  We describe a new non-constructive technique to show that squares are
avoidable by an infinite word even if we force some letters from the alphabet
to appear at certain occurrences. We show that as long as forced positions are
at distance at least 19 (resp. 3, resp. 2) from each other then we can avoid
squares over 3 letters (resp. 4 letters, resp. 6 or more letters). We can also
deduce exponential lower bounds on the number of solutions. For our main
Theorem to be applicable, we need to check the existence of some languages and
we explain how to verify that they exist with a computer. We hope that this
technique could be applied to other avoidability questions where the good
approach seems to be non-constructive (e.g., the Thue-list coloring number of
the infinite path).
