konigsberg bridge problem. konigsberg is now known as kaliningrad, russia
TRANSCRIPT
Konigsberg Bridge Problem
Konigsberg is now known as Kaliningrad, Russia
Konigsberg Bridge Problem
Konigsberg Bridge Problem
Konigsberg Bridge Problem
Is is possible to walk through Konigsberg and cross every bridge exactly once?
A popular puzzle of the day was this:
1736: Leonhard Euler Proved that such a walk is impossible.
In doing so, he was the first person to make use of Vertex-Edge Graphs.
Konigsberg Bridge Problem
The town can be drawn like this.
The town can be drawn like this.
The town can be drawn like this.
Each vertex is a landmass. Each edge is a bridge.
Euler’s insight:
While walking through Konigsberg, each time you visit one of the landmasses, you use up two of the bridges.
Euler’s insight:
Euler’s insight:
Euler’s insight:
Euler’s insight:
Euler’s insight:
Euler’s insight:
Euler’s insight:
Euler’s insight:
Euler’s insight:
Euler’s insight:
Euler’s insight:
Euler’s insight:
Euler’s insight:
• If a landmass/vertex has an odd number of bridges/edges, you must start or end on it.
• If you have more than two vertices with an odd number of edges, then it is impossible!
• If you have zero or two, then it is always possible.
3
3
3
5
This has 4 odd vertices, so it is impossible.
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Draw the bold black contour of the Puzzlers Paradise Palm without taking your pencil off the paper or going along the same line twice.
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Draw the bold black contour of the Puzzlers Paradise Palm without taking your pencil off the paper or going along the same line twice.
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Draw the bold black contour of the Puzzlers Paradise Palm without taking your pencil off the paper or going along the same line twice.
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Draw the bold black contour of the Puzzlers Paradise Palm without taking your pencil off the paper or going along the same line twice.
From Puzzlersparadise.com
Draw the bold black contour of the Puzzlers Paradise Palm without taking your pencil off the paper or going along the same line twice.
From Puzzlersparadise.com
Draw the bold black contour of the Puzzlers Paradise Palm without taking your pencil off the paper or going along the same line twice.
From Puzzlersparadise.com
Draw the bold black contour of the Puzzlers Paradise Palm without taking your pencil off the paper or going along the same line twice.
From Puzzlersparadise.com
Draw the bold black contour of the Puzzlers Paradise Palm without taking your pencil off the paper or going along the same line twice.
From Puzzlersparadise.com
Draw the bold black contour of the Puzzlers Paradise Palm without taking your pencil off the paper or going along the same line twice.
From Puzzlersparadise.com
Draw the bold black contour of the Puzzlers Paradise Palm without taking your pencil off the paper or going along the same line twice.
From Puzzlersparadise.com
Draw the bold black contour of the Puzzlers Paradise Palm without taking your pencil off the paper or going along the same line twice.
From Puzzlersparadise.com