‘THE SEVEN BRIDGES OF Königsberg’, as well-educated readers of this blog will know, is a famously unsolveable problem in mathematics and the basis of graph theory. It’s not possible to design a walk over the seven bridges (as they were in the 18thC) in such a way as to cross each one only once. It’s lucky I’d never heard of the problem before I spent a wonderful Saturday making a round trip of the six vehicle ferries of Greater Sydney, challenging myself to see if I could cross them all without ever retracing my path. Four ferries cross the Hawkesbury River, one crosses Berowra Creek, and the other crosses the Parramatta River.

You have to go a surprisingly long way to catch them all. It was mostly a pretext to run any gremlins out of the motorbike I have spent hours repairing back into rideable condition, and to ride in some stunningly beautiful parts of Sydney, but it seems to me a pointlessly satisfying navigation exercise—you can work it out as a problem of nodes like Euler did, by trial and error with google maps like I did, or any other way. Cross every ferry once, no u-turns or retracing your path. There’s a large, but finite, number of ways you can do it.

The vehicle ferries, for the record, are:

• Berowra Waters
• Mortlake Ferry (AKA Putney Punt)
• Lower Portland
• Sackville
• Webbs Creek
• Wisemans Ferry

I did it in ~280km, taking a bit over 7.5 hours. Beware: some of the ferries run 24/7, while others have limited hours. There is some unpaved road north of the Hawkesbury River. None of the ferries have a toll; you do not need to pay the ferryman.

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