Henry Ernest Dudeney/Puzzles and Curious Problems/324 - The Two Snakes/Solution

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Puzzles and Curious Problems by Henry Ernest Dudeney: $324$

The Two Snakes
Suppose two snakes started swallowing one another simultaneously,
each getting the tail of the other in its mouth,
so that the circle formed by the snakes becomes smaller and smaller.
What will eventually happen?


Solution

Dudeney is vague:

We cannot say how much of each snake must be swallowed before a vital organ is sufficiently affected to cause death.

Each snake, of course, has a stomach which is a fraction of its actual length, and of a limited size, and when one snake has swallowed enough of the other to fill its stomach, there it will stop.

It is of course theoretically possible, for snakes which have large enough stomachs, for part of its own tail to be inside its own stomach.

In the extreme, one supposes there will be a tight hard ball of many layers of extremely full snakes, both digesting each other torpidly, until both are dead.

Unless, of course, a snake's skin is proof against the digestive juices of the stomach of the other, in which case one also presumes they will eventually regurgitate each other.


Dudeney continues:

But we can say what will not happen -- that the snakes will go on swallowing one another until both disappear altogether!
But where it will really end is impossible to say.

The author of this page has resolutely refused to google it.


Sources

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