MathDB

30

Part of 1997 AMC 12/AHSME

Problems(1)

Pairs of Different Adjacent Digits

Source:

1/18/2009
For positive integers n n, denote by D(n) D(n) the number of pairs of different adjacent digits in the binary (base two) representation of n n. For example, D(3) \equal{} D(11_2) \equal{} 0, D(21) \equal{} D(10101_2) \equal{} 4, and D(97) \equal{} D(110001_2) \equal{} 2. For how many positive integers n n less than or equal to 97 97 does D(n) \equal{} 2?
<spanclass=′latex−bold′>(A)</span> 16<spanclass=′latex−bold′>(B)</span> 20<spanclass=′latex−bold′>(C)</span> 26<spanclass=′latex−bold′>(D)</span> 30<spanclass=′latex−bold′>(E)</span> 35 <span class='latex-bold'>(A)</span>\ 16\qquad <span class='latex-bold'>(B)</span>\ 20\qquad <span class='latex-bold'>(C)</span>\ 26\qquad <span class='latex-bold'>(D)</span>\ 30\qquad <span class='latex-bold'>(E)</span>\ 35