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AMO 2027 Grades 6-7 SET 15 - Self-study Question 6

AMO · AMO 2027 Grades 6-7 SET 15 - Self-study

Question 6

An ATM password at Fred’s Bank is composed of four digits from 0 to 9, with repeated digits allowable. If no password may begin with the sequence 9, 1, 1, then how many passwords are possible?

**Editorial note for this self-study exercise:** Treat a password as a string of four digits, so leading zeroes are allowed. Only the first three positions forming 911 are forbidden.