At a rally on July 5th, 2018, Trump stated the following: "Lets say I'm debating Pocahontas, right? I promise you I'll do this. I will take - You know those little kits they sell on television for two dollars? 'Learn Your Heritage!' Guy says 'I was born in Scotland!' Turns out he was born in Puerto Rico and that's OK. That's good. You know. Guy says 'I was born in Germany' well he wasn't born in Germany he was born someplace else. I'm gonna get one of those little kits and in the middle of the debate when she proclaims that she's of Indian heritage because her mother said she has high cheek bones. That's her only evidence - That her mother said that she has high cheek bones. We will take that little kit and say - But we have to do it gently because we're in the 'me too' generation so we have to be very gentle. And we will very gently take that kit and we will slowly toss it, hoping it doesn't hit her and injure her arm even though it only weighs probably two ounces. And we will say 'I will give you a million dollars to your favorite charity, paid for by Trump, if you take the test and it shows you're an Indian.' You know. And lets see what she does, right?"
On October 15th, 2018, Warren released the results of a DNA test which indicated that she has Native American Heritage. Warren further demanded that Trump send a million dollars to NIWRC, a nonprofit working to protect Native American women from violence.
The DNA test results indicated the following: "While the vast majority of the individual’s ancestry is European, the results strongly support the existence of an unadmixed Native American ancestor in the individual’s pedigree, likely in the range of 6-10 generations ago."
On that same day, a reporter questioned Trump in Warner Robins, GA regarding the issue. The dialogue was as follows:
Reporter: "Senator Warren released some of her DNA results that show a strong likelihood that she does have native American roots."
Trump: "How much? 1/1000th?"
Reporter: "Do you owe her an apology?"
Trump: "No, I don't. Absolutely. Do I owe her? She owes the country an apology. What's the percentage? 1/1000th?"
Reporter: "I don't have the exact numbers."
Trump: "OK. Tell me when you have the percentage. When you have the percentage tell me what the percentage is."
Reporter: "What about the money that you told her you would ... "
Trump: "You mean if she gets the nomination, in a debate where I was gonna have her test it? I'll only do it if I can test her personally. OK? That will not be something I enjoy doing either."
1. The DNA test results do not show that Warren is an Indian
Trump's "challenge" was clear: "take the test and it shows you're an Indian." The DNA test results provided by Warren do not show that Warran is an Indian. Rather, the DNA test results show "the existence of an unadmixed Native American ancestor [...] likely in the range of 6-10 generations ago."
DNA test results showing a Native American ancestor 6-10 generations ago aren't sufficient to show that Warren is an Indian. For simplicity's sake, assume for the moment that each generation going back reduces the content of an individual's heritage by 50% (half from mother, half from father). An ancestor six generations ago would then mean that Warren is approximately 1.56% (1 / 2^6) Indian, and going back 10 generations would be approximately ~0.01% Indian (1 / 2^10).
Would you say that someone is a Korean because he is 1.56% Korean? Or that someone is an Arab because he is 1.56% Arab? No, you wouldn't. In common parlance, the meaning of "an Indian" means someone who is substantially more Indian than Warren's test results show.
Trump brought this up when questioned by the reporter. Trump said "What's the percentage? 1/1000th?"
2. Warren failed to comply with the terms of Trump's "challenge"
Trump's "challenge" contemplated that Trump would collect the DNA sample, choose the DNA test provider and otherwise exercise control over the testing. It matters who collects the DNA, who choose the provider and who exercises control over the testing process. It matters because there's an obvious opportunity for fraud and Trump doesn't trust Warren. The only way Trump can be satisfied that the results are legitimate is by exercising control over the testing process.
This did not happen. What did happen was that Warren apparently exercised full control over testing process and Trump was consequently unable to verify the legitimacy of the results. Trump brought this up when questioned by the reporter. Trump said "I'll only do it if I can test her personally. OK?"