Snake Escape Puzzle Solution: Designing Passages A and B

The puzzle published earlier today asked readers to design two escape passages for a long snake and a short snake of equal width. The solution is as follows.

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 cannot.

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

The passages must have no moving parts, trapdoors or levers. Snakes have circular cross-sections with uniform diameter. They can wriggle but cannot squeeze through passages narrower than their width.

Passage A requires a loop longer than the short snake but shorter than the long one. The sketch illustrates the design.

The passage is a tube of the same diameter as the snake. Snakes follow the arrows. When the long snake doubles back and reaches the tube’s junction, its body blocks the path, preventing passage. The short snake encounters no such blockage.

Snakes cannot turn “right” at the join because the gap between the top and bottom tubes is insufficient. The cross section shows two overlapping circles. The snake in the top tube cannot squeeze into the bottom tube, so it must enter the loop. When the long snake completes the loop and reaches the junction again, its body in the top tube blocks the lower tube, preventing passage.

Passage B is simpler. It involves a hole in the floor that the short snake cannot navigate due to its body length, but the long snake can pass. This assumes the snake has non-zero rigidity.

Thanks to readers for all the herpetological jokes posted below the line in the original article. Not all of them were as painful as a snake bite.

The author has been setting a puzzle on alternate Mondays since 2015 and welcomes suggestions. Readers can email puzzles to the address provided.