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Turkey NMO 2008 1st Round - P24 (Combinatorics)

Source:

August 26, 2012
ratiosymmetrygeometric series

Problem Statement

How many of the numbers a1⋅51+a2⋅52+a3⋅53+a4⋅54+a5⋅55+a6⋅56 a_1\cdot 5^1+a_2\cdot 5^2+a_3\cdot 5^3+a_4\cdot 5^4+a_5\cdot 5^5+a_6\cdot 5^6 are negative if a1,a2,a3,a4,a5,a6∈{−1,0,1}a_1,a_2,a_3,a_4,a_5,a_6 \in \{-1,0,1 \}?
<spanclass=′latex−bold′>(A)</span> 121<spanclass=′latex−bold′>(B)</span> 224<spanclass=′latex−bold′>(C)</span> 275<spanclass=′latex−bold′>(D)</span> 364<spanclass=′latex−bold′>(E)</span> 375 <span class='latex-bold'>(A)</span>\ 121 \qquad<span class='latex-bold'>(B)</span>\ 224 \qquad<span class='latex-bold'>(C)</span>\ 275 \qquad<span class='latex-bold'>(D)</span>\ 364 \qquad<span class='latex-bold'>(E)</span>\ 375
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