Brisbane River Ride and the 7 Bridges of Koenigsberg

Brisbane is justly famous for its river cycle path. With five cycleway crossings it draws one into complex choices in graph theory: how to cycle the River Ride by crossing each bridge exactly once only (fractional crossings excluded) without using a boat.


While not as hard as the 7 Koenigsberg bridges problem, which was proved impossible by Euler in 1735, the “River Ride problem” is one that also cannot be solved.

With an odd number of connections of two nodes, you end up on the wrong side to where you begin. You have to cross at least one bridge twice.

Notwithstanding this, it has become something of an early morning ritual for Brisbane cyclists to “traverse the bridges” in vain search of a topological loophole. We set out to observe and document the some hundreds of cyclists who daily toil with this conundrum, the social behaviour now more fascinating than the original problem.

Fearing for the mental well-being of the cycling populance engaged in such futility, Anna Bligh has acted quickly to start construction of an additional 6th cycle bridge. Soon it will be possible cross all cycle bridges exactly once. New legislation has been mooted that requires only pairs of cycle bridges to be built in future.

We begin by entering the bike highway at the Mt Cootha overpass. At this point the path could be described as (a) continuous and smooth (function).

I notice a steel frame hybrid with mudguards that I find somehow fascinating and I quickly latch onto the back.

Across the first bridge:

Past the “Francis lookout”, implying that we have climbed, and indeed in the distance:

Past the 2nd bridge (where trolls live).

Chasing the ochre T-shirt:

Over Oxley creek (tributary bridges not counted):

Past the Patrick Rafter Arena (where the rider is taunted by a topologically complex scupture)

The 3rd cycle bridge:

Getting closer:

A tower that predates the bridges. Thought to regulate ferry crossing problems.

Riders in obvious torment (“which side are we going to end up on this time…”):

Approaching the 4th and newest cycle bridge. Opened last month causing these unforseen problems.

Closer view. Note the cyclist in the boat. This is cheating.

Southbank. The 7 here clearly referring to the Koenigsberg bridges.

The 5th cycle bridge:

… the one with the coffee shop in the middle.

A cyclist with very hairy legs comes between me and the ochre T-shirt!

Sign warning that more entangled conditions ahead as path weaves over and under car & cycle bridge crossings.

Mathematicians working day and night trying to sort it all out:

Closing in…
.. but dropped again.

While such bridge problems may appear trivial, one needs only to look at the fate of Koenigsberg. Almost completely destroyed by the RAF in WWII (reducing the number of bridges) then renamed Kalingrad and becoming part of Russia. Brisbane’s 6th cycle bridge will open early next year.


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One Response to Brisbane River Ride and the 7 Bridges of Koenigsberg

  1. 123leah says:

    Not me

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