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# Article: Dr Georgiou's maths challenge: can you solve these Eulerian graphs?

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1. Here's the challenge. :dumbells: Post your answers and I'll update everyone with the full solutions on Friday! :yay:

http://www.thestudentroom.co.uk/cont...ulerian-graphs
2. (Original post by Puddles the Monkey)
Here's the challenge. Post your answers and I'll update everyone with the full solutions on Friday!

http://www.thestudentroom.co.uk/cont...ulerian-graphs
This. Is. Awesome!
3. Tagging some folks might enjoy this Who else...?
4. (Original post by Puddles the Monkey)
Tagging some folks might enjoy this Who else...?
Thanks for the tag!
5. Wow.. this is D1. Never thought I'd find it useful xD
6. a lorra lorra laffs

thanks Puddles
7. (Original post by Student403)
Wow.. this is D1. Never thought I'd find it useful xD
I like that there's actually a way of figuring this out with logic. My method would be random experimentation followed by throwing the pencil out the window
8. (Original post by Puddles the Monkey)
I like that there's actually a way of figuring this out with logic. My method would be random experimentation followed by throwing the pencil out the window
PRSOM
9. (Original post by Puddles the Monkey)
Here's the challenge. Post your answers and I'll update everyone with the full solutions on Friday!

http://www.thestudentroom.co.uk/cont...ulerian-graphs
Hooray! Decision maths is coming in useful

The first graph is quite simple - it has two vertices of odd order hence is semi-eulerian. So, we must start or finish on either of these vertices.

One route to solve graph 1 is BAEDACDBC.

As for graph 2, there are four vertices of odd order. They are A, B, H and E. It is not possible to traverse each edge only once without repeating an edge. The way of solving this optimally is by using the Chinese Postman problem.

Graph 3 is Eulerian - each vertex has an even order. There are many routes to traverse this one in this case - I'm too lazy to list one atm .

EDIT: For graph 3, the number of times a vertex will appear in a route is half of its degree. You can use this to your advantage when trying to find a route

EDIT 2: A route for graph 3 is ABKFEKDEHGFCDIJKCJGKIHKA (I hope I wrote this correctly
10. (Original post by Dapperblook22)
Hooray! Decision maths is coming in useful
11. (Original post by Puddles the Monkey)
That's fine, I love Decision maths; my D1 exam is this Friday and D2 is next Wednesday .
12. (Original post by Dapperblook22)
That's fine, I love Decision maths; my D1 exam is this Friday and D2 is next Wednesday .
Good luck...! I think you will do well
13. (Original post by Puddles the Monkey)
Good luck...! I think you will do well
Thanks
14. Only just seen this, haven't looked at the answers but:

First one:
Spoiler:
Show
B-C-D-B-A-D-E-A-C
Second and third I can't do without a pencil
15. (Original post by Dapperblook22)
That's fine, I love Decision maths; my D1 exam is this Friday and D2 is next Wednesday .
Good luck with it

16. (Original post by She-Ra)
Good luck with it

Yes, I will be completely finished when D2 ends
17. (Original post by Puddles the Monkey)
Tagging some folks might enjoy this Who else...?
me!
18. Ah I remember this from my first further maths applied module back in 1999 (before D1 was even a thing).

Sadly, never did anything more with this sort of thing at university, but I did enjoy my little project on knot theory and group theory.

I'm now interested in how Euler proved his theorem...maybe proof by contradiction?
19. Anyone else doing the challenge?
20. Graph 1:
Spoiler:
Show
BAEDACDB

Graph 2:
Spoiler:
Show
AHIJCDEFGHKIDKJGKABEKFCKB

Graph 3:
Spoiler:
Show
AKIJCDEFGHIDKCFKGJKHEKBA

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