## Math Puzzles in the Film "Fermat's Room"

12/19/2013

The Spanish film La habitación de Fermat (translated as "Fermat's Room" in English) is a thriller film first shown in 2007. The film outperformed many counterparts of the genre and has been impressive in the history of thriller films due to its special plot: murder via math.

In the film, three top mathematicians and an inventor were invited to a house in a place of "nowhere" to solve math puzzles (enigmas). For each puzzle they had one minute in time. If the time was exceeded without a correct answer, the room would shrink a bit. As difficulty increases through the puzzles, they were facing a destiny of being squeezed to death by the walls of the room.

Here we summarized some puzzles appearing in the film. See if you can solve each of the puzzles in 60 second and survive till the very end!

1.       What's the order of the following numbers: 8, 5, 4, 9, 1, 7, 6, 3, 2

(The question was originally in Spanish, but the statement above is already made adapted to the English language, so there is no need to worry that you don't know Spanish.)

2.       You have a 4-minute hourglass and a 7-minute hourglass. How to measure exactly 9 minutes by using only these two hourglasses?

3.       There are three opaque boxes containing candies in front of you. One box contains only chocolate candies, one contains only mint candies, and the other contains a mixture of both candies. The three boxes are labelled Chocolate, Mint, and Mixture, but none of the labels on the boxes is correct (none of the labels is consistent with the contents in the box under it). You can take one candy each time from each box to see what it is. How many times at least do you need to open a box and take out a candy in order to re-put correct labels to all three boxes?

4.       There are three switches outside a room. One switch controls a lamp bulb while the other two are fakes. You can turn on or off the switches outside the room and then enter the room to see if the bulb is on. (Note: You are not able to see the light of the bulb from outside.) How many times at least will you need to enter the room in order to decide which switch controls the bulb? (All the switches are off when you start.)

5.       A mother is 21 years older than her son, and six years later, her age will be five times her son's age. Where is the FATHER right now?

6.       A dialogue takes place between two men, A and B.

A: What are the ages of your three children?

B: If you multiply their ages, you get 36; if you add the ages, you get your room number.

A: Of course I know my room number, but the information is still not enough!

B: Oh really. Then my oldest child plays the piano. Does this help?

A: Yes! Now I can tell their ages.

What are the ages of the three children of B?

7.       In front of you are two closed gates. One gate will lead you to freedom, and the other is actually blocked. Each gate is kept by a guard. One guard always tell the truth while the other never. You can only ask one of them one question. What question should you ask so as to know which door leads to freedom?