2014 Canadian MO Problems/Problem 1

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a11+a1+a2(1+a1)(1+a2)++an(1+a1)(1+a2)(1+an)=(111+a1)+(11+a11(1+a1)(1+a2))++(1(1+a1)(1+a2)(1+an1)1(1+a1)(1+a2)(1+an))=11(1+a1)(1+a2)(1+an)11(21a1)(21a2)(21an)=112n=2n12n