A mathematician goes to the movies

Could Ferris Bueller’s day off have really happened? Let’s crunch the numbers.

As a kid I loved Ferris Bueller. As an adult I think he has all the makings of a sociopath. But back then I didn’t see such flaws. Instead I saw him as a teenage Robin Hood – taking from the old to give to the young, namely himself. But as much as I wanted to believe that a high school student could pack that much fun into just one day, the story needed to add up, numerically speaking.

Yes, I am well aware this classic teen movie is a work of fiction. But I was interested in knowing if Ferris and company could actually have crammed in as much as they did during the time that they had. That’s all. And yes, this is my idea of a good time.

The deadline we have is Ferris’ parents returning home at 6pm. So let’s get started.

Morning

Bueller residence

John Hughes wrote the script for Ferris Bueller’s Day Off in just one week. It helped that Hughes was a Chicago native and had an intimate knowledge of the city. The school Ferris attended – Shermer High – and the house of his best friend Cameron were both real locations in Hughes’ childhood suburb. Very handy. Ferris’ house was also a real location, but a bit farther out – 3,280 km to be precise, in Long Beach, Los Angeles. Oh dear. Falling over at the starting line! But not to worry – Cameron’s house happens to be a perfect place to start our timeline. We just need to work out what time that was.

By the middle of second period of the school day, Ferris had just stepped into the driver’s seat of a rare 1961 Ferrari 250 GT California Spider. According to the Chicago public school timetable this puts us at 9:30am. “Che bella.” Time to swing by the school and pick up Ferris’ girlfriend, Sloane.

9:45am

Shermer High School

The shortest route from Cameron’s house to their high school is 12 km. Given that the journey was in a 30 mi/h (48 km/h) speed zone and their car could accelerate from 0 to 100 in 6.3 secs, I estimate that they got there in 15 minutes. They spent 2 minutes at the school and then they were off to the big city. This mid-morning transit takes approximately 45 minutes, so let’s put them in downtown Chicago by 10:30am.

10:30am

Downtown parking garage

Here’s another real-world film location. The carpark used in the film was only 580 m away from their first port of call. So far, so good. After handing over their US$110,000 car to dubious parking attendants, it’s exactly a 5-minute walk to Chicago’s tallest skyscraper, Willis Tower, as long as they averaged a brisk 6.96 km/h. Let’s say they spent 20 minutes here before power-walking another 5 minutes (or 748 steps) to their next stop, the Chicago Board of Trade. Here they watched some 1100 pit traders making deals via a trading sign language combining 34 individual hand signals. But as fascinating as this sounds, research puts the maximum teenage attention span at 20 minutes, so by 11:20am they’d have had enough of hand-to-hand capitalism and started thinking about lunch. Time for a fancy French restaurant somewhere north of the city.

12:00pm

Chez Quis

No self-respecting fine-dining establishment would serve meals before midday, so we can’t feed our trio any earlier than 12:00pm. That gives them 40 minutes to make their way to the lunch spot – Chez Quis. This was never a real restaurant, but nonetheless a real location only 3.54 km from the Chicago Board of Trade. These 40 minutes are covered via a leisurely 5.31 km/h stroll from the Chicago Board, burning a respectable 200 calories (837 kJ) each in the process. This means our teen heroes could arrive bang on 12:00pm, with big appetites and primed to steal a booking from Abe Froman, “Sausage King of Chicago”. The morning timeline fits perfectly. Now for the afternoon.

1:25pm

Wrigley Field

After lunch we find our truants off to a game of baseball at Chicago’s iconic Wrigley Field. Day games during the 1980s didn’t start until 1:25pm and a trip from the restaurant to the stadium would only take 15 minutes in the early afternoon. This allows 70 minutes for lunch, easily accommodating the 600 chews required for starters, mains and desserts – 55 mouthfuls, 13 chews per mouthful. Splendid! Now to the ball game.

A whole game usually takes three hours, which would blow out our entire timeline. However, during a scene in a downtown bar, a game is playing on TV when a sportscaster announces: “Runner on first base, nobody out. That’s the first hit they’ve had since the fifth inning…” This is followed by Ferris catching a foul ball. Eureka! Their game has already had at least five innings. If an innings takes 20 minutes on average, then we can estimate that they have been there at least 100 minutes. If we throw in just half of the sixth innings, then the whole time at the stadium amounts to 110 minutes. Given that at Wrigley Field there are approximately 17,000 seats in range of a foul ball and each person could cover an area of nine seats (their seat + one seat in every direction), it puts the odds at 1 in 1,889. With the average game producing 15 foul balls by the fifth inning, Ferris had a 1 in 126 chance of catching at least one foul ball… But the main prize is the 6pm deadline and there’s a lot to pack in before then.

3:25pm

Art Institute

Leaving Wrigley Field by cab at 3:15pm gets us to The Art Institute of Chicago in 10 minutes. Inside the gallery we only have time for a whirlwind tour of modern art – 15 minutes tops. This has them out on the street by 3:40pm and only a short walk from a German-American Parade taking place a few blocks away.

3:50pm

Twist and Shout

We can place Cameron and Sloane at a public art piece known as Calder’s Flamingo just before they discover Ferris on a parade float. This is situated only five minutes by foot from the art museum. However, in the film they are stuck in a cab… eek! Walk, you lazy fools! We can allow 10 minutes in the cab before Ferris ascends a float to become king for a day. However, this life-changing moment must be over in 25 minutes. That’s all. Sorry, folks. We’re running out of time.

4:50pm

Glencoe Beach

Calder’s Flamingo is 580 m from the parking garage – the same distance that the parking garage was from Willis Tower! Unfortunately, numerical symmetry isn’t proof for meeting the 6pm deadline, so we must keep calculating. Another 5-minute walk has us back in the Ferrari by 4:20pm. Then it’s a 30-minute drive to their next location, Glencoe Beach, where each of the Ferrari’s wheels rotate 8250 times to cover the required 38.3 km. It’s only a small addition to the 240 km – or 51,720 wheel rotations – already accumulated by the carpark attendants’ joyride that our trio has just discovered.

This realisation induces the catatonic episode in Cameron, during which his blink rate dropped from 12-15 blinks/min down to zero. Here, we can only allow 10 minutes.

5:05pm

Some random jacuzzi

Next we see Ferris and Sloane relaxing in a jacuzzi trying to motivate an unresponsive Cameron to join them. This location isn’t given any context in the film and our timeline is getting super tight! Let’s give them 5 minutes to get there and 15 minutes in the water. However, the scene is problematic, as a three-person 1,000L jacuzzi can, at best, heat up at a rate of 3˚C per hour. In 15 minutes that’s a measly 0.75˚C. Perhaps the offer of a cold jacuzzi was enough to keep Cameron out of the water? Luckily for us there isn’t time to worry about it too much since we need to get back to Cameron’s house – at most five minutes away.

5:25pm

Cameron’s house

Finally we have arrived at the climactic scene: a vintage Ferrari jacked up and humming in reverse. If we get to Cameron’s garage by 5:25pm we only have 30 minutes left in the budget for the Ferrari’s destruction. Yet their plan to wipe the extra 240 km from the odometer by driving in reverse presents us with a serious, possibly terminal, plot hole. The Ferrari’s factory specs have the reverse gear ratio at 13.5 and the redline rpm at 6,500 which, when combined, means their car had a top speed of 61 km/h in reverse. This means for their plan to work they would have needed at least 3 hours and 56 minutes. Luckily we are saved from this mathematical howler by the Ferrari launching backwards through a glass wall. Phew. Time to bring it home.

5:55pm

Sloane’s watch

When Ferris says goodbye to Sloane he looks at her watch. It’s 5:55pm. Only five minutes to get home before his parents. This final scene really needs its own detailed analysis, but having been thoroughly entertained up to this point, I am happy to accept that it was achievable. But more importantly, everything leading up to 5:55pm, excluding some minor mathematical indiscretions, was also achievable. Which, I have to admit, comes as a big surprise.

Yet perhaps it was to be expected. Hughes’ masterpiece was set in a city he understood innately. Like a London cabbie he had a mental map of each location when writing and editing his film. And within those constraints he crafted a brilliant story of mid-’80s teenage rebellion. And we’re glad he did, because there is no way anyone could pull a Ferris Bueller’s day off today. The Ferrari would have its own tracking device. The French restaurant would have image-searched “Chicago Sausage King” to verify Ferris’ claim. And social media would have exploded during Twist and Shout. And that would be it. Ferris Bueller’s day over! But instead we have a rite of passage for any teen wondering what life would be like if they could stop and look around once in a while… and the opportunity for a nerd like me to overanalyse the whole thing on a spreadsheet.

Thank you, Ferris Bueller, you’re still my hero.