I'm so not sure about the "They move in a circle-theory".
The distance between the snakes increase, yes. But I think the snakes would keep moving innwards as the snake they were eating got smaller.
Imagine you have three snakes and but them all in a circle so that they just touch each other like this:
Snake one's mouth touches snake two's end, etc.
If they are to take a bite of each other they can't, because the distance will increase as everyone grows shorter. So imagine you just cut of a centimetre of each snake's tail.
They can no longer touch each other. But if you then move every snake a bit closer to the "centre", then they will once again be able to touch each other. If you keep on like that the circle will obviously become smaller.
...Or?