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
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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]

Hee-Haw: The Wild Ride of "Dominick the Donkey"—the Holiday Earworm You Love to Hate

Delpixart/iStock via Getty Images
Delpixart/iStock via Getty Images

Everyone loves Rudolph the Red-Nosed Reindeer. He’s got the whole underdog thing going for him, and when the fog is thick on Christmas Eve, he’s definitely the creature you want guiding Santa’s sleigh. But what happens when Saint Nick reaches Italy, and he’s faced with steep hills that no reindeer—magical or otherwise—can climb?

That’s when Santa apparently calls upon Dominick the Donkey, the holiday hero immortalized in the 1960 song of the same name. Recorded by Lou Monte, “Dominick The Donkey” is a novelty song even by Christmas music standards. The opening line finds Monte—or someone else, or heck, maybe a real donkey—singing “hee-haw, hee-haw” as sleigh bells jingle in the background. A mere 12 seconds into the tune, it’s clear you’re in for a wild ride.

 

Over the next two minutes and 30 seconds, Monte shares some fun facts about Dominick: He’s a nice donkey who never kicks but loves to dance. When ol’ Dom starts shaking his tail, the old folks—cummares and cumpares, or godmothers and godfathers—join the fun and "dance a tarentell," an abbreviation of la tarantella, a traditional Italian folk dance. Most importantly, Dominick negotiates Italy’s hills on Christmas Eve, helping Santa distribute presents to boys and girls across the country.

And not just any presents: Dominick delivers shoes and dresses “made in Brook-a-lyn,” which Monte somehow rhymes with “Josephine.” Oh yeah, and while the donkey’s doing all this, he’s wearing the mayor’s derby hat, because you’ve got to look sharp. It’s a silly story made even sillier by that incessant “hee-haw, hee-haw,” which cuts in every 30 seconds like a squeaky door hinge.

There may have actually been some historical basis for “Dominick.”

“Travelling by donkey was universal in southern Italy, as it was in Greece,” Dominic DiFrisco, president emeritus of the joint Civic Committee of Italian Americans, said in a 2012 interview with the Chicago Sun-Times. “[Monte’s] playing easy with history, but it’s a cute song, and Monte was at that time one of the hottest singers in America.”

Rumored to have been financed by the Gambino crime family, “Dominick the Donkey” somehow failed to make the Billboard Hot 100 in 1960. But it’s become a cult classic in the nearly 70 years since, especially in Italian American households. In 2014, the song reached #69 on Billboard’s Holiday 100 and #23 on the Holiday Digital Song Sales chart. In 2018, “Dominick” hit #1 on the Comedy Digital Track Sales tally. As of December 2019, the Christmas curio had surpassed 21 million Spotify streams.

“Dominick the Donkey” made international headlines in 2011, when popular BBC DJ Chris Moyles launched a campaign to push the song onto the UK singles chart. “If we leave Britain one thing, it would be that each Christmas kids would listen to 'Dominick the Donkey,’” Moyles said. While his noble efforts didn’t yield a coveted Christmas #1, “Dominick” peaked at a very respectable #3.

 

As with a lot of Christmas songs, there’s a certain kitschy, ironic appeal to “Dominick the Donkey.” Many listeners enjoy the song because, on some level, they’re amazed it exists. But there’s a deeper meaning that becomes apparent the more you know about Lou Monte.

Born Luigi Scaglione in New York City, Monte began his career as a singer and comedian shortly before he served in World War II. Based in New Jersey, Monte subsequently became known as “The Godfather of Italian Humor” and “The King of Italian-American Music.” His specialty was Italian-themed novelty songs like “Pepino the Italian Mouse,” his first and only Top 10 hit. “Pepino” reached #5 on the Billboard Hot 100 in 1963, the year before The Beatles broke America.

“Pepino” was penned by Ray Allen and Wandra Merrell, the duo that teamed up with Sam Saltzberg to write “Dominick the Donkey.” That same trio of songwriters was also responsible for “What Did Washington Say (When He Crossed the Delaware),” the B-side of “Pepino.” In that song, George Washington declares, “Fa un’fridd,” or ‘It’s cold!” while making his famous 1776 boat ride.

With his mix of English and Italian dialect, Monte made inside jokes for Italian Americans while sharing their culture with the rest of the country. His riffs on American history (“What Did Washington Say,” “Paul Revere’s Horse (Ba-cha-ca-loop),” “Please, Mr. Columbus”) gave the nation’s foundational stories a dash of Italian flavor. This was important at a time when Italians were still considered outsiders.

According to the 1993 book Italian Americans and Their Public and Private Life, Monte’s songs appealed to “a broad spectrum ranging from working class to professional middle-class Italian Americans.” Monte sold millions of records, played nightclubs across America, and appeared on TV programs like The Perry Como Show and The Ernie Kovacs Show. He died in Pompano Beach, Florida, in 1989. He was 72.

Monte lives on thanks to Dominick—a character too iconic to die. In 2016, author Shirley Alarie released A New Home for Dominick and A New Family for Dominick, a two-part children’s book series about the beloved jackass. In 2018, Jersey native Joe Baccan dropped “Dominooch,” a sequel to “Dominick.” The song tells the tale of how Dominick’s son takes over for his aging padre. Fittingly, “Dominooch” was written by composer Nancy Triggiani, who worked with Monte’s son, Ray, at her recording studio.

Speaking with NorthJersey.com in 2016, Ray Monte had a simple explanation for why Dominick’s hee-haw has echoed through the generations. “It was a funny novelty song,” he said, noting that his father “had a niche for novelty.”

Florida to Open Its First-Ever Snow Park

Zuberka/iStock via Getty Images
Zuberka/iStock via Getty Images

Millions of tourists flock to Florida each year to ride roller coasters, meet their favorite cartoon characters, and lounge on the beach. The state isn't famous for its winter activities, but that could soon change. As WESH 2 reports, Florida's first-ever snow park is coming to Dade City in 2020.

At Snowcat Ridge, guests will be able to take part in the same snowy fun that's up North. The main attraction of the park will be a 60-foot-tall, 400-foot-long slope packed with snow. A lift will transport visitors to the top of the hill, and from there, they'll use inner tubes to slide back down to ground level. Single, double, and six-person family tubes will be provided to riders.

Guests can also check out the 10,000-square-foot play dome, where they'll use real snow to build snow castles and snow men. The area will even feature a small hill for young visitors who aren't ready for more serious snow-tubing. And because the best part of playing in the snow all day is warming up afterwards, Snowcat Ridge will be home to an Alpine Village, where guests can nibble on snacks and sip cocoa in front of a bonfire.

Dade City is located in Central Florida, an area that hasn't seen snow in nearly 43 years. The arrival of the new park will mark the first time many locals can get a full winter experience close to home.

Snowcat Ridge is expected to open in November 2020.

[h/t WESH 2]

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