Square-free shuffles of words

Let uшvuшv denote the set of all shuffles of the words u and v  . It is shown that for each integer n≥3n≥3 there exists a square-free ternary word u of length n   such that uшuuшu contains a square-free word. This property is then shown to also hold for infinite words, i.e., there exists an infinite square-free word u on three letters such that u   can be shuffled with itself to produce an infinite square-free word w∈uшuw∈uшu.