15.94 (2002)

Define the weight of a group $G$ to be the minimum number of generators of $G$ as a normal subgroup of itself. Let $G = G_1 \ast \dots \ast G_n$ be a free product of $n$ nontrivial groups.
$\qquad$ a) Is it true that the weight of $G$ is at least $n/2$?$\qquad$ b) Is it true if the $G_i$ are cyclic?
$\qquad$ c) Is it true for $n = 3$ (without assuming the $G_i$ cyclic)?

Problem 5.53 (now answered in the affirmative) is the special case with $n = 3$ and all the $G_i$ cyclic.