Trace It!

Probability Level 1

Can you trace this entire figure?

Things to keep in mind while tracing:

1 ) 1) No picking up your writing or tracing tool.

2 ) 2) No doubling back along a line already traced.

No, It's Impossible Yes, I Can

Zandra Vinegar by Zandra Vinegar

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3 solutions

Zandra Vinegar Staff
Nov 16, 2015

Here's one way to do it:

There are several others, but they will all start/end at the same two places (either of which can be the start or the end of the journey).

19 Helpful 0 Interesting 0 Brilliant 0 Confused

I just did opposite to your method :)

Omkar Chavan - 5 years, 6 months ago
Charity Aghahowa
Nov 16, 2015

Start from 1 and work to 10

5 Helpful 0 Interesting 0 Brilliant 0 Confused
Asif Mujawar
Nov 14, 2015

Start from odd vertex

4 Helpful 0 Interesting 0 Brilliant 0 Confused

Hello I can't understand.... Would you please explain

Debmalya Mitra - 5 years, 7 months ago

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Asif means that you need to start at one of the two intersections that have 3 approaches.

Here is the Graph Theory vocabulary for this:

  • The intersections are called vertices (singular=vertex)
  • The number of incoming edges for a given vertex is that vertex's degree.

There are two degree 3 vertices in this graph, one on the far left and one on the far right. And Asif is correct that in order to trace the entire figure in one continuous path, you need to start at one of these vertices and end at the other.

Why?

There's no way to fully use those two degree 3 vertices without stopping or starting at each of them. This is true because just "visiting" a junction in the middle of a journey would require having one incoming route and one outgoing route per visit, so two of the routes connecting to the junction would be used up every visit and some even number would get used in total.

But since every junction besides these two special ones has 2 or 4 incoming edges, it is possible to trace the entire figure in many different ways, so long as you start and stop at the two "special" odd-degree vertices.

Hope that clears things up!

Zandra Vinegar Staff - 5 years, 7 months ago

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Thank you, very much

Debmalya Mitra - 5 years, 7 months ago

What do you Mean by odd vertex?

Vishal Yadav - 5 years, 7 months ago

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An odd vertex is a vertex with odd number of connections

Anand Chitrao - 5 years, 7 months ago

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