What is Euler's Dilemma?

Answer 1

Euler's dilemma is based on the seven bridges of Konigsberg. The question was could one start at one point and return there having cross each bridge once and only once. The answer, as Euler proved, was No.

This question has important consequences for graph theory and, later, for topology. A popular version of the dilemma was to draw figures without lifting pen from paper.

For more on the Bridges of Konigsberg, see the attached link.