Is the set of strings with equal number of 010’s and 101’s regular? Consider the language $$L = \{ w\in \{ 0, 1\}^*: \#_{010}(w) = \#_{101}(w) \}$$
Is $L$ is regular? If it is not regular, can we prove that using the pumping lemma (only with pumping down)?
Try writing a few words that are contained (and not) in your language. See if you can discern some structure that helps answering your question.

Hint: CS teachers are a devious, sadistic bunch. This might be a trick question...