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Turkey NMO 2008 1st Round - P30 (Number Theory)

Source:

August 27, 2012

Problem Statement

In a sequence with the first term is positive integer, the next term is generated by adding the previous term and its largest digit. At most how many consequtive terms of this sequence are odd?
<spanclass=latexbold>(A)</span> 2<spanclass=latexbold>(B)</span> 3<spanclass=latexbold>(C)</span> 4<spanclass=latexbold>(D)</span> 5<spanclass=latexbold>(E)</span> 6 <span class='latex-bold'>(A)</span>\ 2 \qquad<span class='latex-bold'>(B)</span>\ 3 \qquad<span class='latex-bold'>(C)</span>\ 4 \qquad<span class='latex-bold'>(D)</span>\ 5 \qquad<span class='latex-bold'>(E)</span>\ 6