The raft one:
according to my calculations, yes, it's possible (blue points are the daughters):
calculated center of gravity to be origin (0, 0) as follows:
if vector of weights is w = [0, 0, 1, 1, 0, 1, 1, 0, 0, 1, 1, 1], then
sum( sin( k* pi/6) * w[k])
for k = 1, 2, ... 12, is the center...