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2006 China Second Round Olympiad Test 1 #6

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September 28, 2014

Problem Statement

Let SS be the set of all those 2007 place decimal integers 2s1a2a3…a2006‾\overline{2s_1a_2a_3 \ldots a_{2006}} which contain odd number of digit 99 in each sequence a1,a2,a3,…,a2006a_1, a_2, a_3, \ldots, a_{2006}. The cardinal number of SS is
<spanclass=′latex−bold′>(A)</span> 12(102006+82006)<spanclass=′latex−bold′>(B)</span> 12(102006−82006)<spanclass=′latex−bold′>(C)</span> 102006+82006<spanclass=′latex−bold′>(D)</span> 102006−82006{ <span class='latex-bold'>(A)</span>\ \frac{1}{2}(10^{2006}+8^{2006})\qquad<span class='latex-bold'>(B)</span>\ \frac{1}{2}(10^{2006}-8^{2006})\qquad<span class='latex-bold'>(C)</span>\ 10^{2006}+8^{2006}\qquad <span class='latex-bold'>(D)</span>}\ 10^{2006}-8^{2006}\qquad
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