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Python, 94 85 79 75 bytes
EDIT: Thanks Doorknob and Alex A.
EDIT: Thanks Alex A.
EDIT: Now using input() so the input must be a string with the quotes.
Simply counts number of e's and if q, check if e count is odd, then print index.
e=0
i=input()
for j in range(len(i)):
if i[j]<"q":e+=1
el...