@John Fredsted Thank you!! :)

@Kitonum Thank you! That made me understand it. :-)

@Kitonum 

Is it possible to write the code with the set-up that I have? I would really like to keep my procedure as it stands.

@tomleslie  Hi! 

1. The problem says that it is not possible to go back immediately the way you came from, but it is possible to go downwards, because you can walk straight on and then make a right turn and then you are going downwards. My issue is that the algorithm should stop when ri=rj for any 0 <= j <= i-2 (j=0..M) (i=0..N) (ri=[xi,yi])

2. This model that I should use does not allow to go immediately backwards the way you came. The model works fine before I implement (1) the if-test that should break/stop the algortim(i.e. when the path crosses itself)).

Please use the format that I used. 

This works aswell, yes! Thank you. :-)

@taro 

@Kitonum 

Thank you! I saw that I forgot the minus. Nice method.

Yes! This did it! Thank you. The purpose is that I want to write the expression like in the problem text I got. You know: "Show that ......" :)

@YasH 

Hi! Thank you for the answer, but when I tried your snippet, the minus before 2 were missing, but the signs inside the expression were correct. This is what is should look like:

@Kitonum