  Let i.i.d. symmetric Bernoulli random variables be associated to the edges of
a binary tree having n levels. To any leaf of the tree, we associate the sum of
variables along the path connecting the leaf with the tree root. Let M_n denote
the maximum of all such sums. We prove that, as n grows, the distributions of
M_n approach some helix in the space of distributions. Each element of this
helix is an accumulation point for the shifts of distributions of M_n.
