  We report experimental studies of the multi-photon quantum interference of a
two-mode three-photon entangled Fock state $|2, 1\rangle$ + $|1, 2\rangle$
impinging on a two-port balanced beam splitter. When the distinguishability
between the two input paths is increased, we observe a reduction followed by a
resurgence of the quantum interference signal. We ascribe this unusual behavior
to the competition among contributions from distinct numbers of interfering
photons. Our theoretical analysis shows that this phenomenon will occur for any
entangled Fock-state input of the form $|N, M\rangle$ + $|M, N\rangle$ where M,
N > 0. Our results are an indication that wave-particle duality may give rise
to a wide range of, largely unexplored, phenomena in multi-particle
interference.
