This question was asked by mathematician Percy Diaconis in 1988 and was open until this year, when the solution was found by Robert Hough, assistant professor at mathematics department of SBU and Yang Chu, an undergraduate student working with Hough as part of Enhanced REU program sponsored by the Summer Math Foundation. They have posted a preprint in which they provide a full answer to this question.
Read more about it in this article in Quanta magazine.