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a_0 + 2a_1 + 2^2a_2+ ... + 2^{17}a_{17} = 2^10

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April 28, 2009

Problem Statement

For every 0≤i≤17 0 \le i \le 17, a_i \equal{} \{ \minus{} 1, 0, 1\}. How many (a0,a1,…,a17) (a_0,a_1, \dots , a_{17}) 18 \minus{}tuples are there satisfying : a_0 \plus{} 2a_1 \plus{} 2^2a_2 \plus{} \cdots \plus{} 2^{17}a_{17} \equal{} 2^{10}
<spanclass=′latex−bold′>(A)</span> 9<spanclass=′latex−bold′>(B)</span> 8<spanclass=′latex−bold′>(C)</span> 7<spanclass=′latex−bold′>(D)</span> 4<spanclass=′latex−bold′>(E)</span> 1<span class='latex-bold'>(A)</span>\ 9 \qquad<span class='latex-bold'>(B)</span>\ 8 \qquad<span class='latex-bold'>(C)</span>\ 7 \qquad<span class='latex-bold'>(D)</span>\ 4 \qquad<span class='latex-bold'>(E)</span>\ 1
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