Clarification: I recently read that 1 in 200 men in the world are directly related to the infamous Mongolian ruler who died in 1227. I was wondering roughly or by "guestimation" how many children someone today would have to bear to achieve that kind of genetic contribution and how long that would take.
I think that this question probably belongs in /r/AskScience or a similar sub because it isn't a historical question. It's a scientific question based on a historical premise.
Though, I did some digging and found a Smithsonian Article from January that highlights a new study. This study found that 10 other men left genetic legacies similar to Genghis Khan.
In addition, the historical premise that your question is based on has been discussed at length in the questions below:
1 in every 200 men is a descendant of Genghis Khan. Is this really true?
How accurate is this: 8% of Asians are direct descendants from Genghis Khan?"
Are there more direct descendants of Genghis Khan himself than Jewish people?
EDIT: Formatting