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.
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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
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.
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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
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]

Party Like a Hobbit at Chicago’s Lord of the Rings Pop-Up Bar

Gollum and a Ringwraith loom near Bilbo's hobbit hole at Replay Lincoln Park's Lord of the Rings pop-up bar.
Gollum and a Ringwraith loom near Bilbo's hobbit hole at Replay Lincoln Park's Lord of the Rings pop-up bar.
Replay Lincoln Park

One does not simply walk into Mordor, but one does simply walk into The Lord of the Rings pop-up bar in Chicago—as long as you’re at least 21 years old, of course.

Replay Lincoln Park, known for elaborate themed pop-ups for Game of Thrones, South Park, and other entertainment franchises, has transformed its premises into a magical reproduction of Middle-earth aptly called “The One Pop-Up to Rule Them All,” open now through March 23.

Inside, you’ll be able to crouch under an outcropping of tangled tree roots while one of the dreaded Nazgûl lurks above you, high-five a grimacing Gollum, and snap photos with all your favorite Lord of the Rings characters.

nazgul at the lord of the rings pop-up bar at chicago's replay lincoln park
The Nazgûl like to party, too.
Replay Lincoln Park

You might want to skip elevenses to make sure you have plenty of room for a Hobbit-approved feast during your visit. The menu, catered by Zizi’s Cafe, features items like Fried Po-tay-toes, Lord of the Wings, Beef Lembas, and Pippen’s Popcorn.

ent replica at chicago's replay lincoln park pop-up bar
Say hello to a friendly Ent while you munch on "Pippen's Popcorn."
Replay Lincoln Park

According to Thrillist, there will be three different counters in the bar, each with its own specialty drinks. Head to The Prancing Pony for a second breakfast shot (maple whiskey, bacon, and orange juice), or take a trip to Minas Tirith to toss back a palantir shot, made of silver tequila and passion fruit purée. If you’re in the mood for a little dark magic, you can trek over to Mordor and try a “my precious” shot, a fusion of dark rum, orange liquor, and Cajun seasoning.

lord of the rings pop-up bar at chicago's replay lincoln park
The Eye of Sauron is watching you order another round of Mordor shots.
Replay Lincoln Park

For those of you who are happy to accompany your Tolkien-obsessed friends to the pop-up but aren’t exactly tickled at the sight of a moss-covered Ent replica yourselves, take heart in this added bonus: Replay Lincoln Park also boasts more than 60 free arcade games and pinball machines.

[h/t Thrillist]

10 Delicious Facts About McDonald's Shamrock Shake

McDonald's
McDonald's

Many people overdo it with the drinking on St. Patrick's Day, but it's not always Guinness or Jameson that gets them into trouble. Sometimes it's the Shamrock Shake, McDonald's uniquely green and often elusive seasonal treat. Here’s the skinny on the 660-calorie indulgence.

1. The Shamrock Shake wasn't originally known as The Shamrock Shake.

The original name of the cult classic milkshake was slightly less alliterative. It was called the St. Patrick’s Day Green Milkshake. Catchy, no?

2. The Shamrock Shake is a charitable endeavor.

What does the Shamrock Shake have to do with the Ronald McDonald House and the Philadelphia Eagles? Everything, according to the fast food giant. When Eagles tight end Fred Hill’s daughter was being treated for leukemia in 1974, Fred and his wife spent a lot of time in waiting rooms and noticed many other emotionally depleted families doing the same. He thought it would be healthier for families if they had a place to call home while their children were being treated, so he used his football connections to get in touch with a local advertising agency that did work for Mickey D’s. They agreed to give profits from the Shamrock Shake toward a home near the Children’s Hospital in Philadelphia, which ended up becoming the first-ever Ronald McDonald House.

3. Uncle O'Grimacey used to be the Shamrock Shake's ambassador.

Back in the early ‘80s, a fairly offensive character named Uncle O’Grimacey was used to promote the seasonal shake.

4. No McDonald's restaurant is required to offer the Shamrock Shake.

In 2012, it was announced that, for the first time, the Shamrock Shake would be available in all McDonald's nationwide—but not all restaurants have to carry them. Regional managers decide whether their stores will carry the shakes each year.

5. Jimmy Fallon once depleted a New York City restaurant's entire Shamrock Shake supply.

If you’re a New Yorker and you didn’t get a much-craved Shamrock Shake in 2011, it’s probably Jimmy Fallon’s fault. When he caught wind that a Union Square Mickey D's had the elusive dessert, he totally cleaned them out—purchasing more than 100 shakes for his audience. New Yorkers were not pleased with Fallon.

6. The Shamrock Shake got an ice cream offshoot (that didn't fare so well).

Despite the smashing success of the shake, the Shamrock Sundae was a dismal failure. Introduced in 1980, it was discontinued after just a year. Apparently people prefer their unnaturally green desserts in shake form as opposed to scoop form. Though this year, they're trying again: in honor of the Shamrock Shake's 50th anniversary, McDonald's is also introducing an Oreo Shamrock McFlurry.

7. There have been many super-sized versions of the Shamrock Shake.

For a few years, a giant shake was poured into the Chicago River to help contribute to the green hue it’s dyed every year. A donation was also made to the Ronald McDonald House.

8. The McDonald's app will help you track down a Shamrock Shake.

Are you one of those unfortunate souls who has to hunt the shake down every year? McDonald's official app can help. In 2020, for the first time in three years, the Shamrock Shake will be offered at all McDonald's locations. If you're not sure of the nearest one near you, the McDonald's app has a full directory to help.

9. You can make your own Shamrock Shake at home.

If you still can’t find a shake, you have one other option: make your own.

10. In 2017, McDonald's engineered a special Shamrock Shake straw.

In 2017, McDonald's unveiled an amazing innovation for Shamrock Shake lovers: the STRAW. Short for Suction Tube for Reverse Axial Withdrawal, the STRAW was designed by real engineers at the aerospace and robotics engineering firms JACE and NK Labs—specifically with the Shamrock Shake in mind. What sets the device apart from conventional straws is the sharp bend in its shape and the three, eye-shaped holes in addition to the opening at the bottom end. The extra holes are positioned in a way that allows drinkers to take a sip of a new layered version of the frosty treat that’s equal parts top mint layer and bottom chocolate layer.

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