MathDB
Pairs of Different Adjacent Digits

Source:

January 18, 2009

Problem Statement

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=latexbold>(A)</span> 16<spanclass=latexbold>(B)</span> 20<spanclass=latexbold>(C)</span> 26<spanclass=latexbold>(D)</span> 30<spanclass=latexbold>(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