  Hardy-like proofs for some quantum mechanical properties, such as Hardy-like
nonlocality and Hardy-like contextuality, provide us two probabilistic no-go
theorems by logical contradictions. Inspired by this, one may conjure that
there are some other nonclassical properties which can also be revealed by
Hardy-like arguments. In this work, we present an unconventional kind of
quantum pigeonhole effects using Hardy-like arguments and show how to
systematically construct them. Besides, we introduce a kind of
``projected-stabilizer state", say projected-coloring graph states, associated
with a special type of coloring graphs called projected-coloring graph states.
We build a one-to-one connection between a given projected-coloring graph
(state) and a Hardy-like quantum pigeonhole paradox. In this sense a Hardy-like
quantum pigeonhole paradox may also be referred to as a ``quantum coloring
paradox".
