Konigsberg Bridge

Konigsberg is a city which was the capital of East Prussia but now is known as Kaliningrad in Russia. The city is built around the River Pregel where it joins another river. An island named Kniephof is in the middle of where the two rivers join. There are seven bridges that join the different parts of the city on both sides of the rivers and the island.


City of Konigsberg

People tried to find a way to walk all seven bridges without crossing a bridge twice, but no one could find a way to do it. The problem came to the attention of a Swiss mathematician named Leonhard Euler (pronounced "oiler").

In 1735, Leonhard Euler (1707-1783) presented the solution to the problem before the Russian Academy. He explained why crossing all seven bridges without crossing a bridge twice was impossible. While solving this problem, he developed a new mathematics field called graph theory, which later served as the basis for another mathematical field called topology. 

Euler simplified the bridge problem by representing each land mass as a point and each bridge as a line. He reasoned that anyone standing on land would have to have a way to get on and off. Thus each land mass would need an even number of bridges. But in Konigsberg, each land mass had an odd number of bridges. This was why all seven bridges could not be crossed without crossing one more than once.

The problem could have been solved if ONE bridge was removed or added. Which bridge would you remove? Where could you add a bridge?