Apparently the only food a cockroach won't eat is cucumbers. Apparently it is because of a chemical, trans-2-nonenal, present in cucumber. Ants don't like it either.
Yes, cucumbers is coming up alot. I also found this site. Depending on the type of cockroach, They won't eat leaves which are green or yellow or damp, i.e. any leaves containing moisture are unsuitable.
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