MathDB
Crazy powers

Source: Problem #20 2016 AMC 10A

February 3, 2016
AIME2016 AMC 10AAMC 10

Problem Statement

For some particular value of NN, when (a+b+c+d+1)N(a+b+c+d+1)^N is expanded and like terms are combined, the resulting expression contains exactly 10011001 terms that include all four variables a,b,c,a, b,c, and dd, each to some positive power. What is NN?
<spanclass=latexbold>(A)</span>9<spanclass=latexbold>(B)</span>14<spanclass=latexbold>(C)</span>16<spanclass=latexbold>(D)</span>17<spanclass=latexbold>(E)</span>19<span class='latex-bold'>(A) </span>9 \qquad <span class='latex-bold'>(B) </span> 14 \qquad <span class='latex-bold'>(C) </span> 16 \qquad <span class='latex-bold'>(D) </span> 17 \qquad <span class='latex-bold'>(E) </span> 19