Difference between revisions of "1989 AIME Problems/Problem 10"
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== Problem == | == Problem == | ||
| + | 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 <math>D^{}_{}</math> be the difference between the mode and the arithmetic mean of the sample. What is the largest possible value of <math>\lfloor D^{}_{}\rfloor</math>? (For real <math>x^{}_{}</math>, <math>\lfloor x^{}_{}\rfloor</math> is the greatest integer less than or equal to <math>x^{}_{}</math>.) | ||
== Solution == | == Solution == | ||
| + | {{solution}} | ||
== See also == | == See also == | ||
| + | * [[1989 AIME Problems/Problem 11|Next Problem]] | ||
| + | * [[1989 AIME Problems/Problem 9|Previous Problem]] | ||
* [[1989 AIME Problems]] | * [[1989 AIME Problems]] | ||
Revision as of 23:11, 24 February 2007
Problem
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 .)
Solution
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