I worked hard on this one. For years I have been fascinated by puzzles that appear in movies. Some of notable examples include the overwhelming jigsaw puzzle in Citizen Kane, the mathematical game Nim as it appears in Last Year at Marienbad, and the maze in Labyrinth. For those of you who are interested in exploring further, see the web page on mathematics in the movies.

Harry Potter and the Boggling Bottles. When I read the first Harry Potter book I was fascinated by the logic puzzle that occurs near the end of the book. The author doesn't give quite enough information for the reader to be able to solve the puzzle, but it is clearly a real well thought-out problem. So I set about figuring out what you can and can't deduce from the given information.

A Pentomino Odyssey. After compiling the puzzles based on the movie 2001 for the January Boggler, I was left with one extra puzzle, which I delayed till this issue. I was familiar with the first question (the shortest Pentomino game on an 8x8 board) from Martin Gardner's original writeup of Pentominoes in his Scientific American column Mathematical Games.
     Revisiting that beautiful problem, I became curious about shortest possible games on other size boards. I explored all square board sizes up to 14 by 14, then chose the most interesting cases for this puzzle. I wrote to Pentominoes inventor Solomon Golomb, and he set about exploring the problem further, especially on rectangular boards.

EXTENSION: Here's a summary of the best known solutions on various sized boards.

Mathematics Takes a Bow. I asked many people for interesting mathematical problems in recent major movies. The most interesting recommendation was Good Will Hunting. I rented the movie and was pleased to see that the camera lingers long enough on the problem given at the beginning of the movie that I could actually transcribe it. I was disappointed to find that the problem has nothing to do with how it was described, but pleased to see that it was a real piece of mathematics.
     Searching the web I found a fascinating story about the mathematics in Good Will Hunting on the web site for the American Mathematical Society, which is the organization for professional mathematicians.
     This led me to contact physics professor Patrick O'Donnell of University of Toronto, originally hired as an extra on the film (he is the bearded patron in a bar scene), who provided most of the mathematics that actually appears in the film. Patrick graciously explained that the filmmakers were intent on treating the mathematics seriously.
     First they listened to a lecture by an MIT mathematician, and wrote down bits of jargon which they wove into the script. Then Patrick pulled together bits of mathematics from a wide variety of papers, inspired by the words in the script. As commonly happens, the story was edited for dramatic effect, which is why the problem on the blackboard has nothing to do with advanced Fourier series.
     As stated, the problem asks for answers in terms of generating functions, which I have always found unnecessarily obscure. So I rephrased the problem in terms of spreadsheets.