  Recently, Boutonnet, Chifan, and Ioana proved that McDuff's examples of
continuum many pairwise non-isomorphic separable II$_1$ factors are in fact
pairwise non-elementarily equivalent. Their proof proceeded by showing that any
ultrapowers of any two distinct McDuff examples are not isomorphic. In a paper
by the first two authors of this paper, Ehrenfeucht-Fra\"isse games were used
to find an upper bound on the quantifier complexity of sentences distinguishing
the McDuff examples, leaving it as an open question to find concrete sentences
distinguishing the McDuff factors. In this paper, we answer this question by
providing such concrete sentences.
