What does it take for a third world country to produce Nobel prize winners?

Not Peace Prize of course. Assume the usual bad state of Government-run education, while tuition for private education is exorbitantly high and catering to privileged kids who prefer PPE (political science, philosophy, economic, etc) courses to reduce wear and tear while studying?

Of course there is a Nobel award in Economics so you’ve answered your own question.

I’m not sure I understand the question. What exactly do you mean by “Third World”? It’s not a term I’ve heard much in recent years, since the end of the Cold War and the rapid development of many countries that used to be considered part of the Third World. Google’s Ngram Viewer seems to agree that it’s on the decline. Far more often I see countries classified by HDI.

Wikipedia has a list of Nobel laureates by country. Even if you exclude the literature and peace prizes, the former Third World countries Venezuela, Brazil, Argentina, Saint Lucia, Mexico, India, Pakistan, Egypt are all represented. I think all of those have Medium to High HDI scores these days, though.

The honest answer is for the best and brightest in the third world to emigrate to Europe or North America, do research here and then win the prize.