AMC 10 Step by Step
2018 AMC 10AProblem 18P16-20~4 minPrint

How many nonnegative integers can be written in the form a737+a636+a535+a434+a333+a232+a131+a030,a_7\cdot3^7+a_6\cdot3^6+a_5\cdot3^5+a_4\cdot3^4+a_3\cdot3^3+a_2\cdot3^2+a_1\cdot3^1+a_0\cdot3^0, where ai{1,0,1}a_i\in \{-1,0,1\} for 0i70\le i \le 7 ?

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Problem © Mathematical Association of America (MAA), American Mathematics Competitions. Reproduced for non-commercial educational use. Solution and commentary are original to this site.