Fermat’s Room, the Spanish math-mystery film making its American premiere at the Tribeca Film Festival, begins with a warning: “If you don’t know what prime numbers are, you should just leave now.”

This was a bold joke, and also an odd bit of bravado, as the ensuing film didn’t require any math knowledge at all. The story ostensibly revolves around a proof of the strong Goldbach Conjecture, which posits that every even number greater than 2 can be written as the sum of two prime numbers. (Fermat's Last Theorem, despite what you might suspect, doesn't come up at all.) But Goldbach fades from prominence within the first half hour, as four mathematicians—an aging genius, a young wunderkind, a hottie, and a grizzled pragmatist—convene, at Fermat’s behest, at a drawing room within a remote abandoned warehouse.

At this point, your nerd quotient, rather than enhancing your enjoyment of the movie, detracts from it a touch. The gimmick of the titular room is that it literally shrinks unless its occupants can solve riddles and logic puzzles within a given time limit. (The directors explained in a post-screening Q&A that they built a shrinking set, and indeed the claustrophobia is convincing.) It’s a fun premise, but it’s hard to suspend disbelief when revered mathematicians and supposed puzzle freaks struggle with old chestnuts that would barely garner 30 points in Professor Layton and the Curious Village. Like the first riddle:

A candy-store owner receives three opaque boxes of mislabeled candy. One contains sweet candies, one contains mints, and the third contains a mix of sweets and mints. The three boxes are, correspondingly, labeled “Sweets,” “Mints,” and “Mix,” but none of the labels is on its correct box. How many pieces of candy must the shopkeeper remove to determine the actual contents of the three boxes and relabel them properly?

(If you’ve never heard this one before, the solution is in the footnotes.¹)

A classic riddle, but that’s the thing: It’s a classic. Geeks have already heard the puzzles in Fermat’s Room. It’s a forgivable sin, though, for two reasons. First, there are only so many clever logic problems that can be conveyed to a general audience in 30 seconds of dialogue, and even though the directors made some of the simplest possible choices, a couple audience members still complained in the Q&A session that they couldn’t follow along.²

Second, I can overlook the use of old riddle-book fare because director-screenwriters Luis Piedrahita and Rodrigo Sopeña did create one original enigma, and it’s the biggest one: the room itself. The origin of the room is the central thread of the film, which wends through a bottomless spiral of twists. The surprises arrive with a refreshingly light touch. Piedrahita and Sopeña are clever but also careful not to seem too proud of themselves.

The film’s resolution isn’t perfect—in particular, the explanation of Fermat and Pascal’s roles in the grand scheme was a little too breezy—but Fermat’s Room is still a polished exercise in artful misdirection. From that opening joke about prime numbers, in fact from the moment the film’s title appears on screen, you’re being charmed into false assumptions, which is the mark of any good mystery flick or, for that matter, any good riddle.

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1. Candy-box solution: The storekeeper only needs to remove one piece of candy, from the box labeled “Mix.” The key piece of information is that all of the labels are on the wrong box. From this we know that the “Mix” box definitely does not contain a mix. So if the shopkeeper removes, say, a mint from the “Mix” box, he knows that box is actually full of mints. He then knows that the “Sweets” box must contain a mix (since he knows it doesn’t contain sweets and he has already established where the mint box is), and, by process of elimination, he knows that the “Mints” box contains the sweets. ↑

2. Subtitles also had something to do with this. The riddles flashed on and off the screen pretty quickly as the characters fired off their Spanish dialogue. ↑