Competition time

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May 22, 2007
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Kawasaki
halffastcycling.com
#1
Not a caption competition this time. A problem-solving competition. The usual prize is up for grabs. Are your little grey cells ready for a challenge?

Showa Kinen Koen in Tachikawa is a park that has bike-only paths, joined together by roundabouts. The bike paths have separate lanes in each direction. It's great fun to trundle around in there with no traffic lights or cars or pedestrians.



On a long ride that passes the park, I want to enter through one gate of the park and exit by another. I have to pay to go in the park. I want to 'do' the whole park, to get my money's worth, but I don't want to waste time.

Here's the official map.

http://www.showakinen-koen.jp/map/img/map.pdf

I can turn around either at gates (A B C D E) where there are U-turn points, or by going around a roundabout (1 2 3 4). I must ride clockwise around the roundabouts - no sneaky short-cuts. If I want to U-turn at a roundabout, I must go all the way around it. Each roundabout is 200m all the way around.

I must enter at Gate B, and exit at Gate D.

Q1 What is the optimum (i.e. the shortest) route through the park that passes along all of the bike lanes in both directions?

Q2 What distance would I travel if I rode that route? (Hint: You will probably need to measure distances using either the map or an online mapping tool like RideWithGPS.)
Edit: The maths need not be hard. Graph theory could be applied, but it's probably easier to work it out empirically with a pencil and paper.

Another edit: Here are the distances between points, so you don't even have to measure them.


 
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May 22, 2007
3,617
1,454
143
Kawasaki
halffastcycling.com
#6
Earlier this evening I attempted to negotiate the awarding of an exclusive, time-limited "Competition Winner" avatar badge with @TCC. He wants to see whether there's any interest in such cerebral matters before committing valuable server resources.

So [casts eyes about desk] this exclusive 'Dog Towel' adorable and highly absorbent ornament will go to the first posted solution that either matches mine or is convincingly more accurate than my own. (Conditions apply. You pay only $29.99 shipping and handling.) Extra credit will be given if you can guess where the prize came from in the first place. @jdd you can use it to dry off after your swim or clean your bike or whatever (if you win).

 
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