Snakes on a Plane

by Christopher, 2009-07-03 06:07:52

Tags: puzzle mathematics

I wrote this puzzle in the summer of 2006, originally posting it to the newsgroup rec.puzzles (Google groups archive here). It was called "an excellent snake-touching puzzle" on Ed Pegg Jr's blog. I can't remember where I got the idea for the title, though. Oh well.

A 2-dimensional plane contains every snake in this puzzle, of which there are at least one. You may think of a snake as a curve with one end called the snout, one end called the tail, and the rest called the middle. Snakes can't overlap or cross each other, because they're on a plane. The snakes satisfy the following conditions:

1. Each snake is touching exactly three other snakes: one with its snout, one with its middle, and one with its tail.
2. Each snake is touched by one snake snout, one snake middle, and one snake tail.
3. No two snakes touch each other in more than one place.
4. No snake touches itself.
5. No two snakes touch snout to snout, middle to middle, or tail to tail.

What's the minimum number of snakes on the plane satisfying these conditions?

Here's the solution.

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