Difference between revisions of "1997 AHSME Problems/Problem 30"

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==Problem==
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For positive integers <math>n</math>, denote <math>D(n)</math> by the number of pairs of different adjacent digits in the binary (base two) representation of <math>n</math>. For example, <math> D(3) = D(11_{2}) = 0 </math>, <math> D(21) = D(10101_{2}) = 4 </math>, and <math> D(97) = D(1100001_{2}) = 2 </math>. For how many positive integers less than or equal <math>97</math> to does <math>D(n) = 2</math>?
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<math> \textbf{(A)}\ 16\qquad\textbf{(B)}\ 20\qquad\textbf{(C)}\ 26\qquad\textbf{(D)}\ 30\qquad\textbf{(E)}\ 35 </math>
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== See also ==
 
== See also ==
 
{{AHSME box|year=1997|num-b=29|after=Last Question}}
 
{{AHSME box|year=1997|num-b=29|after=Last Question}}

Revision as of 18:18, 23 August 2011

Problem

For positive integers $n$, denote $D(n)$ by the number of pairs of different adjacent digits in the binary (base two) representation of $n$. For example, $D(3) = D(11_{2}) = 0$, $D(21) = D(10101_{2}) = 4$, and $D(97) = D(1100001_{2}) = 2$. For how many positive integers less than or equal $97$ to does $D(n) = 2$?

$\textbf{(A)}\ 16\qquad\textbf{(B)}\ 20\qquad\textbf{(C)}\ 26\qquad\textbf{(D)}\ 30\qquad\textbf{(E)}\ 35$

See also

1997 AHSME (ProblemsAnswer KeyResources)
Preceded by
Problem 29
Followed by
Last Question
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