ID numbers that have say x digits each. If a firm has 800 employees, what is the smallest number of digits

Question

A firm wants to assign its employees ID numbers that have say x digits each. If a firm has 800 employees, what is the smallest number of digits (that is, the smallest x) that the firm can use for each ID number? Assume that repetition of digits is permitted. 

Answer 1

If we assume that digits can be repeated and that all digits (including 0) can be used for each digit,

then there are 10 potential digits for each position.

If we have 1 digit, then we have 10 potential id numbers.

If we have 2 digits, then we have 10 x 10 or 100 potential numbers. Still not enough.

if we have  3 digits, then we have 10 x 10 x 10 or 1000 potential id numbers, which is more than enough.

So, for 800 employees, 3 digits are the minimum needed for each id number.