Did you solve it? Are you as s-s-smart as a snake?

Earlier today I asked you this slippery question. Here it is again with the solution.

Snakes in a cage

Two snakes of equal width are in a cage. One is long and the other is short.

Design two escape passages, A and B, that lead from the bottom of the cage such that

The short snake can escape down A, but the long snake can’t.

The long snake can escape down B, but the short snake can’t.

The passages must have no moving parts, trapdoors or levers. Assume that the snakes have circular cross-sections, and the diameter is the same at all points along their bodies. The snakes can wriggle but they can’t squeeze through passages that are narrower than they are wide.

Solution

Passage A must have some kind of a loop, where the loop is longer than the small snake but shorter than the long one. Here’s a sketch of an escape route that works.

The passage is a tube that has the same diameter as the snake. The snakes will follow the arrows. When the long snake doubles back and reaches the place where the tube meets itself, it cannot get through because its body is blocking the way. The short snake does not have that problem and can pass.

Note that a snake cannot turn “right” at the join. This is because the gap from the top to the bottom tube is not wide enough. To show this I have drawn the cross section at the join. It has the outline of two overlapping circles. When the snake is in the top tube, it cannot squeeze into the bottom tube, so it must follow the arrows and go into the loop. When the long snake goes round the loop and meets itself again, its body in the top tube will cut off part of the lower tube, so it will not be able to get through.

Passage B is simpler. You just need the passage to pass though some kind of hole in the floor that the short one will not be able to move over without falling in, but that will not pose a problem for the long one. (We need to assume non-zero rigidity in the snake.)

Thanks for all the herpetological jokes below the line in the original post. Not all of them were as painful as a snake bite!

I’ll be back in two weeks.

Source: Kvantik Magazine 2014.

I’ve been setting a puzzle here on alternate Mondays since 2015. I’m always on the look-out for great puzzles. If you would like to suggest one, email me.