The Flying Squirrel-Frog Puzzle

While I enjoy reading The New York Times for its news coverage, I especially look forward to each Monday when they post a new math puzzle online in their Numberplay column.

Several months ago, I shared a Numberplay puzzle from former Key Curriculum editor Dan Bennett. Now I’d like to recap the Numberplay puzzle from last week:

A flying squirrel-frog is being chased by two cats. Here is how the chase goes:

Step 1: The cats go half the distance from where they started to where the squirrel-frog is.

Step 2: The squirrel-frog jumps into the air and glides down, landing on the opposite side of the cat farthest from it, exactly as far from that cat as when it jumped.

These steps repeat until the cats get close enough to swipe the squirrel-frog down, or else realize they will never catch the squirrelly animal.

In which starting configurations will the cats catch the flying squirrel-frog? In which configurations will the flying squirrel-frog escape?

When I read this problem, I immediately wondered whether I could model it with Sketchpad. Before long, I had a working version ready to go. Below you can try it with Web Sketchpad.

Start by dragging the cats and the squirrel-frog to any location you like. Then, press Move Cats and Move Squirrel Frog to run the simulation once. Continuing pressing the two buttons, one after the other, to see whether the cats catch the squirrel-frog.

I played with this sketch for a while, trying many different starting locations for the cats and the squirrel-frog. I made some observations, talked about them with my colleague, Scott, and then looked in the Comments section of the Numberplay blog to see how other people had approached the puzzle.

What observations and conjectures do you have?

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