Movie: Fermat’s Room

I’m not sure that the indie film Fermat’s Room deserved to win four awards or deserved a nomination for “Best Film” at the Sitges International Film Festival, but it’s got enough gems to keep mathy folks entertained for almost 90 minutes. 

Take, for instance, this great line:

The more you study logic, the more you value coincidence.

In a moment, I’ll tell you about all the great math problems within the film. But first, let me tell you a little about the movie itself.

The general idea (without being a spoiler) is this: Four mathematicians are trapped in a shrinking room. Every so often, a math puzzle appears on a PDA, and they have one minute to enter the correct answer. If they take longer than a minute, the room starts shrinking — literally. Behind each wall is a hydraulic press that pushes toward the center until the correct answer is entered. While working out these riddles, there are two greater puzzles that they are attempting to solve — who would have done this, and how can they escape?

My favorite scene is when the young, brash, theoretical mathematician and the middle-aged, stoic, applied mathematician think they may have found a way to stop the hydraulic presses. “Will it work?” asks the theoretical mathematician.

“The only way to find out is to do it,” says the applied mathematician.

Upon hearing this, the young mathematician starts writing equations on a piece of paper, attempting to prove (theoretically) that their solution will work. The applied mathematician, who has already started to implement the solution, shakes the theoretical mathematician’s shoulder, as if to say, “No, really, we need to try it and see if it works, not just prove that a solution exists.”

It’s a fantastic and not-so-subtle commentary on the tension between theoretical and applied mathematicians. I laughed out loud.

But it’s got more than just great lines. It contains a treasure trove of famous math puzzles. I’ve listed several of them below — without context, so as not to spoil the movie; and without solutions, so as not to spoil your fun in solving them. Enjoy!

1. En que orden estan los siguentes numeros? 5, 4, 2, 9, 8, 6, 7, 3, 1
   (Note: It’s a huge hint that this problem is presented in Spanish. If presented in English, the order of the numbers would be different, and the problem would read as follows: What is the order of the following numbers? 8, 5, 4, 9, 1, 7, 6, 3, 2)
2. Three boxes contain marbles. One box contains red marbles, another contains blue marbles, and the third contains a mixture of red and blue marbles. The boxes are labeled “Red,” “Blue,” and “Mixture,” but none of the boxes contains the correct label. What is the least number of marbles you could remove to know the contents of each box?
3. You have two egg timers, one that measures four minutes and one that measures seven minutes. How can you use them to measure exactly nine minutes?
4. (This one’s my favorite from the movie. I originally read it in a Martin Gardner book.) A professor tells his students, “I have three daughters, and the product of their ages is 36. How old are my daughters?”
   His students work on the problem for a few minutes, then a woman in the class says, “I’m sorry, professor, but that’s not enough information to solve the problem.”
   “Ah, yes,” he says. “I should have told you that the sum of their ages is equal to my house number.”
   “I’m sorry, sir,” she says. “That is still not enough information to solve the problem.”
   The professor asks, “Will it help if I tell you that the oldest one plays piano?”
   “It will,” says the woman. “I now know the ages of your daughters.”
   Based on the information, can you determine the ages of the professor’s daughters?