  2D Percolation path exponents $x^{\cal P}_{\ell}$ describe probabilities for
traversals of annuli by $\ell$ non-overlapping paths, each on either occupied
or vacant clusters, with at least one of each type. We relate the probabilities
rigorously to amplitudes of $O(N=1)$ models whose exponents, believed to be
exact, yield $x^{\cal P}_{\ell}=({\ell}^2-1)/12$. This extends to half-integers
the Saleur--Duplantier exponents for $k=\ell/2$ clusters, yields the exact
fractal dimension of the external cluster perimeter, $D_{EP}=2-x^{\cal
P}_3=4/3$, and also explains the absence of narrow gate fjords, as originally
found by Grossman and Aharony.
