EULER TRAIL PUZZLE

What is an Euler trail ?
An Euler trail ( Euler path ) is a trail in a finite graph which visits every edge exactly once.

• An Euler trail is a walk on the edges of a graph which uses each edge exactly once.
• Euler trail is also called an Euler chain, Euler walk, Euler path.

Here is the puzzle as you could see in the picture. Your job is to cross each line exactly once without lifting your pen. 

In the following figure consider every marked line as a single line and each must be crossed once without lifting you pen.

Here are some examples already done, but in each case, one line is left ( marked red ) to be crossed . See the figures.

Have you got the solution ?

well, this is impossible to do however hard you try. 

Explanation

Consider the figure below and find the numbers of line reaching the centre of each box.

In the figure you could see that there are three centre points with odd number of lines and hence it is not possible to cross all the edge. If the centre point would have even number of points, then it can be done. Also if three were two centre point with odd number of line, then also it would be possible, but in this case, there are three.

• Euler trail was first put forward by Leonhard Euler while solving the famous problem of Konigsberg bridges in 1736.