  In a classic paper Schr\"oder posed four combinatorial problems about the
number of certain types of bracketings of words and sets. Here we address what
these bracketings look like on average. For each of the four problems we prove
that a uniform pick from the appropriate set of bracketings, when considered as
a tree, has the Brownian continuum random tree as its scaling limit as the size
of the word or set goes to infinity.
