TIME quiz

Can You Solve the World’s Trickiest Math Problems?

We've assembled the ultimate quiz of common misconceptions.

All questions courtesy Alex Bellos, author of The Grapes of Math: How Life Reflects Numbers and Numbers Reflect Life.



Correction appended Aug. 14, 6:35 p.m.

TIME Education

How to Learn to Love Math

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Monashee Frantz—Getty Images/OJO Images RF

Students have been taught that math is about right and wrong, rather than trial and error

Over the three years Jordan Ellenberg was writing his book, he repeatedly encountered the same reaction to its subject. “I’d be at a party, and I’d tell someone what my book was about, and then I’d be like — ‘Hey, where’d you go?’” What topic was so awful and off-putting as to make people flee at its mere mention? Math.

Ellenberg, a professor of mathematics at the University of Wisconsin–Madison, has now published that book, How Not to Be Wrong, and rather than putting people off, it will make its readers want to stick around. Ellenberg tells engaging, even exciting stories about how “the problems we think about every day — problems of politics, of medicine, of commerce, of theology — are shot through with mathematics.” Understanding the role of math in these issues, he writes, “gives you access to insights accessible by no other means.”

Knowledge of math, Ellenberg enthuses, is like “a pair of X-ray specs that reveal hidden structures underneath the messy and chaotic surface of the world,” like “an atomic-powered prosthesis that you attach to your common sense, vastly multiplying its reach and strength.”

Sounds pretty great, doesn’t it? So then why does math fill so many of us with dread? I put that question to Ellenberg when we spoke by phone last week. “We teach math as if it’s about applying a prescribed formula, circling the right answer, and going on to the next problem without thinking about what it is we’re doing,” Ellenberg replied. “But that’s so not what math is. Math is a fundamentally creative enterprise, a fundamentally humanistic enterprise. It’s a lens through which we can see the world better.”

Ellenberg sees the results of rote mathematics instruction in his undergraduates: “It can be hard for my students to get into the mind-set of trying different things. Often, during my office hours, I’ll get a student who says of an assignment, ‘I didn’t know where to start.’ I tell them, ‘Of course you didn’t know where to start! You’re doing this for the first time, so try a few things and see what works.’ But this approach is foreign to students who have been taught that math is a series of formulas. They don’t realize that math is all about trial and error, about experimenting. That’s true of advanced math, but I think we can push that mind-set down into the earlier grades as well.”

Ellenberg acknowledges that his approach would require a paradigm shift. “People are not used to taking a loose and easy approach to math. They get very tight and tense around math because they have so much fear and anxiety about it,” he noted. In addition, he said, “People dislike math because they don’t like being told that they’re wrong. And it’s not incorrect to see math as a realm where there are right and wrong answers. But the thing is: knowledge in math does not come about because the teacher says it’s so. Math is a realm where people can demonstrate the rightness of answers to themselves. So if part of what creates the fear of math is wanting to avoid being wrong, then learning to like math is about learning to be willing to mess up.”

Paul is the author of the forthcoming book Brilliant: The Science of How We Get Smarter. Read more at her blog, where this post first appeared.

TIME Video Games

Here’s How Far Mario Travels in Super Mario Bros.

Mario
James Coldrey / Getty Images

I’m not great at math (stay in school, kids!), perhaps because I never liked it much. But this is a good use of math.

Nick Greene over at Mental Floss fielded one of the most pressing and important reader questions we’ll ever grapple with in our lifetimes: How far does Mario travel in Super Mario Bros.?

Greene calculated Mario’s steps based on a stance-width of 26 inches – a little more than shoulder-width apart — and assumed that Mario would be the small, pre-mushroom Mario.

The final tally:

  • 3.4 miles, assuming no visits to bonus areas or warp zones
  • 1218.5 feet swimming (about 7.5 laps in an Olympic-sized pool)
  • 3.7 miles, assuming visits to bonus areas
  • Another 344 feet swimming, assuming visits to underwater bonus areas

Kind of puts your entire childhood into perspective, no? I would have guessed dozens and dozens of miles, but we’re actually dealing with a moderately-paced, hour-long treadmill workout.

Granted, the treadmill workout is one without jumping, consuming shape-shifting mushrooms, spitting fireballs and trying to avoid being killed by various animals. I bet Mario burns more calories than we think. He’s still a bit on the pudgy side, but don’t forget that he subsists almost entirely on pizza.

How Far Does Mario Have to Run (and Swim) in Super Mario Bros.? [Mental Floss]

MORE: The History of Video Game Consoles – Full

TIME Math

And the World’s Favorite Number Is…

British mathematics writer Alex Bellos launched a worldwide survey asking people which number is their favorite after being posited the question many times while chatting with students or at lectures over the years and seeing that people take the choice seriously

A survey launched by a British mathematics writer has found that seven is the world’s favorite number, reports The Guardian. The results of the online survey were published on Tuesday, with three, eight and and four coming second, third and fourth.

Alex Bellos said he started the survey because of his belief that people have strong feelings about numbers, something he learned from giving talks about math in schools, colleges and festivals. “I am always asked for my favorite number – it’s guaranteed this question will come up,” he said.

Bellos, whose new book is entitled The Grapes of Math, claimed he received over 30,000 responses within a few weeks of launching the survey, with total responses currently standing at 44,000. Out of all the submissions, almost half of the votes cast were for the numbers between one and 10. The least favorite number turned out to be 110, which was the lowest number to receive no votes.

The writer suggested that the reason for seven’s popularity is its prevalence in global culture, from Snow White and the Seven Dwarves, to the existence of seven days in a week.

“We love seven because it is unique. It reflects our uniqueness. Of course it’s the world’s favorite number,” he said.

[Guardian]

TIME Education

Dad’s Rant About Common Core Math Problem Goes Viral

Dad with engineering degree calls math problems "ridiculous" in viral rant, just as Indiana drops the Common Core. Ouch.

Common Core, this is not your week. First you get publicly dumped by the entire state of Indiana, then a dad with an engineering degree calls your math strategy “ridiculous” in a viral Facebook post. The frustrated father pointed out that if anyone at his job approached a problem in the way he’s saying is recommended by the Common Core, they’d be fired. This is embarrassing, considering the program was designed as a set of national curriculum standards that would teach kids the skills they need for real-world careers. The post has almost 6,000 likes, and has been shared over 61,000 times on TheBlaze.com.

On Monday, Indiana became the first state to officially give up on the Common Core. Governor Mike Pence’s decision was seen as a victory for conservatives who believe the national standards dilute state’s power to determine local school curriculum. “I believe our students are best served when decisions about education are made at the state and local level,” Pence said in a statement. “By signing this legislation, Indiana has taken an important step forward in developing academic standards that are written by Hoosiers, for Hoosiers, and are uncommonly high, and I commend members of the General Assembly for their support.”

The new law doesn’t radically change Indiana’s curriculum, it just strikes any mention of the “Common Core” and asks the state’s board of education to adopt new standards that correspond to national and international college-readiness expectations. Oklahoma is also taking steps to create a state curriculum that resembles the Common Core (for testing purposes) but doesn’t use the name.

Backlash against the Common Core has been especially fervent in conservative states. There’s been fierce opposition in states like South Carolina, where Governor Nikki Haley said, “They’re still trying to put us all in one basket, and we’re not to be put in one basket.”

Secretary of Education Arne Duncan antagonized parents and gave fuel to the opposition late last year when he said that the anti-Common Core movement was mostly “white suburban moms who — all of a sudden — their child isn’t as brilliant as they thought they were, and their school isn’t quite as good as they thought they were,” for which he later apologized.

But the real problem may be parents like Jeff Severt, the engineering degree dad whose detailed criticism of what he says was a Common Core designed math question, was about the recommended strategy, not his child’s score. Severt, who said on Glenn Beck’s show that he had a “meltdown” trying to help his son with the math assessment that asked students to use a complicated number line strategy to solve a simple subtraction problem. The assignment was to find the error and then write a letter to him telling the errant student how to use the number line method solve the problem. Severt’s response is below:

Dear Jack,

Don’t feel bad. I have a Bachelor of Science Degree in Electronics Engineering which included extensive study in differential equations and other higher math applications. Even I cannot explain the Common Core Mathematics approach, nor get the answer correct. In the real world, simplification is valued over complication. Therefore:

427 – 316 = 111

The answer is solved in under 5 seconds: 111. The process used is ridiculous and would result in termination if used.

Sincerely, Frustrated Parent

 

Yikes.

TIME creationism

Creationism in Schools—On the Taxpayer’s Dime

Back to the future? At South Carolina's Bob Jones University, Dr. Maude Stout "teaches the controversy" over evolution in 1948.
Back to the future? At South Carolina's Bob Jones University, Dr. Maude Stout "teaches the controversy" over evolution in 1948. Francis Miller—Time Life Pictures/Getty Images

Vouchers are increasingly being used to teach kids to question not just evolution, but cosmology, biology, even math.

Science loves balance. Gasses rush in to fill vacuums; cells seek homeostasis; an action is never quite satisfied until there has been an equal and opposite reaction. So it’s perhaps fitting that just days after the science wires were buzzing over a new (and thrilling) confirmation of the Big Bang, there is a new (and dispiriting) report on Politico.com about the growth of taxpayer-funded anti-science education in American schools.

According to Politico, 14 states will spend a collective $1 billion in 2014 on vouchers for private and religious schools that teach kids to mistrust not only the science of evolution, but also cosmology, geology, biology and even math. Twelve other states—including bright blue New York—are considering following their lead.

Occasionally the programs don’t just “teach the controversy,” as their backers like to say, but something darker. Evolution, according to one set of texts, is a “wicked and vain philosophy.” Children are taught to “discuss the importance of a right view of evolution,” a view that does not—no surprise—include an enthusiastic embrace of Darwin.

The problem with teaching children like this—apart from the fact that it’s simply incorrect—is that it disqualifies them from full participation in the larger world. It’s awfully hard to be part of the global conversation about the Big Bang breakthrough when understanding the science requires you to accept that the universe is 13.8 billion years old, while your teachers are telling you it’s less than 10,000. It’s awfully hard to be mathematically literate when your geometry and algebra classes are being interrupted to discuss the role numbers play in the Bible.

All of this is being shouted about and litigated over, with the usual parties involved: the ACLU is suing to prevent New Hampshire’s and Colorado’s voucher programs from going forward; Republican political leaders—including Sen. Lamar Alexander, Rep. Eric Cantor and La. Governor Bobby Jindal—are calling for even more-ambitious voucher programs. The Koch Brothers and their billions are pushing for additional public subsidies to pay for the expanded programs.

Backers of the non-science curriculum, of course, frame their goals in the noble-sounding idea of allowing families to “choose the best learning options for their children,” in the phrasing of the website for Florida-based Step Up For Students, which provides scholarships for low-income kids to attend private schools. But their thinking is more troubling than that. Bob Tuthill, the group’s head, told Politico that topics like the age of the Earth and the reasons for the Civil War are simply too controversial for the government to mandate how they should be taught. Once your anti-science ideology is bumping up against the whole Civil-War-was-about-states’-rights-not-slavery school of thought, you’ve got to rethink the company you’re keeping.

Even schools that take pains to give a nod to scientists do it in a qualified way that undoes their ostensible point—as when the website of a Philadelphia private school applauds “the men and women of science,” but cautions that “our understanding is not complete until we filter it” through Scripture. But science already has a filtration process in place, thank you very much. It’s called peer review and many of those peers are people of deep faith and spirituality themselves; they’ve simply learned to keep their religious beliefs and their scientific rigor far enough apart so that both are served well.

None of this non-science comes free. At the same time a Gallup poll reveals that 46% of Americans believe human beings were created in their present form, one international survey found American kids finishing 26th of 34 countries in math and 21st in science. Paul Peterson, the head Harvard University’s Program on Educational Policy and Governance is oddly sanguine about where this could lead, according to Politico, predicting that the free-market system will weed out the schools that teach science badly, because parents will quit sending their kids there.

The problem is, before that happens the American economy will already have weeded out the children who graduated from those schools—at least when it comes to competing for the highest skilled, best-paying jobs. And the global economy, which increasingly depends on innovation and high tech, will weed a little bit more of America out too.

TIME Television

Game of Thrones Spoilers Are Now Being Used to Discipline Unruly Children

Jack Gleeson as King Joffrey on HBO's 'Game of Thrones.'
King Joffrey approves of this tactic. HBO

One Belgian teacher has figured out a diabolical scheme worthy of King Joffrey

Teachers have long sought a foolproof method for holding their students’ attention and discouraging them from acting out. One educator in Belgium seems to have found a solution to that particular problem: revealing Game of Thrones spoilers.

Belgian daily Het Nieuwsblad reports that one math teacher, after confirming his students are fan of the HBO series based on George R.R. Martin’s A Song of Fire and Ice novels, told them he would reveal deaths from the as-yet unreleased seasons of the TV show if they did not remain quiet during class. (Despite growing concerns about Martin’s writing pace, the books — which the Belgian teacher has read — remain ahead of the TV series.)

The tactic is proving effective so far, although one classmate who reads ahead could easily undermine his whole plan. For now, however, the teacher’s approach remains evil and brilliant in equal measures — fitting qualities for a Game of Thrones-based scheme.

[Het Nieuwsblad via Warming Glow]

TIME Food and Beverage Industry

Why Everything Is Going to Cost $3.14 on Friday

Jay Myrdal—Getty Images

In celebration of Pi Day, restaurants and bars around the country are hosting tons of nerdy math-themed promotions this Friday, March 14 (3.14), most involving pizzas or slices of pie for $3.14. Also: cheap drinks!

Here are a few possible options for geeking out—and saving some cash—on Friday, 3.14.2014:

Boston
Boston.com recommends pie for breakfast at the Beacon Hill Hotel, where a slice sells for $3.14 on Friday, while the Salvatore’s, a local Italian chain, offers a selection of flatbread pizza pies for $3.14 that day.

Chicago
Check out the huge list of 3.14-themed promotions and deals at restaurants and bakeries in the Windy City rounded up at Chicago on the Cheap. Most feature a $3.14 price on pizza or pie, but there are also basic buy one slice of pizza, get one free offers.

Princeton, N.J.
New Jersey’s quaint college town takes March 14 seriously. Not only is 3.14 Pi Day, it’s also the day that longtime town resident, university professor, and all-around genius Albert Einstein was born. Accordingly, Princeton goes all out with an entire weekend honoring Pi Day and Einstein’s birthday, including free guided walking tours of Einstein’s neighborhood, a “Top Chef” pie-making competition, and a Rubik’s Cube demonstration.

St. Louis
Pi Pizza, with a handful of locations in Missouri and a sister branch District of Pi restaurant in Washington, D.C., is naturally host to a range of special Pi Day events and deals, including a promotion in which your second pizza is $3.14 after paying full price for the first.

Northeast
Based in Maine, with locations also in New Hampshire and Massachusetts, the Portland Pie Company is host to discounted pizza deals and a $3.14 pint special during lunch and happy hour.

Southeast
Your Pie, a restaurant chain with locations in Georgia, Florida, South Carolina, and Tennessee, is hosting its “fifth annual celebration of the circle” this Friday, with the base price of its customizable craft pizzas starting at $3.14.

TIME gender

Study: Employers Assume Women Are Worse At Math

Even when the evidence suggests it's not true

We all know that women can be just as good at math as men. But that doesn’t mean either sex acknowledges it.

A new study published yesterday in the Proceedings from the National Academy of Sciences (PNAS) found that hiring managers of either sex are less likely to hire a woman to solve a math problem, even after she proves her skills are equal to those of a man.

During a lab experiment, “hiring managers” were asked to pick their preferred applicant for a job based on a person’s appearance, and thus gender. The “job” at hand was a math problem that both genders generally complete at equal levels. The managers were twice as likely to choose the man over the woman.

And it only got worse when applicants were asked to self-report how they had solved the problem. Men were more likely to brag about their success, while women—characteristically—tended to downplay theirs. The managers responded by again choosing the man for the job. If more information about the applicant’s performance at the task was offered, the managers still discriminated, but at a reduced level.

This study provides more insight as to why women are far less likely to major in math or science, let alone attempt to work in either field in a professional capacity.

In October 2013, Eileen Pollack wrote a New York Times Magazine story called “Why Are There Still So Few Women In Science?,” that seeks to answer a larger question about gender bias and the sciences.

That the disparity between men and women’s representation in science and math arises from culture rather than genetics seems beyond dispute.

TIME Food & Drink

Math Proves You Should Always Order the Bigger Pizza

Pizza
Getty Images

Go on, just do it

If there’s one thing we can all agree on, it’s that pizza is delicious. Everyone loves pizza. Like, the United States government even took the time recently to prove that.

So, that’s one of the reasons why you should always opt for the bigger pie when you’re out at a pizzeria with friends (or alone — we don’t judge) so that you simply have more delicious pizza to enjoy. The other reason, though, is that it’s pretty much always a much better deal.

Some heroes at NPR crunched the numbers, looking at 74,476 prices from 3,678 pizza places across the U.S. They point out that a 16-inch pizza, for example, is really four times the size of an eight-inch pizza, though most people would probably think it would be double. On average, consumers spend $16.59 for a 16-inch pie. To get the same amount of pizza, they’d have to spend $33 on four eight-inch pies.

If math isn’t your thing, just trust us on this one. It’s a much, much better deal. So next time you’re out for pizza just go ahead and opt for the largest size. Can’t argue with math!

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