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List S Positive Integers Not Distinct

2050SpecialistCombinatoricsAlgebraNumber Theory

AIME · 1984 · Problem 4

Let $S$ be a list of positive integers--not necessarily distinct--in which the number $68$ appears. The average (arithmetic mean) of the numbers in $S$ is $56$. However, if $68$ is removed, the average of the remaining numbers drops to $55$. What is the largest number that can appear in $S$?
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