Prove that there exists a constant c>0 such that in every nontrivial finite group G there exists a sequence of length at most cln∣G∣ with the property that each element of G equals the product of some subsequence. (The elements of G in the sequence are not required to be distinct. A subsequence of a sequence is obtained by selecting some of the terms, not necessarily consecutive, without reordering them; for example, 4,4,2 is a subesequence of 2,4,6,4,2, but 2,2,4 is not.) Putnamlogarithmsinequalitiescollege contests