An interview is not a fairness competition. They are rarely fair and subjective. The end goal of any interview is to enter into a contract which exchanges money for time. The setting of an interview is an informational asymmetric paradigm. Your one sided fairness won’t make the process fair.
You may still want to keep letting your interviewer know that you solved the question before. However, this doesn’t make the process fair. It’s a story that you’re probably telling yourself to make it feel better ;)