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Turkey NMO 2007 1st Round - P20 (Combinatorics)

Source:

October 4, 2012

Problem Statement

The 99 consequtive sections of a paper strip are colored either red or white. If no two consequtive sections are white, in how many ways can this coloring be made?
<spanclass=latexbold>(A)</span> 34<spanclass=latexbold>(B)</span> 89<spanclass=latexbold>(C)</span> 128<spanclass=latexbold>(D)</span> 144<spanclass=latexbold>(E)</span> 360 <span class='latex-bold'>(A)</span>\ 34 \qquad<span class='latex-bold'>(B)</span>\ 89 \qquad<span class='latex-bold'>(C)</span>\ 128 \qquad<span class='latex-bold'>(D)</span>\ 144 \qquad<span class='latex-bold'>(E)</span>\ 360