15 Pi Day Math Problems to Solve

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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.
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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
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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
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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
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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
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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
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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.
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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
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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
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"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
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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.
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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
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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
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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 Boredom-Busting Classes and Activities You Can Do at Home

A good workout is just one way to pass the time while socially isolating.
A good workout is just one way to pass the time while socially isolating.
jacoblund/iStock via Getty Images

Staying home as much as possible is the best way to stop the spread of novel coronavirus, according to health experts. If you’ve already taken this step to protect yourself and your community, you may be faced with a different problem: the crushing boredom that comes with spending all your time indoors. Fortunately, there have never been more ways to keep busy on the internet. In an effort to lift spirits and stimulate minds in isolation, businesses, artists, and institutions have found new ways to keep people connected from afar. From virtual field trips to free workout classes, here are the best boredom-busting activities to check out.

1. Take a free workout class with the YMCA.

Your local gym may be closed, but that doesn’t mean you have to postpone your workout routine for the foreseeable future. The YMCA has launched a new series of free, online fitness classes for people stuck at home. The on-demand videos include barre, bootcamp, yoga, tai chi, and weightlifting. After breaking a sweat for 30 minutes, you may even forget you’re not at the gym.

2. Meditate with the Monterey Bay Aquarium’s jellyfish.

Taking care of your mental health is as important as maintaining your physical health while social distancing. If you want to start your day in a good head space, tune into the Monterey Bay Aquarium’s morning “MeditOceans” on YouTube. After closing to the public, the California aquarium started uploading 10- to 15-minute guided meditations set to soothing footage of marine life or scenes from nature. We recommend starting with their video of undulating jellyfish.

3. Take a virtual field trip to a National Park.

Combat claustrophobia by taking a virtual tour of some of the country’s most majestic national parks. The Hidden Worlds of the National Parks project from Google Arts & Culture offers virtual, 360-degree tours of five National Park System sites, all guided by real park rangers. The diverse destinations include the Kenai Fjords in Alaska; Hawai’i Volcanoes in Hawai’i; Carlsbad Caverns in New Mexico; Bryce Canyon in Utah; and Dry Tortugas in Florida. You can view all the properties from your phone or computer, and if you have a virtual reality headset, you can transport yourself out of your home with an immersive experience.

4. Take an Improv Class from Second City.

Improv comedy is difficult to do alone. With Second City, you can take a class with other students and master instructors from the comfort of your home. Second City has helped launch the careers of such comedy heavyweights as Steve Carell, Bill Murray, Amy Poehler, and Tina Fey. Even though its physical theaters in Chicago, Toronto, and Los Angeles are closed during the coronavirus crisis, comedy classes will continue online. In addition to improv, students can take virtual lessons in comedic songwriting, pitching TV shows, stand-up, sketch comedy, and more from Second City’s pro teachers. If you’re not willing to pay $195 to $295 for a four- to eight-week online course, you can take a one-time drop-in improv or stand-up class for $25.

5. Learn about Women’s History with The New-York Historical Society.

Whether you’re teaching someone home from school or looking to educate yourself in your spare time, there are plenty of remote resources online. The New-York Historical Society is sharing its expertise in the form of a free digital curriculum on women’s history in America. The online course materials cover the period from 1920 to 1948, starting with the flappers of the Jazz Age and ending with women in the postwar era. You can view the entire unit, which includes archival photos and documents, on the NYHS’s website.

6. Join the D.C. Library’s quarantine book club.

If you already plan on reading a ton of books in isolation, you can turn the solitary activity into a social one by joining a quarantine book club. The D.C. Public Library recently announced its book club D.C. Reads is going digital, and now anyone can participate from home. This month’s pick is With the Fire on High by Elizabeth Acevedo. If you have a Washington, D.C. library card, you can use it to download the e-book for free. Book club discussions will take place on March 28 and April 4 at 2 p.m. through the library’s Twitter account.

7. Draw with Wendy Macnaughton.


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A post shared by wendy macnaughton (@wendymac) on

Whether you consider yourself a novice or a Picasso, you can benefit from making art with others. Every weekday at 10 a.m. PST, Wendy Macnaughton (illustrator of the cookbook Salt, Fat, Acid, Heat) hosts drawing classes in her Instagram Stories. All participants need is paper and a pencil. Artists of all ages can draw along, though Macnaughton states classes are just long enough to keep kids occupied for parents “to get a little work done or take a shower and take a couple deep breathes.”

8. Tour the American Museum of Natural History.

As long as you have an internet connection, the impressive halls of the American Museum of Natural History in New York City are just a few clicks away. Every day at 2 p.m. EST, the institution is sharing tours of its exhibits and collections as Facebook Lives. Some special sneak peeks published to the AMNH Facebook page so far include a tour of the Hall of Reptiles and Amphibians and a look at its trilobite collection led by curator and trilobite paleontologist Melanie Hopkins.

9. Take a cooking class with Milk Street.

Not sure what to do with your quarantine food supply? Taking a cooking class is a great place to start. Through the end of April, Milk Street (from America’s Test Kitchen co-founder Christopher Kimball) is making its online culinary lessons free to everyone. Topics include baking, cooking without a recipe, and using certain kitchen tools. After a few weeks of classes, you’ll know your way around everything from a chef’s knife to an Instant Pot.

10. Get Creative with the Museum of Contemporary Art Denver.

While it’s closed, the Museum of Contemporary Art Denver is using its social media to keep followers engaged with their creative sides. Every Tuesday on Instagram, the institution will post a new challenge to its Stories. This week’s challenge is finding something to read and posting about it to Instagram to help the museum compile the ultimate reading list. Past challenges have included setting aside 30 minutes to make art and sharing photos of pets wearing wigs.

11. Learn guitar with Fender.

At the risk of driving your quarantine-mates crazy, you can use isolation as an opportunity to get in touch with your inner rockstar. Fender is giving the first 100,000 users who create a new account on Fender Play three months of free online lessons. The instructional videos led by talented musicians are high-quality, and you can access them from your phone, tablet, or computer. And if you don't have a guitar at home, the program also includes lessons for bass guitars and ukuleles.

9 Classic Board Games You Can Play Online

This man may have just sunk his opponent's biggest ship on the Battleship app.

This man may have just sunk his opponent's biggest ship on the Battleship app.

Ryan Herron/iStock via Getty Images

An energetic round of Monopoly, Catan, or another classic board game is a great way to bond with friends and family. Crowding around a coffee table, on the other hand, isn’t a great way to practice social distancing. Luckily, many of the best board games have been adapted for smartphones and other devices, so you can still indulge in all the thrills of a family game night during isolation—read on to find out about nine of our favorites.

1. Catan Universe

Catan (The Settlers of was dropped in 2015) has been giving serious board gamers a chance to show off their strategy skills for 25 years, and the Catan Universe app has the same appeal. You and two friends can play the basic version of the board game for free, but there are also several other versions—including the “Cities & Knights” and “Seafarers” expansions and a stand-alone challenge called “Rise of the Inkas”—that you can purchase within the app if you’re looking for new adventures.

Download: iOS, Android

2. Boggle With Friends

With the virtual version of Boggle, you can hone your word search skills in single-player mode until you’re sure you’ll come out on top against your friends and family. Not only will you not have to rearrange all those cubes each round, you won’t have to keep score, either—the program does it all for you.

Download: iOS, Android

3. Clue

If anybody knows how it feels to be sequestered in a house with increasingly tense and anxious housemates, it’s Miss Scarlet, Colonel Mustard, and the rest of Clue’s classic cast of characters. Wander the ominous rooms of Tudor Mansion to find the truth about Mr. Boddy’s untimely demise with the beautifully animated $4 Clue app. 

Download: iOS, Android

4. Battleship

For just $4 or $5, depending on your device, you can play the classic version of Battleship and a “Commander’s Mode,” where each commander comes with special abilities that shake up the tactical options for sinking your opponent’s ships. The app also features animated effects and nautical backdrops that really help bring your heroic maritime fantasies to life.

Download: iOS, Android

5. Monopoly

Embrace your entrepreneurial spirit and become the business mogul you were always meant to be—with absolutely no real-world stress or consequences—by investing in the $4 Monopoly app. It’s almost exactly the same as the game you know and (maybe) love, but there are a few additional features that might make your virtual game night even better, including customizable house rules and a “quick mode,” which promises a round that lasts no longer than an hour.

Download: iOS, Android

6. Scattergories

If you can text faster than you can write, you might actually prefer this free online edition of Scattergories to the original one. Fill the virtual room with friends or family and earn points for typing a city that starts with G, an element that starts with C, or any number of other category-letter match-ups. The app has autocorrect capabilities, so you don’t have to worry about losing the round over a spelling error, and you can also dispute the app if it rejects a response that your group considers acceptable.

Download: iOS, Android

7. Risk: Global Domination

The free Risk: Global Domination app offers the thrill of the original game without the necessity of sitting huddled around a tiny world map for hours (or days) at a time. Recommended for anyone whose favorite film scenes are those where generals in tight pants and three-cornered hats are plotting out ambushes with wooden figurines on a giant table.

Download: iOS, Android

8. Scrabble GO

Few things are as uniquely satisfying as landing a triple word score with quiz, quartzy, or another high-scoring Scrabble word—even if it’s no longer than two letters. The free Scrabble GO app gives you the chance to get that feeling from the comfort of your own secluded couch, no calculator necessary.

Download: iOS, Android

9. The Game of Life

It’s never too late in Life to earn an advanced degree or become a brain surgeon, and it’ll only cost you $3. The layout of the board is pretty similar to the one in the real-life game, and the app even includes animated versions of those beloved sphere-topped blue and pink player pieces.

Download: iOS, Android

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