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]

10 Rad Gifts for Hikers

Greg Rosenke/Unsplash
Greg Rosenke/Unsplash

The popularity of bird-watching, camping, and hiking has skyrocketed this year. Whether your gift recipients are weekend warriors or seasoned dirtbags, they'll appreciate these tools and gear for getting most out of their hiking experience.

1. Stanley Nesting Two-Cup Cookset; $14

Amazon

Stanley’s compact and lightweight cookset includes a 20-ounce stainless steel pot with a locking handle, a vented lid, and two insulated 10-ounce tumblers. It’s the perfect size for brewing hot coffee, rehydrating soup, or boiling water while out on the trail with a buddy. And as some hardcore backpackers note in their Amazon reviews, your favorite hiker can take the tumblers out and stuff the pot with a camp stove, matches, and other necessities to make good use of space in their pack.

Buy it: Amazon

2. Osprey Sirrus and Stratos 24-Liter Hiking Packs; $140

Amazon

Osprey’s packs are designed with trail-tested details to maximize comfort and ease of use. The Sirrus pack (pictured) is sized for women, while the Stratos fits men’s proportions. Both include an internal sleeve for a hydration reservoir, exterior mesh and hipbelt pockets, an attachment for carrying trekking poles, and a built-in rain cover.

Buy them: Amazon, Amazon

3. Yeti Rambler 18-Ounce Bottle; $48

Amazon

Nothing beats ice-cold water after a summer hike or a sip of hot tea during a winter walk. The Yeti Rambler can serve up both: Beverages can stay hot or cold for hours thanks to its insulated construction, and its steel body (in a variety of colors) is basically indestructible. It will add weight to your hiker's pack, though—for a lighter-weight, non-insulated option, the tried-and-true Camelbak Chute water bottle is incredibly sturdy and leakproof.

Buy it: Amazon

4. Mappinners Greatest 100 Hikes of the National Parks Scratch-Off Poster; $30

Amazon

The perfect gift for park baggers in your life (or yourself), this 16-inch-by-20-inch poster features epic hikes like Angel’s Landing in Zion National Park and Half Dome in Yosemite National Park. Once the hike is complete, you can scratch off the gold foil to reveal an illustration of the park.

Buy it: Amazon

5. National Geographic Adventure Edition Road Atlas; $19

Amazon

Hikers can use this brand-new, updated road atlas to plan their next adventure. In addition to comprehensive maps of all 50 states, Puerto Rico, Canada, and Mexico, they'll get National Geographic’s top 100 outdoor destinations, useful details about the most popular national parks, and points on the maps noting off-the-beaten-path places to explore.  

Buy it: Amazon

6. Adventure Medical Kits Hiker First-Aid Kit; $25

Amazon

This handy 67-piece kit is stuffed with all the things you hope your hiker will never need in the wilderness. Not only does it contain supplies for pain, cuts and scrapes, burns, and blisters (every hiker’s nemesis!), the items are organized clearly in the bag to make it easy to find tweezers or an alcohol wipe in an emergency.

Buy it: Amazon

7. Hiker Hunger Ultralight Trekking Poles; $70

Amazon

Trekking poles will help increase your hiker's balance and stability and reduce strain on their lower body by distributing it to their arms and shoulders. This pair is made of carbon fiber, a super-strong and lightweight material. From the sweat-absorbing cork handles to the selection of pole tips for different terrain, these poles answer every need on the trail. 

Buy it: Amazon

8. Leatherman Signal Camping Multitool; $120

Amazon

What can’t this multitool do? This gadget contains 19 hiking-friendly tools in a 4.5-inch package, including pliers, screwdrivers, bottle opener, saw, knife, hammer, wire cutter, and even an emergency whistle.

Buy it: Amazon

9. RAVPower Power Bank; $24

Amazon

Don’t let your hiker get caught off the grid with a dead phone. They can charge RAVPower’s compact power bank before they head out on the trail, and then use it to quickly juice up a phone or tablet when the batteries get low. Its 3-inch-by-5-inch profile won’t take up much room in a pack or purse.

Buy it: Amazon

10. Pack of Four Indestructible Field Books; $14

Amazon

Neither rain, nor snow, nor hail will be a match for these waterproof, tearproof 3.5-inch-by-5.5-inch notebooks. Your hiker can stick one in their pocket along with a regular pen or pencil to record details of their hike or brainstorm their next viral Tweet.

Buy it: Amazon

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LEGO and IKEA Have Designed a New Line of Storage Boxes With the Help of Child Psychologists

IKEA
IKEA

Putting together IKEA furniture can remind grownups of their days playing with LEGO bricks. The two brands serve very different demographics, and now they've joined forces to create these ready-to-assemble products designed to appeal to both kids and adults.

As ThomasNet reports, BYGGLEK (Swedish for “to build and play") puts IKEA's practical, minimalist spin on the traditional LEGO toy. The key is a plastic storage bin featuring LEGO-compatible studs on its interior and exterior. Instead of using the floor as their play place and making rooms minefields for barefooted parents, kids can contain their creations within the box. When playtime is over, adults simply pick up the box holding the LEGO masterpiece and move it out of the way. The BYGGLEK boxes come in clean, neutral tones, so parents can show off their kids' handiwork on a canvas that fits the style of their home.

Opportunities for artistic expression for children often lead to headaches for the grownups who clean up after them. In order to make play a more organized experience without inhibiting creativity, LEGO and IKEA collaborated with child psychologists. The resulting product is a win for everyone: It allows parents to organize messes without deconstructing their child's work-in-progress.

IKEA and LEGO's BYGGLEK collection includes four products: A large box, a medium box, a set of three small boxes, and a basic 201-piece LEGO set for kids 5 and up. Prices range from $10 to $15; you can order yours today from IKEA.

[h/t ThomasNet]