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AMO 2027 Grades 8-9 SET 16 - Self-study Question 9

AMO · AMO 2027 Grades 8-9 SET 16 - Self-study

Question 9

Exercise 5. For years, telephone area codes in the United States and Canada consisted of a sequence of three digits. The first digit was an integer between 2 and 9, the second digit was either 0 or 1, and the third digit was any integer from 1 to 9.

(a) How many area codes were possible?

(b) How many area codes starting with a 4 were possible?

**Editorial input convention:** Use only the stated position rules, with endpoints 2 and 9 included and repetitions allowed. Enter the answers to a and b in that order, separated by one semicolon, with no spaces. Format example, not the answer: 10;2.