15 Pi Day Math Problems to Solve

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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
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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
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
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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.
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
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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.
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]

David Lynch's Amazon T-Shirt Shop is as Surreal as You'd Expect It to Be

Dominique Faget, AFP/Getty Images
Dominique Faget, AFP/Getty Images

David Lynch, the celebrated director behind baffling-but-brilliant films like Eraserhead, Blue Velvet, Mulholland Drive, and Twin Peaks, is now selling his equally surreal T-shirts on Amazon.

Each shirt bears an image of one of Lynch’s paintings or photographs with an accompanying title. Some of his designs are more straightforward (the shirts labeled “House” and “Whale” feature drawings of a house and a whale, respectively), while others are obscure (the shirt called “Chicken Head Tears” features a disturbing sculpture of a semi-human face).

This isn’t the first time Lynch—who is celebrating his 73rd birthday today—has ventured into pursuits outside of filmmaking. Previously, he has sold coffee, designed furniture, produced music, hosted daily weather reports, and published a book about his experience with transcendental meditation. Art, in fact, falls a little closer to Lynch’s roots; the filmmaker trained at the Pennsylvania Academy of the Fine Arts before making his mark in Hollywood.

Lynch’s Amazon store, known as Studio: David Lynch, currently sells more than 40 T-shirts and hoodies, ranging in size from small to triple XL, with prices starting at $26. As for our own feelings on the collection, we think they’re best reflected by this T-shirt named “Honestly, I’m Sort of Confused.”

Check out some of our favorites below:

T-shirt that says "Honestly, I'm Sort of Confused"
"Honestly, I'm Sort of Confused"

Buy it on Amazon

Studio: David Lynch Octopus T-shirt
Amazon

Buy it on Amazon

T-shirt that says Peace on Earth over and over again. The caption is pretty on the nose.
"Peace on Earth"

Buy it on Amazon

T-shirt with an image of a screaming face made out of turkey with ants in its mouth
"Turkey Cheese Head"

Buy it on Amazon

T-shirt with an odd sculpted clay face asking if you know who it is. You get the idea.
"I Was Wondering If You Know Who I Am?"

Buy it on Amazon

T-shirt with an image of a sculpted head that is not a chicken. It is blue, though.
"Chicken Head Blue"

Buy it on Amazon

T-shirt with a drawing of a lobster on it. Below the drawing, the lobster is labeled with the word lobster. Shocking, I know.
"Lobster"

Buy it on Amazon

T-shirt with an abstract drawing of what is by David Lynch's account, at least, a cowboy
"Cowboy"

Buy it on Amazon

20 Black-and-White Facts About Penguins

iStock/fieldwork
iStock/fieldwork

Happy Penguin Awareness Day! To celebrated, here are a few fun facts about these adorable tuxedoed birds.

1. All 17 species of penguins are found exclusively in the Southern Hemisphere.

A group of penguins on an iceberg.
iStock/axily

2. Emperor Penguins are the tallest species, standing nearly 4 feet tall. The smallest is the Little Blue Penguin, which is only about 16 inches.

Three emperor penguins
iStock/Fabiano_Teixeira

3. The fastest species is the Gentoo Penguin, which can reach swimming speeds up to 22 mph.

A gentoo penguin swimming underwater
iStock/chameleonseye

4. A penguin's striking coloring is a matter of camouflage; from above, its black back blends into the murky depths of the ocean. From below, its white belly is hidden against the bright surface.

Penguins swimming in the ocean
iStock/USO

5. Fossils place the earliest penguin relative at some 60 million years ago, meaning an ancestor of the birds we see today survived the mass extinction of the dinosaurs.

Emperor penguins with chicks
iStock/vladsilver

6. Penguins ingest a lot of seawater while hunting for fish, but a special gland behind their eyes—the supraorbital gland—filters out the saltwater from their blood stream. Penguins excrete it through their beaks, or by sneezing.

Penguin swimming in the ocean
iStock/Musat

7. Unlike most birds—which lose and replace a few feathers at a time—penguins molt all at once, spending two or three weeks land-bound as they undergo what is called the catastrophic molt.

Gentoo penguin chick molting
iStock/ChristianWilkinson

8. All but two species of penguins breed in large colonies of up to a thousand birds.

A colony of king penguins
iStock/DurkTalsma

9. It varies by species, but many penguins will mate with the same member of the opposite sex season after season.

Two chinstrap penguins
iStock/Legacy-Images

10. Similarly, most species are also loyal to their exact nesting site, often returning to the same rookery in which they were born.

Magellanic penguin nesting in the ground
iStock/JeremyRichards

11. Some species create nests for their eggs out of pebbles and loose feathers. Emperor Penguins are an exception: They incubate a single egg each breeding season on the top of their feet. Under a loose fold of skin is a featherless area with a concentration of blood vessels that keeps the egg warm.

Penguin eggs
iStock/Buenaventuramariano

12. In some species, it is the male penguin which incubates the eggs while females leave to hunt for weeks at a time. Because of this, pudgy males—with enough fat storage to survive weeks without eating—are most desirable.

A group of emperor penguins and chick
iStock/vladsilver

13. Penguin parents—both male and female—care for their young for several months until the chicks are strong enough to hunt for food on their own.

Penguin chick and parent on a nest
iStock/golnyk

14. If a female Emperor Penguin's baby dies, she will often "kidnap" an unrelated chick.

Three emperor penguin chicks
iStock/AntAntarctic

15. Despite their lack of visible ears, penguins have excellent hearing and rely on distinct calls to identify their mates when returning to the crowded breeding grounds.

Gentoo penguins
iStock/Goddard_Photography

16. The first published account of penguins comes from Antonio Pigafetta, who was aboard Ferdinand Magellan's first circumnavigation of the globe in 1520. They spotted the animals near what was probably Punta Tombo in Argentina. (He called them "strange geese.")

A group of magellanic penguins on the seacoast
iStock/encrier

17. An earlier, anonymous diary entry from Vasco da Gama's 1497 voyage around the Cape of Good Hope makes mention of flightless birds as large as ducks.

A cape penguin in South Africa
iStock/ziggy_mars

18. Because they aren't used to danger from animals on solid ground, wild penguins exhibit no particular fear of human tourists.

Man videotaping a penguin in Antarctica
iStock/Bkamprath

19. Unlike most sea mammals—which rely on blubber to stay warm—penguins survive because their feathers trap a layer of warm air next to the skin that serves as insulation, especially when they start generating muscular heat by swimming around.

Penguin swimming in the ocean
iStock/Musat

20. In the 16th century, the word penguin actually referred to great auks (scientific name: Pinguinus impennis), a now-extinct species that inhabited the seas around eastern Canada. When explorers traveled to the Southern Hemisphere, they saw black and white birds that resembled auks, and called them penguins. 

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