A sample of 121 integers is given, each between 1 and 1000 inclusive, with repetitions allowed. The sample has a unique mode (most frequent value). Let be the difference between the mode and the arithmetic mean of the sample. What is the largest possible value of ? (For real , is the greatest integer less than or equal to .)
This problem is copyrighted by the American Mathematics Competitions.
Instructions for entering answers:
For questions or comments, please email firstname.lastname@example.org.