Koltanowski's most sensational chess entertainment was the ancient exercise known as the Knight's tour, in which a lone knight traverses an otherwise empty board visiting each square once only. Of the countless patterns for achieving this feat, there are trillions of sequences for performing the more restricted version known as the re-entrant tour, wherein the knight on its 64th move lands on its original starting square. For Koltanowski, who claimed to have a "phonographic memory" (a keen memory for sequences), the trick relied on mastering just one re-entrant pattern. He could begin on any square in the sequence and complete the tour by rote. However, it was his original twist that gave Koltanowski's performance dramatic value well beyond the mechanical moving of the knight through the memorized sequence.