Question

19. A brand-new school district needs to generate ID numbers for its student body. The district anticipates a total enrollment of 75,000 students within the next ten years. Will a five-digit ID number using the symbols 0, 1,…, 9 be enough? Explain your reasoning.

Answer 1

yes

Explanation:

75000 is a 5-digit number, as are all the numbers up to 75000. 5 digits are sufficient to assign each student a unique number.

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Comment on the answer

Usually, at least one check digit would be used to guard against errors such as transposition of digits. Many school districts have a lifetime longer than 10 years, so it seems likely the number of students in 50 years (for example) will exceed the 100,000 students that can be given 5-digit numbers. A 7-digit numbering scheme seems more appropriate, or a scheme that uses a combination of digits and letters.