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What’s the Bare Minimum Number of People for a Mars Habitat?
(www.universetoday.com)
This is a most excellent place for technology news and articles.
Considering humanity was knocked down to about 1200 people about 800,000 years ago and we survived without any technology to speak of, let alone genetic testing that would help determine maximum diversity, I'd say you might be surprised.
That assumes that everyone will be willing to have children with just about anyone, regardless of their personal opinion of them, and regardless of whether or not they even want children to begin with. You can't selectively breed humans without massive human rights violations.
many things were very different then.