  For two-path interferometers, the which-path predictability $\mathcal{P}$ and
the fringe visibility $\mathcal{V}$ are familiar quantities that are much used
to talk about wave-particle duality in a quantitative way. We discuss several
candidates that suggest themselves as generalizations $P$ of $ mathcal{P}$ for
multi-path interferometers, and treat the case of three paths in considerable
detail. To each choice for the \emph{path knowledge} $P$, the
\emph{interference strength} $V$ -- the corresponding generalization of
$\mathcal{V}$ -- is found by a natural, operational procedure. In experimental
terms it amounts to finding those equal-weight superpositions of the path
amplitudes which maximize $P$ for the emerging intensities. Mathematically
speaking, one needs to identify a certain optimal one among the Fourier
transforms of the state of the interfering quantum object. Wave-particle
duality is manifest, inasmuch as P=1 implies V=0 and V=1 implies P=0, whatever
definition is chosen. The possible values of the pair $(P,V)$ are restricted to
an area with corners at $(P,V)=(0,0)$, $(P,V)=(1,0)$, and $(P,V)=(0,1)$, with
the shape of the border line from $(1,0)$ to $(0,1)$ depending on the
particular choice for $P$ and the induced definition of $V$.
