Did Noah have woodpeckers on the ark?

Woodpeckers are not specifically mentioned. Whatever birds were on the ark would have had the genetic material from which our current woodpeckers developed via natural selection and may have had some of the same characteristics, but woodpeckers themselves as we know them need not have been on the ark. The Bible states that various numbers of each kind were taken on the ark, and kinds do not equate to our modern classification system. The answer is that it is not possible to precisely know, but it is certain that at least their ancestral kind of bird were.