Fermat’s Room (2007)

Rated: Unrated, perhaps PG-13, although the previews are R.
Length: 88 minutes
Grade: A-B-AA=A-
Budget: Unknown
Box Office: Unknown—Blockbuster Exclusive

Written and Directed by: Luis Piedrahita and Rodrigo Sopena
Starring: Lluis Homar, Alejo Sauras, Elena Ballesteros, Santi Millan, and Federico Luppi.

Summary:

When four mathematicians are mysteriously summoned to a secret meeting to solve a new enigma, they discover their lives threatened by a room that closes in on them when they fail to solve logic puzzles quickly enough.

Entertainment Value: A-

Okay, this is a foreign film in Spanish, and that is going to dissuade a lot of you from the beginning. But, for those of you who at least sometimes watch foreign films, this was really quite good. Perhaps it’s because I’m a philosopher and have an unnatural affection for the mind puzzles they were solving in this movie, but this was a fascinating blend of intriguing characters, mental activity, and a plot that just kept getting more and more complicated and intriguing. This had been on my “to-watch” list for awhile, and all I can say is that it was well worth the time.

Superficial Content: B-
Drugs/Alcohol B, Sex/Nudity B+, Violence B, Language C
Characters drink casually. There is no real sexuality, but there is a reference to “unspeakable” things at one point. The violence is both the overall premise, some fighting, and descriptions of a car crash harming a small girl. Language is medium, made milder by being in the subtitles, obviously.

Significant Content: A

High intelligence almost always breeds overblown egos, and the thrill of solving-problems is a form of idolatry. Yet many of the things highly intelligent people invest their lives in solving amount to nothing of any consequence in the end.

Artistic/Thought Value: A

There is some interesting thought value to the overall movie, obviously, but a lot of the thought value comes from the individual problems contained in the movie. That’s why this is a film that should only be watched on DVD and never at a theater, and you should pause to try to solve the problems, other than the second one with all the 1s and 0s, which you can’t solve at home.

The puzzles:
Since Wikipedia did me the favor of already listing them, I’ll repeat them here for your pleasure. They’re all famous logic puzzles.
0. A shepherd has a wolf, a sheep, and a cabbage, and he needs to get all three objects across a river in his boat, but he can only take one other object at a time with him. Obviously, he can’t leave the sheep with the wolf or the cabbage with the sheep on either side ever, or something will get eaten. How can he perform this task successfully?
1. A candy merchant receives 3 opaque boxes. One box contains mint candies, another contains anise candies, and the last box contains a mixture of mint and anise. The boxes are labeled Mint, Anise, and Mixed. All of the boxes are labeled incorrectly. What is the minimum number of candies the merchant will have to sample to correctly label each box?
2. You can’t do this one anyhow.
3. The third enigma describes a sealed room containing one light bulb. Outside of the room there are three switches, only one of which operates the bulb. The puzzle solver begins outside the room, able to operate the switches in any way he sees fit, but when the door is opened for the first time, he must determine which switch operates the light. The enigma is to determine how this is to be done.
4. The fourth enigma is to describe how one can use a four-minute hourglass and a seven-minute hourglass to measure a period of nine minutes.
5. The fifth enigma is stated as follows: "A student asks his teacher, 'How old are your three daughters?' The teacher replies, 'If you multiply their ages you get 36. If you add their ages you get my house number.' 'I am missing a detail,' protests the student. 'Oh yes,' says the teacher, 'the older one plays piano.' How old are the 3 daughters?"
6. The sixth enigma is a Knights and Knaves puzzle. Two doors are guarded by two men, one of whom always lies and one of whom always tells the truth; however, the puzzle solver does not know which man is which. One of the doors leads to freedom and one to captivity. The enigma is to determine a single question that, if asked of one of the guards, would reveal the door to freedom with certainty.
7. The seventh enigma is an elementary algebra problem with a twist. A mother is 21 years older than her son. In 6 years, the son will be one-fifth his mother's age. The enigma asks what the father is currently doing.

Discussion Questions:
~Given all the mysterious conditions surrounding the meeting, did you find it surprising that the invitees entered the castle and then the room itself at all? Were you surprised that they complied with the condition to not bring cell phones? How much did the fact that no one else seemed reluctant factor into this? Would “less intelligent” people have even entered the room?
~One character says, “I’m sick of people saying I’m right simply because of who I am.” What did he mean by this? Why did he find this frustrating?
~When the characters discuss a preference for invisibility or flying, one says, The only reason to be invisible is to do bad things. When we do good things, we want to be seen.” What do you think of this assertion? What good things could be done while invisible?
~Mathematics and the central problem of this movie (Goldbach’s Conjecture that all even numbers are the sum of two prime numbers) revolve around proving things to be true, above and beyond merely believing that they probably are. Can you know something is true without actually having a proof for it? Do you believe Goldbach’s Conjecture is true even though it hasn’t been proved?
~What do you think of the final decision regarding the paperwork? What does this action demonstrate about the importance of mathematics of this sort?
~Even if something like a mathematical puzzle or proof has no practical application, does that mean it’s worthless to work on it? Can things be beautiful without being useful? Is usefulness the only justification for an endeavor?
~What elements of idolatry do you see in this movie?
~What is the connection between intelligence and immorality in this movie? Do you believe that intelligent people are generally more or less likely to be immoral?
~Deception plays a substantial role in this movie, both explicit lies and also errors or assumptions allowed to go on uncorrected. Which of these deceptions seem wrong to you?
~What does it say about Americans that we often do not like to watch foreign movies? Is it a style issue or is it the extra effort involved in reading the subtitles? Do you tend to look down on people who don’t watch foreign films?

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Overall Grade: A-

Interesting, thoughtful, and certainly a great mystery-thriller, even if you have to read the dialogue.