The snake that comes out of the egg at '1' has to go in two directions. This is only possible in one way. The snake at '2' can only start in one way too. Cell 2 is not an option, because the snake would have to make a sharp turn. The snake at '3' only has one option because the snake at '1' eliminates the other option. Cell 4 can only be reached by one snake. Because that snake needs to be 7 cells long there is only one way to reach that spot.
Results from the tips.