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AMO · 2027 · Grades 8-9 · Self-study SET 20 Question 10

AMO

Question 10

A number has only the digit 1 when written in base 3, but its last digit is 0 when written in base 2. What is the largest four-digit number in base 10 with this property? Enter its ordinary base-10 value, without padding it with a leading zero.