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AMO 2017 Secondary 3 (Grade 9) Question 21

AMO · AMO 2017 Secondary 3 (Grade 9)

Question 21

Mel sells pretzel nuggets only in packs of $5$, $6$, or $11$. What is the greatest total number of nuggets that cannot be purchased using whole packs?

Source correction: the printed example says $8$ can be purchased, but that is impossible with these pack sizes; both $8$ and $9$ are impossible.

Question illustration