Königsberg · East Prussia · 1736

Cross every bridge over the Pregel exactly once — no bridge twice, none skipped. Leonhard Euler proved it cannot be done. See for yourself, then find out why.

Pregel River N

Your Walk 0 / 7

Choose a landmass to begin your walk across Königsberg.

Bridge Log

— no bridges crossed yet —

Landmass Degrees

LandmassBridgesParity

The Eighth Bridge off

Add a fictional bridge straight between the two banks. It changes the parity of the landmasses — and suddenly a walk becomes possible.

Why is it impossible?

In 1736, mathematician Leonhard Euler proved that a route crossing every Königsberg bridge exactly once cannot exist — and in doing so, invented what we now call graph theory.

Euler's insight: every time your walk passes through a landmass (not counting the start or the very end), it uses up two bridges — one in, one out. So every landmass, except possibly your start and your end, must have an even number of bridges.

A walk like this is only possible if the graph has zero or two landmasses with an odd number of bridges. Königsberg has four odd landmasses — so no such walk can exist, no matter where you start.

Fun fact: only 5 of the original 7 bridges survive in modern Kaliningrad — two were destroyed in WWII bombing raids.