Hardy-like quantum pigeonhole paradox and the projected-coloring graph state

A Hardy-like version of the quantum pigeonhole paradox is proposed, which can also be considered as a special kind Hardy's paradox. Besides an example induced from minimal system, general construction this $n$-qubit state discussed. Moreover, by introducing projected-coloring graph and state, pictorial representation presented. This implemented more directly in experiment than original one, since it does not require some sophisticated techniques such weak measurements. In addition, angle paradox, paradoxes even set new record for success probability demonstrating Bell nonlocality.