Difference between revisions of "1989 AIME Problems/Problem 11"
m |
|||
Line 1: | Line 1: | ||
== 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 12|Next Problem]] | ||
+ | * [[1989 AIME Problems/Problem 10|Previous Problem]] | ||
* [[1989 AIME Problems]] | * [[1989 AIME Problems]] |
Revision as of 23:16, 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
This problem needs a solution. If you have a solution for it, please help us out by adding it.