Treebeard's Homepage : Stumpers

# Treebeard's Stumper3 May 2002

Tangled Up Puppet

We're making string puppets in my afternoon Tools & Materials class at Dunn Middle School! I was inspired by the gift of a hopelessly tangled puppet from Mexico. I've noticed that my puppet-in-progress also has an uncanny knack for getting tangled up, and that's the stumper. Consider the simplified three-string puppet shown below. It's easy to make your own with soft cord like shoelaces and a piece of cardboard. Starting with straight untangled strings, I can make each of these braids with just two moves of the puppet piece. Can you tangle and untangle them?

Can you tangle and untangle these puppet strings? You should assume the
top piece is fixed and can't be manipulated, but you can do anything with
the bottom puppet except untie it. How many different moves are possible?
I figure every tangle is just a succession of simple moves one after the other.

To explore this stumper, you should make a simple three-string puppet like mine. I cut the plaque from a scrap of thin plywood, but cardboard works. Be sure you can tell which side is which.

The tangle on the right is especially interesting since it is a classic hair braid. Yes, it's possible to make this with a puppet that's fixed above and below. That means it's also possible to braid your hair without untying it! It's also possible to braid a solid piece of leather, though it looks like it was done in hyperspace! Note that the braided strands are all same-side up.

The hardest part of this stumper might be describing the moves in words. Creating graphics for the moves won't be much easier. But there are a limited number of moves with a three-string rigid puppet, so it should be possible to describe them all. Puppets get tangled-up with one simple move after another, and it must be possible to undo any tangle in the same way!

My fellow Dunn School teacher Dorothy gave me this charming tangled up (and blue) puppet from Mexico a few years ago. I was ready to cut the strings and reassemble it, but Julie managed to untangle it without any cutting. In principle, that's not surprising. If the strings got tangled without cutting, then it must be possible to untangle them with simple moves in the right order. My "Treebeard" puppet-in-progress is on the right, facing a two-week deadline.

"Tangled Up Puppet" is a classic song by Harry Chapin. What other puppet songs can you find?