GO Talent - Problem Solvers - Intermediate
Welcome to GO Talent - Problem Solvers - Intermediate!
This is our sample lesson. This session is likely to take around an hour to complete, and each week we have an online meeting. Sessions can be completed anywhere, anytime, and most work can be completed using our online portfolio.
In this session our focus is on Classic Maths Problems. Classic maths problems are those that have been given to us throughout history and have stood the test of time as fascinating puzzles.
Today we are looking at the Seven Bridges of Konigsberg problem.
Time for some imagining... Konigsberg (which translates as 'king's barrow) was a city in Germany (now Russia) that straddled two sides of a river, the Pregel River. Budapest (in Hungary) is much the same, with the river Danube flowing through it, just in case you were wondering!
Here is a painting of what Konigsberg Castle looked like before World War One.
Image credit: public domain, unknown author
So, the river had two islands in it, and seven bridges that crossed the river and connected the islands. Here's a diagram...
Image licensed for use with attribution: CC BY SA 3.0
So the puzzle is (drum roll please!) can you, a visitor to the lovely city of Konigsberg, walk around and see the whole city and only cross each bridge once?
What do you think? How you might check this out?
Things to ponder:
- it doesn't matter where you start or end
- you don't need to start and end in the same place, just make sure you visit every part of town and cross every bridge once
- do you think it would help if there were more or less bridges?
- do you think it would help if the position of the bridges was different?
Here are three useful hints:
1. to help keep things straight, it is useful to imagine visiting landmarks in the city... in the picture below some landmarks have been added! Or draw your own version and label each piece of the town.
Image credit: By Original uploader was Xiong at en.wikipedia - Transferred from en.wikipedia, CC BY-SA 3.0, https://commons.wikimedia.org/w/index.php?curid=4522113
2. re-create the map as network diagram. Make each bridge into a line (or path) each piece of land as a dot (or node). Then move your pencil around the network by moving along the paths to the nodes.
3. reduce the complexity of the puzzle - imagine there are only six bridges? How does this change what happens?
Now let's think about the solution:
Leonhard Euler was a mathematician from Switzerland 'solved' this puzzle in 1735, by not solving it!! Read more about it here.
Try out this similar puzzle:
Can you create a similar network puzzle? Have a go and publish your work in a new blog post in your Problem Solver's Blog (here there would usually be a link to a short tutorial on how to do this).
In Developing your problem solving skills today, find out about a 'classic' mathematician, maybe someone like Euler. What do you have in common with this person?
Unless specified otherwise, all images on this page are from openclipart.org, licensed for unlimited commercial use