The Seven Bridges

The citizens of Königsberg tried for years to walk their seven bridges without repeating one. Euler ended the search in 1736 without leaving his desk: he shrank the city to four dots and seven lines, counted something embarrassingly simple, and invented graph theory on the way. Walk the bridges, get stuck, then see the city the way Euler saw it.

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Stylized map of Königsberg morphing into Euler's graph of four landmasses and seven bridgesNORTH BANKSOUTH BANKKNEIPHOFLOMSEKrämerbrücke — Merchants' BridgeSchmiedebrücke — Blacksmiths' BridgeGrüne Brücke — Green BridgeKöttelbrücke — Giblets BridgeHonigbrücke — Honey BridgeHolzbrücke — Wooden BridgeHohe Brücke — High Bridgebridges crossed 0/7
Königsberg, 1736. The town's favorite impossible errand: cross all seven bridges, each exactly once. Click a landmass to start there, then click any bridge you're standing beside.
Step 1 of 4 — Take the stroll

Walk through any landmass and you spend its bridges two at a time — one to arrive, one to leave. A landmass with an odd number of bridges will eventually hand you a way in with no way out. The only places allowed to be odd are where the walk starts and where it ends — and you only have two feet. Er, two walk-ends.

Königsberg's four landmasses count 3, 3, 5 and 3 bridges: odd, odd, odd, odd. Four ends demanded, two supplied. No cleverness closes that gap — the failure was never in the walkers, it was in the counting.