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 
, denote 
by the number of pairs of different adjacent digits in the binary (base two) representation of . For example, 
, 
, and 
. For how many positive integers less than or equal 
to does 
?
See also
| 1997 AHSME (Problems • Answer Key • Resources) | ||
| Preceded by Problem 29 |
Followed by Last Question | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 • 26 • 27 • 28 • 29 • 30 | ||
| All AHSME Problems and Solutions | ||
