Difference between revisions of "1994 AIME Problems/Problem 4"

Revision as of 23:24, 28 March 2007

Find the positive integer $n\,$ for which

$\lfloor \log_2{1}\rfloor+\lfloor\log_2{2}\rfloor+\lfloor\log_2{3}\rfloor+\cdots+\lfloor\log_2{n}\rfloor=1994$

.

(For real $x\,$ , $\lfloor x\rfloor\,$ is the greatest integer $\le x.\,$ )

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@@ Line 1: / Line 1: @@
 == Problem ==
+Find the positive integer <math>n\,</math> for which
+<center><math>
+\lfloor \log_2{1}\rfloor+\lfloor\log_2{2}\rfloor+\lfloor\log_2{3}\rfloor+\cdots+\lfloor\log_2{n}\rfloor=1994</math></center>.
+(For real <math>x\,</math>, <math>\lfloor x\rfloor\,</math> is the greatest integer <math>\le x.\,</math>)
 == Solution ==
+{{solution}}
 == See also ==
-* [[1994 AIME Problems]]
+{{AIME box|year=1994|num-b=3|num-a=5}}

1994 AIME (Problems • Answer Key • Resources)
Preceded by Problem 3	Followed by Problem 5
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All AIME Problems and Solutions