Fig. 2.

Using chess to illustrate block-city distance and Euclidean distance. White draws the game by moving the King along the blue line, which allows him both to approach his Pawn (threatening promotion) and to catch the black Pawn. In chess, block city and Euclidean distances are equivalent (in this examples, six moves in both cases to reach the square where the two arrows meet). This position was composed by Richard Réti in 1921