  We propose in this work a definite theoretical implementation of the
three-box paradox - a scheme in which a single quantum particle appears to be
present with certainty in two separate boxes - with spin-1 atoms. We further
show how our setup can give rise to a "Cheshire cat grin" type of situation, in
which an atom can apparently be found with certainty in one of the boxes while
one of its properties (the angular momentum projection along a specifically
chosen axis) appears to be in a different box. The significance of our findings
are discussed relative to the status of the properties of a system obtained
from weak measurements.
