Difference between revisions of "1996 AIME Problems/Problem 2"
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== Problem == | == Problem == | ||
For each real number <math>x</math>, let <math>\lfloor x \rfloor</math> denote the greatest integer that does not exceed x. For how man positive integers <math>n</math> is it true that <math>n<1000</math> and that <math>\lfloor \log_{2} n \rfloor</math> is a positive even integer? | For each real number <math>x</math>, let <math>\lfloor x \rfloor</math> denote the greatest integer that does not exceed x. For how man positive integers <math>n</math> is it true that <math>n<1000</math> and that <math>\lfloor \log_{2} n \rfloor</math> is a positive even integer? | ||
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== Solution == | == Solution == | ||
n must satisfy these inequalities: | n must satisfy these inequalities: | ||
Revision as of 13:56, 24 September 2007
Problem
For each real number 
, let 
denote the greatest integer that does not exceed x. For how man positive integers 
is it true that 
and that 
is a positive even integer?
Solution
n must satisfy these inequalities:
There are 4 for the first inequality, 16 for the second, 64 for the third, and 256 for the fourth.
