No , You NEED to choose 2 challenges . No bonus for 2 challenges . <| sep |> In this video , you are not rotating the entire circle but only the countably infinite set of points which has been marked in by numbers in the video . This part of the video is a nice illustration of weird things which can happen with infinity it is essentially Hilbert ' s hotel ' sparadoxoftheGrandHotel , but don ' t think it has too much to do with how the Banach Tarski paradox actually works Note I did not watch the entire video . The proof of the Banach Tarski paradox requires some amount of mathematical sophistication to understand , but it relies on two essential facts the axiom of choice without which it cannot be done the free group on two generators is non