Alex chose positive integers a, b, c, d, e, f and completely multiplied out the polynomial product (^ means exponent btw):

(1 - z)^a(1 + x)^b(1 - x + x²)^c(1+x²)^d(1+x+x²)^e(1+x+x²+x³+x^4)^f

After she simplified her result, she discarded any term involving x to any power larger than 6 and was astonished to see that what was left was 1 - 2x. If a d + e + f and b c + d and e c, what value of a did she choose?
a) 17
b) 19
c) 20
d) 21
e) 23

Can someone help please? This problem is from the Fermat math contest. This is question 25 from the contest.

Question

Alex chose positive integers a, b, c, d, e, f and completely multiplied out the polynomial product (^ means exponent btw):

(1 - z)^a(1 + x)^b(1 - x + x²)^c(1+x²)^d(1+x+x²)^e(1+x+x²+x³+x^4)^f

After she simplified her result, she discarded any term involving x to any power larger than 6 and was astonished to see that what was left was 1 - 2x. If a > d + e + f and b > c + d and e > c, what value of a did she choose?
a) 17
b) 19
c) 20
d) 21
e) 23

Can someone help please? This problem is from the Fermat math contest. This is question 25 from the contest.

anonymous · Answer

Link to contest: http://www.cemc.uwaterloo.ca/contests/past_contests/2010/2010FermatContest.pdf Link to solutions for contest (I don't understand the solution): http://www.cemc.uwaterloo.ca/contests/past_contests/2010/2010FermatSolution.pdf