15 Pi Day Math Problems to Solve

iStock
iStock

Happy Pi Day! For decades, math lovers have been honoring this crucial irrational constant on March 14 (or 3/14, the first three digits of the ratio of a circle's circumference to its diameter) every year. The U.S. House of Representatives even passed a non-binding resolution in 2009 to recognize the date. Join the celebration by solving (or at least puzzling over) these problems from a varied collection of pi enthusiasts.

PI IN SPACE

Blue-tinted stars in galaxy.
iStock

Pi is a vital number for NASA engineers, who use it to calculate everything from trajectories of spacecraft to densities of space objects. NASA's Jet Propulsion Laboratory, located in Pasadena, California, has celebrated Pi Day for a few years with a Pi in the Sky challenge, which gives non rocket engineers a chance to solve the problems they solve every day. The following problems are from Pi in the Sky 3 (and you can find more thorough solutions and tips there). JPL has brand-new problems for this year's event, Pi in the Sky 5.

1. HAZY HALO

Saturn's moon, Titan.
This undated NASA handout shows Saturn's moon, Titan, in ultraviolet and infrared wavelengths. The Cassini spacecraft took the image while on its mission to gather information on Saturn, its rings, atmosphere and moons. The different colors represent various atmospheric content on Titan.
NASA, Getty Images

Given that Saturn's moon Titan has a radius of 2575 kilometers, which is covered by a 600-kilometer atmosphere, what percentage of the moon's volume is atmospheric haze? Also, if scientists hope to create a global map of Titan's surface, what is the surface area that a future spacecraft would have to map?

 
 

[Answer: 47 percent; 83,322,891 square kilometers]

2. ROUND RECON

NASA's Earth-orbiting Hubble Space Telescope took this picture June 26, 2003 of Mars.
NASA's Earth-orbiting Hubble Space Telescope took this picture June 26, 2003 of Mars.
NASA, Getty Images

Given that Mars has a polar diameter of 6752 kilometers, and the Mars Reconnaissance Orbiter comes as close to the planet as 255 kilometers at the south pole and 320 kilometers at the north pole, how far does MRO travel in one orbit? (JPL advises, "MRO's orbit is near enough to circular that the formulas for circles can be used.")

 
 

[Answer: 23,018 km]

3. SUN SCREEN

Mercury is seen in silhouette, lower left of image, as it transits across the face of the sun.
In this handout provided by NASA, the planet Mercury is seen in silhouette, lower left of image, as it transits across the face of the sun on May 9, 2016 as viewed from Boyertown, Pennsylvania. Mercury passes between Earth and the sun only about 13 times a century, with the previous transit taking place in 2006.
NASA/Bill Ingalls, Getty Images

If 1360.8 w/m^2 of solar energy reaches the top of Earth's atmosphere, how many fewer watts reach Earth when Mercury (diameter = 12 seconds) transits the Sun (diameter = 1909 seconds)?

 
 

[Answer: 0.05 w/m^2]

PUTTING THE PI IN PIZZA

Pizza on wooden table
iStock

People often celebrate Pi Day by eating pie, but what is considered a "pie" is subjective. Pizza Hut considers its main offerings pies, and got into the spirit of Pi Day in 2016 by asking their customers to solve several math problems from English mathematician and Princeton professor John Conway, with promises of free pizza for winners for 3.14 years. Below are two of his fiendishly tricky problems. Unfortunately, even if you solve them, your chance at free pizza is long gone.

4. 10-DIGIT GUESS

Floating blue numbers
iStock

I'm thinking of a 10-digit integer whose digits are all distinct. It happens that the number formed by the first n of them is divisible by n for each n from 1 to 10. What is my number?

 
 

[Answer: 3,816,547,290]

5. PUZZLE CLUB

Old door
iStock

Our school's puzzle club meets in one of the classrooms every Friday after school.

Last Friday, one of the members said, "I've hidden a list of numbers in this envelope that add up to the number of this room." A girl said, "That's obviously not enough information to determine the number of the room. If you told us the number of numbers in the envelope and their product, would that be enough to work them all out?"

He (after scribbling for some time): "No." She (after scribbling for some more time): "Well, at least I've worked out their product."

What is the number of the school room we meet in?

 
 

[Answer: Room #12 (The numbers in the envelope are either: 6222 or 4431, which both add up to 12 and the product is 48.)]

COM-PI-TITIVE MATH

Blackboard with math and science equations on it
iStock

Po-Shen Loh coached the U.S. Mathematical Olympiad team to victory in 2015 and 2016. The back-to-back win was particularly impressive considering Team USA had not won the International Mathematical Olympiad (or IMO) in 21 years. When not coaching, Loh is an associate math professor at Carnegie Mellon University. His website, Expii, challenges readers weekly with a large range of problems. Expii has celebrated Pi Day for several years now—this year it published a video that uses an actual pie to help us visualize pi better—and the following problems are from its past challenges.

6. PIESTIMATE

Pi on blackboard
iStock

Pi has long been noted as one of the most useful mathematical constants. Yet, due to the fact that it is an irrational number, it can never be expressed exactly as a fraction, and its decimal representation never ends. We have come to estimate π often, and all of these have been used as approximations to π in the past. Which is the closest one?

A) 3
B) 3.14
C) 22/7
D) 4
E) Square root of 10

 
 

[Answer: C]

7. PHONE TAG

Yellow rotary phone.
iStock

When Expii's founding team registered the organization in the United States, they needed to select a telephone number. As math enthusiasts, they claimed pi in the new 844 toll-free area code. What is Expii's seven-digit telephone number? (Excluding the area code.)

 
 

[Answer: 314-1593; in case you forget to round, you get their FAX number!]

8. PI COINCIDENCE

Metal pentagon
iStock

The number pi is defined to be the ratio circumference/diameter for any circle. We also all know that the area of a circle is pir^2. Is it a sheer coincidence that they are both the same pi, even though one concerns the circumference and one concerns the area? No!

Let's do it for a regular pentagon. It turns out that for the appropriate definition of the "diameter" of a regular pentagon, if we define the number theta to be the ratio of the perimeter/diameter of any regular pentagon, then its area is always thetar^2, where r is half of the diameter. For this to be true, what should be the "diameter" of a regular pentagon?

A) The distance between the farthest corners of the pentagon.
B) The diameter of the largest circle that fits inside the pentagon.
C) The diameter of the smallest circle that fits around the pentagon.
D) The distance from the base to the opposite corner of the pentagon.
E) Other, not easy to describe.
F) It's a trick question.

 
 

[Answer: B]

9. WHAT'S IN A NAME?

Globe on chalkboard
iStock

"Expii" brings to mind a number of nice words like "experience," "explore," "explain," "expand," "express," and more. The truth behind the name, however, is based on the most beautiful equation in mathematics:

e^pii + 1 = 0

What is (-1)^-i/pi?

Round your answer to the nearest thousandth.

 
 

[Answer: Euler's number, also known as e, or 2.718 (rounded off)]

GETTING EXCITED FOR PI DAY

Calculator and blocks that read
iStock

The Mathematical Association of America was founded in 1915 to promote and celebrate all things mathematical. It has thousands of members, including mathematicians, math educators, and math enthusiasts, and of course they always celebrate Pi Day. The first two problems are by Lafayette College professor Gary Gordon, while the following four have been sprung on the 300,000+ middle and high school students who participate in the association's annual American Mathematics Competitions. Top scorers in these competitions will sometimes go on to compete on the MAA-sponsored Team USA at the IMO.

10. FLIPPING A COIN

Thumb flipping a coin.
iStock

Alice and Bob each have a coin. Suppose Alice flips hers 1000 times, and Bob flips his 999 times. What is the probability that the number of heads Alice flips will be greater than the number Bob flips?

 
 

[Answer: 50 percent. Alice must have either more heads or more tails than Bob (since she has one additional flip), but not both. These two possibilities are symmetric, so each has a 50 percent probability.]

11. CUTTING CHEESE

Wheel of gouda
iStock

You are given a cube of cheese (or tofu, for our vegan readers) and a sharp knife. What is the largest number of pieces one may decompose the cube using n straight cuts? You may not rearrange the pieces between cuts!

 
 

[Answer: ((n^3)+5n+6)/6). The trick is that the sequence starts 1, 2, 4, 8, 15, so stopping before the fourth cut will give the wrong impression.]

12. BUYING SOCKS

Socks hanging on a line
iStock

Ralph went to the store and bought 12 pairs of socks for a total of $24. Some of the socks he bought cost $1 a pair, some $3 a pair, and some $4 a pair. If he bought at least one pair of each kind, how many pairs of $1 socks did Ralph buy?

A) 4
B) 5
C) 6
D) 7
E) 8

 
 

[Answer: D]

13. THE COLOR OF MARBLES

Blue and red marbles.
iStock

In a bag of marbles, 3/5 of the marbles are blue, and the rest are red. If the number of red marbles is doubled, and the number of blue marbles stays the same, what fraction of the marbles will be red?

A) 2/5
B) 3/7
C) 4/7
D) 3/5
E) 4/5

 
 

[Answer: C]

14. SODA CANS

Tops of soda cans.
iStock

If one can holds 12 fluid ounces of soda, what's the minimum number of cans required to provide a gallon (128 ounces) of soda?

 
 

[Answer: 11 (you can't have a fraction of a can)]

15. CARPET COVERAGE

Feet on a pink rug
iStock

How many square yards of carpet are required to cover a rectangular floor that is 12 feet long and 9 feet wide?

A) 12
B) 36
C) 108
D) 324
E) 972

 
 

[Answer: A]

11 Fun Facts About Them!

Joan Weldon and James Arness star in Them! (1954).
Joan Weldon and James Arness star in Them! (1954).
Warner Home Video

In the 1950s, Elvis was king, hula hooping was all the rage, and movie screens across America were overrun with giant arthropods. Back then, Tarantula (1955), The Deadly Mantis (1957), and other “big bug” films starring colossal insects or arachnids enjoyed a surprising amount of popularity. What kicked off this creepy-crawly craze? An eerie blockbuster whose impossible premise reflected widespread anxieties about the emerging atomic age. Grab a Geiger counter and let’s explore 1954's Them!.

1. Them!'s primary scriptwriter once worked for General Douglas MacArthur.

When World War II broke out, the knowledge Ted Sherdeman had gained from his career as a radio producer was put to good use by Uncle Sam, landing him a position as a radio communications advisor to General MacArthur. However, the fiery conclusion of the war left Sherdeman with a lifelong disdain for nuclear weapons. In an interview he revealed that upon hearing about the 1945 bombing of Hiroshima, he “just went over to the curb and started to throw up."

Shifting his focus from radio to motion pictures, Sherdeman later joined Warned Bros. as a staff producer. One day he was given a screenplay that really made his eyes bug out. George Worthing Yates, best known for his work on the Lone Ranger serials, had decided to take a stab at science fiction and penned an original script about giant, irradiated ants attacking New York City. "The idea appealed to me very much,” Sherdeman told Cinefantastique, "because, aside from man, ants are the only creatures in the world that plan to wage war, and nobody trusted the atomic bomb at that time.” (His statement about animal combat is debatable: chimpanzee gangs will also take organized, warlike measures in order to annex their rivals’ territories.)

Although he loved the basic concept, Sherdeman felt that the script needed something more. Screenwriter Russell S. Hughes was asked to punch up the script, but died of a heart attack after completing the first 50 pages. With some help from director Gordon Douglas, Sherdeman took it upon himself to finish the screenplay. Thus, Them! was born.

2. Two main ants were built for the movie.

Them! brought its spineless villains to life using a combination of animatronics and puppetry, courtesy of an effects artist by the name of Dick Smith. He constructed two fully functional mechanical ants for the production, with the first of these being a 12-foot monster filled with gears, levers, motors, and pulleys. Operating the big bug was a job that required a small army of technicians who’d pull sophisticated cables to control the ant’s limbs off-camera. These guys worked in close proximity and often crashed into each other as a result, prompting Douglas to call them “a comedy team.”

The big insect mainly appears in long shots, and for close-ups, Smith built the front three quarters of a second large-scale ant and mounted it onto a camera crane. During scenes that required swarms of ants, smaller, non-motorized models were used. Blowing wind machines moved the little units’ heads around in a lifelike manner.

3. Them! features the Wilhelm Scream.

Fifty-nine minutes in, the ants board a ship and one of them grabs a sailor, who unleashes the so-called "Wilhelm Scream." You can also hear it when James Whitmore’s character is killed, and the sound bite rings out once again during the movie’s climax. Them! was among the first movies to reuse this distinctive holler, which was originally recorded three years earlier for the 1951 western Distant Drums. Since then, it’s become something of an inside joke for sound recording specialists. The scream has appeared in Titanic (1997), Toy Story (1995), Reservoir Dogs (1992), Batman Returns (1992), the Star Wars saga (1977-present), all three The Lord of the Rings movies (2001-2003), and countless other films.

4. Leonard Nimoy makes an appearance.

In one brief scene, future Star Trek star Leonard Nimoy plays an Army man who receives a message about an alleged “ant-shaped UFO” sighting over Texas. He then proceeds to poke fun at the Lone Star State, because, as everybody knows, insectile space vessels are highly illogical.

5. Many different sounds were combined to produce the screeching ant cries.

Throughout the movie, the monsters announce their presence with a haunting wail. Douglas’s team created this unforgettable shriek by mixing assorted noises, including bird whistles, which were artificially pitched up by sound technicians.

6. Sandy Descher had to sniff a mystery liquid during her signature scene.

Like Steven Spielberg’s Jaws, Them! has a deliberate pace and the massive insects don’t make an onscreen appearance until the half hour mark. Douglas took credit for this restrained approach, saying, “I told Ted, let’s tease [the audience] a little bit before you see the ant. Let’s build up to it."

So instead of showing off the big bugs, the opening scene follows a little girl as she wanders through the New Mexican desert, listlessly clutching her favorite doll. That stunning performance was delivered by child actress Sandy Descher. Later, in one of the most effective title drop scenes ever orchestrated, a vial of formic acid is held under her character’s nose. Suddenly recognizing the aroma, the traumatized youngster screams “Them! Them!” Descher never found out what sort of liquid was really sloshing around in that container.

“They used something that did smell quite strange. It wasn’t ammonia, it was something else,” she told an interviewer. Still, the mysterious brew had a beneficial effect on her performance. “They tried to create something different and it helped me a lot with that particular scene,” Descher said.

7. Them! was originally going to be filmed in 3D and in color.

To hear Douglas tell it, the insect models looked a lot scarier in person. “I put green and red soap bubbles in the eyes,” he once stated. “The ants were purple, slimy things. Their bodies were wet down with Vaseline. They scared the bejeezus out of you.” For better or for worse, though, audiences never got the chance to savor the bugs’ color scheme.

At first, Warner Bros. had planned on shooting the movie in color. Furthermore, to help Them! compete with Universal’s brand-new, three-dimensional monster movie, Creature From the Black Lagoon, the studio strongly considered using 3D cameras. But in the end, the higher-ups at Warner Bros. didn’t supply Douglas with the money he’d need to shoot it in this manner. Shortly before production started on Them!, the budget was greatly reduced, forcing the use of two-dimensional, black and white film.

8. The setting of the climactic scene was changes—twice.

Yates envisioned the final battle playing out in New York City’s world-famous subway tunnels. Hughes moved the action westward, conjuring up an epic showdown between human soldiers and the last surviving ants at a Santa Monica amusement park. Finally, for both artistic and budgetary reasons, Sherdeman set the big finale in the sewers of Los Angeles.

9. Warner Bros. encouraged theaters to use Them! as a military recruitment tool.

The film’s official pressbook advised theater managers who were screening Them!& to contact their nearest Armed Forces recruitment offices. “Since civil defense in the face of an emergency figures in the picture, make the most of it by inviting [a] local agency to set up a recruiting booth in the lobby,” the filmmakers advised. Also, the document suggested that movie houses post signs reading: “What would you do if (name of city) were attacked by THEM?! Prepare for any danger by enlisting in Civil Defense today!”

10. The movie was a surprise hit.

Studio head Jack L. Warner predicted that Them!, with its far-fetched plot, wouldn’t fare well at the box office. So imagine his surprise when it raked in more than $2.2 million—enough to make the picture one of the studio's highest-grossing films of 1954.

11. Them! landed Fess Parker the role of TV's Davy Crockett.

When Walt Disney went to see Them!, he had a specific objective in mind: Scout a potential Davy Crockett. At the time, Disney was developing a new television series that would chronicle the life and times of the iconic frontiersman, and James Arness, who plays an FBI agent in Them!, was on the short list of candidates for the role. Yet as the sci-fi thriller unfolded, it was actor Fess Parker who grabbed Disney’s attention. Director Gordon Douglas had hired Parker to portray the pilot who ends up in a psych ward after an aerial encounter with a gargantuan flying ant. And while his character only appears in one scene, the performance impressed Disney so much that the struggling actor was soon cast as Crockett.

By the Texan’s own admission, his good fortune may’ve been the product of bargain hunting. “Walt probably asked, ‘How much would Arness cost?’ and then ‘This fellow [Parker], we ought to be able to get him real economical,” Parker once said.

Watch Alexei From Stranger Things Drink a Slurpee For 12 Hours Straight

Netflix
Netflix

*Warning: This article contains spoilers for Stranger Things season 3.*

As if we needed a reminder of how much we miss a certain late Stranger Things character, Netflix just went and drilled it into our hearts again.

As reported by CNET, the streaming service recently released a video tribute to the Russian scientist Alexei (Alec Utgoff), showing him sipping his Slurpee on a loop for 12 hours. Yep, you read that right: 12 hours of nonstop Slurpee-sipping.

The video is captioned: "To honor our Slurpee sipping hero, we are pouring one out for our pal. Sip along!"

In season 3 of the Netflix hit, Alexei opens the portal between Hawkins and the Upside Down to help the Soviets in their research. When the fan-favorite character gets kidnapped by Jim Hopper, his request is a cherry Slurpee in exchange for information ... and he won't compromise on the flavor.

Tragically, Alexei doesn't make it to the end of the season. And in true Stranger Things fashion, his death was totally unexpected and left fans shocked.

While you're still mourning the fallen character, just try and enjoy the oddly mesmerizing video of Alexei sipping away.

SECTIONS

arrow
LIVE SMARTER