The Seven Bridges of Königsberg/Section 9

by Leonhard Euler

Let us now return to the Konigsberg problem (Figure 1). Since there are five bridges, a, b, c, d, e, leading to (and from) island A, the letter A must occur three times in the expression describing the route. The letter B must occur twice, since three bridges lead to B; similarly D and C must each occur twice. That is to say, the series of eight letters that represents the crossing of the seven bridges must contain A three times and B, C and D each twice; but this is quite impossible with a series of eight letters. Thus it is apparent that a crossing of the seven bridges of Königsberg in the manner required cannot be effected.