chunk: Solution: Two problems are posed, the first of which is resolved by word-play. Much later, after the solutions to Knot VII, Carroll returns to Knot VI, to describe the second problem in detail, and to rebut criticisms of readers (who were identified by name) that they were duped.
  Knot VII, Petty Cash. The aunt and niece encounter "by a remarkable coincidence" others who are travelling not only on the same train, but at the same station, on the same day, at the same hour. Lunch bills are muddled due to the aunt's reluctance in writing down numbers that could "easily" be memorised.
  Solution: Carroll gives a solution which "universally" produces an answer, then gives detailed critiques of several other approaches that only "accidentally" give a solution.
  Knot VIII, De Omnibus Rebus. The travellers of Knot VI are leaving Kgovjni with relief, when a mathematical problem occurs to one of them.