I suspect that if you have a sequence w_0, ... w_n with the property but all possible remaining words in your sequence following w_n are the wrong color, then y

I suspect that if you have a sequence w_0, ... w_n with the property but all possible remaining words in your sequence following w_n are the wrong color, then you can use set w_0' = concat(w_0, ... w_n) and declare victory.