I came across a funny example of problem formation yesterday (cc @Meaningness).
@thilogross, a researcher in Bristol (where I live), showed that Bristol's version of the Königsberg bridge problem (https://en.wikipedia.org/wiki/Seven_Bridges_of_K%C3%B6nigsberg …) *is* soluble, and walked the resulting 33 mile circuit...
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The original walk is here: https://www.bristolcivicsociety.org.uk/bristol-bridges-walk/ … (new version at https://reallygross.de/ops/bridgewalk as there are now more bridges!) Now the interesting bit for me is how much of the work was just defining the problem:pic.twitter.com/2ejPqmLgr9
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Euler's solution involved a creative act of seeing-as, abstracting landmasses as nodes and bridges as lines. But once he'd done that, 18th-century Königsberg maps pretty cleanly onto the problem.pic.twitter.com/A8m3FhyNJo
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Modern Bristol however is a mess. It's roughly two islands in a river, like Königsberg, but there's also two little islets off the west island, and a tributary branching off the river. Also there are a LOT of bridges:pic.twitter.com/nKavotTKPW
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More importantly, there are a bunch of decisions to be made about what counts as a bridge. This is purpose-dependent: rail- and car-only bridges don't count in this solution because the whole point is to be able to walk it.
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Then you have to decide whether bridges like these are two bridges or one bridge. (In this case they all get counted as two.)pic.twitter.com/JudF3BRAvd
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Finally you have to decide how big the bridges have to be to count. The two bottom bridges off the islet count in this image. The top ones are little lock gates and are excluded.pic.twitter.com/1dgATEzXeW
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Anyway after spending way too much time on this I think I actually have to walk it some time. Though a new bridge is being built, so the route might completely change by the time I get to it!
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We should do it! Though it's a few years since I walked anything over 20 miles, so I'd probably be pretty tired and grumpy by the end!
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Replying to @drossbucket
It could be done in parts on different days maybe. We might want to take longer to include the coffee and cake stops.
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Replying to @_awbery_
Yes, those are important, and the instructions do helpfully include some pub stops too... (I do also fancy doing it in one day, but that's going to be hard in daylight hours for the next few months anyway)
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