The Königsberg bridges problem
Behold the turtle only makes progress when he sticks his neck out.
James Bryant Conant
Background
The Königsberg bridges problem originates in the city of Königsberg, Prussia (now Kaliningrad, Russia). This city was built on the banks and islands of the Pregel (Pregolya) River.
The map shows how the seven bridges are situated on an upper bank, lower bank, Island 1, & Island 2.
Problem
As the residents of Königsberg travel around their city, a curious question is poised:
Is it possible to take a route that crosses each bridge only once? And if so, how?
Hints:
- Try a guess and check strategy.
- Use diagrams to show different path variations of bridge passage.
- Discover that an odd number of bridgex in combination with the two island seems to always traps you without another bridge to cross to get to a remaining bridge.
- Systematically start at each bridge to eliminate starting points that won't work.
1735 Leonhard Euler, of Switzerland, uses graph theory to determine a solution of the Königsberg bridge problem.