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(x1 x2 .. x1998) = 7x10^1996 (x1 + x2 + .. + x1998)

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April 23, 2009

Problem Statement

(x1x2x1998) \left(x_{1} x_{2} \ldots x_{1998} \right) shows a number with 1998 digits in decimal system. How many numbers (x1x2x1998) \left(x_{1} x_{2} \ldots x_{1998} \right) are there such that \left(x_{1} x_{2} \ldots x_{1998} \right) \equal{} 7\cdot 10^{1996} \left(x_{1} \plus{} x_{2} \plus{} \ldots \plus{} x_{1998} \right) ?
<spanclass=latexbold>(A)</span> 0<spanclass=latexbold>(B)</span> 1<spanclass=latexbold>(C)</span> 2<spanclass=latexbold>(D)</span> 3<spanclass=latexbold>(E)</span> 4<span class='latex-bold'>(A)</span>\ 0 \qquad<span class='latex-bold'>(B)</span>\ 1 \qquad<span class='latex-bold'>(C)</span>\ 2 \qquad<span class='latex-bold'>(D)</span>\ 3 \qquad<span class='latex-bold'>(E)</span>\ 4