Didn't really know where to post this but I'll give it a go here if nobody minds!
I have come across a game called Tied in Knots but I'm not sure it is possible to complete it successfully every time. The rules are:
1.Have everyone stand in a circle.
2.Reach out with their left hand, and grasp someone's hand.
3.Reach out with the right hand, and grasp someone else's hand. Each player must be holding hands with two different people.
4.Challenge them to undo themselves into a circle.
It can work with any size group, but small to medium size groups work best.
The groups must always have an even number.
I have used this as a childrens' club activity. They usually managed to untangle themselves (sometimes with a bit of cheating, else they'd twist their arms off!); it was always fun. It is not guaranteed to finish with everyone in one circle - they could form two or more groups.
Your link didn't open Jonathan-Joe but I looked it up on youtube and the video I saw was one of a bunch of kids doing it with a rope. However it wasn't clear how they started off. Skin the snake looks like good fun but it is the Tied in Knots game that I'd like to learn more about.