two snakes(pythons,actually)of same size and shape start swallowing each other by the tail with the same speed. What will happen ultimately?

This is a nice question that makes you think a lot. In a cartoon, you would probably see the two snakes stuck together in a ring that gets smaller and smaller and then dissapears with a loud "pop!". If you imagine a picture that is more true to life, it seems that when the ring gets smaller and thicker, then swallowing becomes more and more difficult so the snakes would probably get stuck and choke at some point.

The cartoon image makes no sense: the mass of the snakes is always preserved, so they cannot both dissapear. The real life image seems to challenge the mathematical notion of "eating at the same speed": Why can't we picture two snakes completely eat each other up at the same speed? This is where the subtle deception takes place: Suppose that each snakes weighs 10 kilograms and eats 1 kilogram per minute. Then each snake could eat the other one in 10 minutes. Lets see what happens: after 5 minutes, snake A has eaten 5 kilograms of snake B, so it has gained 5 kilogram. However, it has also lost 5 kilograms which were eaten up by snake B. So the weight of snake A is still 10 kilograms; similarly the weight of snake B is still 10 kilograms. So, instead of having half the job done, they are still at the beginning. Five minutes later, they still have 10 more kilograms to eat, and so on: they have to go on forever, they can never finish up.

Zoologists would probably know if it sometimes happens that snakes eat up their own tails. It looks silly and it would probably be fatal (if they cannot spit it out). But I have seen so many dogs run after their own tails that I would not be surprized to learn that snakes do it to.