Difference between revisions of "1985 AIME Problems/Problem 10"
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<math>\lfloor 2x \rfloor + \lfloor 4x \rfloor + \lfloor 6x \rfloor + \lfloor 8x \rfloor</math>, | <math>\lfloor 2x \rfloor + \lfloor 4x \rfloor + \lfloor 6x \rfloor + \lfloor 8x \rfloor</math>, | ||
| − | where <math>x</math> is a [[real number]], and <math>\lfloor z \rfloor</math> denotes the greatest [[integer | + | where <math>x</math> is a [[real number]], and <math>\lfloor z \rfloor</math> denotes the greatest [[integer]] less than or equal to <math>z</math>? |
== Solution == | == Solution == | ||
{{solution}} | {{solution}} | ||
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* [[1985 AIME Problems/Problem 11 | Next problem]] | * [[1985 AIME Problems/Problem 11 | Next problem]] | ||
* [[1985 AIME Problems]] | * [[1985 AIME Problems]] | ||
| + | * [[Floor function]] | ||
Revision as of 21:06, 19 November 2006
Problem
How many of the first 1000 positive integers can be expressed in the form
,
where 
is a real number, and 
denotes the greatest integer less than or equal to 
?
Solution
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