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AMO · 2027 · Grades 4-5 · Self-study SET 33 Question 11

AMO

Question 11

The keys to nine rooms are all mixed up in a box. What is the least number of key trials needed to guarantee that every key can be matched to its room lock?

There are exactly nine distinct keys, each opening exactly one different lock. Count physical key-in-lock trials; a match known by deduction needs no trial. Find the worst-case guarantee, not a lucky outcome. Enter one whole number.