  Here we present the most general framework for $n$-particle Hardy's
paradoxes, which include Hardy's original one and Cereceda's extension as
special cases. Remarkably, for any $n\ge 3$ we demonstrate that there always
exist generalized paradoxes (with the success probability as high as
$1/2^{n-1}$) that are stronger than the previous ones in showing the conflict
of quantum mechanics with local realism. An experimental proposal to observe
the stronger paradox is also presented for the case of three qubits.
Furthermore, from these paradoxes we can construct the most general Hardy's
inequalities, which enable us to detect Bell's nonlocality for more quantum
states.
