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Articles by Gary Antonick
The Primes in Evenland Puzzle
Photo Sorting it all out at a Julia Robinson Mathematics Festival held at Stanford University in May 2012. Is your kid entranced by math but discouraged by math contests? If so, take heart — here’s Dr. Cathy O’Neil, who received a Ph.D. in mathematics from Harvard and subsequently taught math at Barnard College. I think math contests for kids kind of suck.
Numberplay: The Danger of Praise
We hear that kind of praise all the time. But it’s devastating. Joshua Zucker is the director of the Julia Robinson Mathematics Festival. I had asked him about the role of praise in teaching. He continued: I have no problem with praising effort. It’s praising intelligence by itself that’s the problem. That kind of praise will eventually shut you down. This experiment is my favorite. A bunch of kids were given some fairly easy math problems.
Martin Gardner's 'The Annotated Alice'
This week we continue to celebrate the life of the popular science and math writer Martin Gardner, who would have been 99 years old next week, on Oct. 21. Mr. Gardner published more than 100 books in a variety of fields: philosophy, religion, magic and — as many Numberplay readers are probably aware — recreational math puzzles. I recently wondered — of everything Mr. Gardner has written, which has been his biggest seller?
After the Party Problem
This week we continue to celebrate the life of the mathematician Paul Erd?s, who would have celebrated his 100th birthday on March 26. Our challenge will be to explore a classic often associated with Dr. Erd?s — the Party Problem. Before we get to the problem — as I was preparing last week’s post, “The Improbable Life of Paul Erd?s,” I found myself amazed and flabbergasted by the probabilistic method, one of Dr. Erd?s’s most significant accomplishments.
The 64 Mathematicians Puzzle
Physics professor Marco Moriconi has contributed a number of terrific puzzles to Numberplay including Gas Stations, Ant on a Rubber Band, Student Groups, the Five-Pirate Puzzle and Spaghetti Loops. This week we feature a slightly-altered version of another one of his favorites. 64 mathematicians attending a conference each learn a nice, new theorem. The next day at lunch (at the spectacular Niteroi Contemporary Art Museum) they meet in pairs to share all their newly learned results.
Martin Gardner: The Two Child Problem
This week we continue to celebrate the life of recreational mathematician Martin Gardner, who would have been 98 on Sunday, Oct. 21. This week’s puzzle is one of my favorites from Mr. Gardner. The puzzle is seemingly simple, slightly ambiguous and astonishingly difficult. Stanford faculty member Nick McKeown puts it well: “We humans just haven’t evolved to solve this kind of problem.” Here’s how the problem appeared in Mr. Gardner’s 1956 Mathematical Games column in Scientific American.
Béla Bollobás: The Spread of Infection on a Square Grid
Our puzzle this week was suggested by the Hungarian-born British mathematician Béla Bollobás, one of the world’s leading mathematicians in combinatorics. Professor Bollobás was a longtime collaborator of Paul Erd?s, considered by many to be one of the 20th century’s greatest mathematicians, and was selected as a plenary speaker at the Erd?s Centennial, a conference held last week in Budapest to honor the 100th anniversary of the birth of Professor Erd?s.
A Numberplay Farewell
This – after seven years – is my last Numberplay column for The Times. It’s been a terrific, wild ride, full of new friendships and rewarding discovery. But it’s now time to focus on new projects: teaching a course on the art of logic in Shanghai, developing an online program on the psychology of reasoning at Stanford and helping to create a national math tournament in Nigeria. Before my experience with Numberplay, I thought I understood problem-solving.
Ian Stewart: Calculating the Cosmos
In this view of the Milky Way galaxy using infrared, the Hubble Space Telescope reveals a rich tapestry of more than half a million stars. This week’s challenge was suggested by Ian Stewart, the world-class mathematician and best-selling author, whose Calculating the Cosmos: How Mathematics Unveils the Universe has just been published.
Would You Bet Against Your Candidate?
Would you ever bet against your favorite sports team? Or your preferred presidential candidate? This kind of emotional hedge makes sense: if your side loses, your disappointment will be partly offset by your financial gain. But would you actually place this bet? In this week’s challenge, suggested by Carey Morewedge of Boston University, we take this on as a thought experiment with a very real upcoming presidential election.
Horse Racing - NYTimes.com
Alan Garcia astride Watery Moon winning the sixth race at opening day at the Keeneland track in Lexington, Ky., in April. This week’s challenge was inspired by Todd Unger, chief digital officer and chief marketing officer of the Daily Racing Form, horse racing’s dominant multiplatform media and e-commerce company. Let’s experience a bit of that equestrian energy with — You have 25 horses, and can run five horses in a race at a time.
The Prisoners’ Paradox
This week’s challenge was suggested by Greg Ross, creator and curator of the Futility Closet, the online miscellany of compendious amusements. The puzzle is from the first of his two eponymous book-form compilations of closet tidbits, which I happened to pull off the bookshelf recently and completely derail an evening. Let’s try — Three condemned prisoners share a cell. A guard arrives and tells them that one has been pardoned. “Which is it?” they ask. “I can’t tell you that,” says the guard.
Lines and Squares
A sculpture of San Francisco by Liz Hickok, made of Jell-O and gelatin squares and other shapes. This week’s challenge was suggested by Jack Dieckmann, a math teaching expert at Stanford University. Jack is a core member of the popular YouCubed, a Stanford-based online resource for K-12 math teachers founded by math teaching superstar Jo Boaler and her college Cathy Williams.
The World’s Greatest Detective
This week’s challenge was suggested by Po-Shen Loh, professor of mathematics at Carnegie Mellon University. After a summer of travel around the world speaking about math, Po is back at Carnegie Mellon, working with 200+ students in a unique class focused on creative problem-solving. This week he brings that creative impulse to Numberplay to acknowledge the recent birthday of Agatha Christie, the English crime novelist born on Sept. 15, 1890.
Walk Signals - NYTimes.com
Our puzzle this week was suggested by Seth Cohen, who teaches astronomy and physics at St. Paul’s School in New Hampshire. We last saw Seth a year ago, when he illuminated us with Bulbs and More Bulbs. Let’s now join him for a race through town. Here’s — Let’s say that you are in a square city with a perfectly square grid of streets which is 3 blocks by 3 blocks (a very small city). Think of a tic-tac-toe board, where each line is a street.
Crossing the Pool
This week’s puzzle was suggested by Steve Humble (@drmaths), an author and mathematics educator from Newcastle University. Steve was relaxing by the pool in Murcia, Spain recently and thought of this athletic challenge. Here’s Steve with — It’s a lovely hot summer day, and your last day of vacation. You find yourself sitting by a circular pool, and fancy a martini from the bar, which is directly opposite you (along the diameter). You have three options.
Game of Thrones - NYTimes.com
Our challenge this week was suggested by Laura Feiveson, an M.I.T.-trained economist at the Federal Reserve Board and a frequent contributor to Numberplay. Here’s Laura: The upcoming presidential election has put me in the mood for some game theory. (I’m an economist, after all.) As we were inundated with news of the workings of our daft primary system a few months ago (ahem, caucuses?), I was reminded of some of the voting systems I learned about in economics graduate school.
The Problem with SET®
This week’s puzzle was suggested by Jordan Ellenberg, professor of mathematics at the University of Wisconsin, and author of How Not to be Wrong, one of Bill Gates’s recommended summer reads. Our current challenge is based on SET®, the highly-addictive visual perception card game. Before we take on Jordan’s challenge: Congratulations to Gwen Jorgensen, who won the Olympic triathlon this past Sunday, giving the United States its first gold medal in the event.
Olympic Strategies, Part 2
“Great spirits have always encountered violent opposition from mediocre minds,” wrote Albert Einstein in 1940. The expression is a terrible cliché at this point, but it’s always intrigued me. What does “violent opposition” look like? Are only mediocre minds susceptible? And how do these great spirits respond?
Olympic Strategies, Part 1
The 2016 Rio Olympics have begun, unleashing Hungarian swimmer Katinka Hosszu, American shooter Ginny Thrasher, and a whole pack of Brazilian gymnasts. I’ve enjoyed The Times’ coverage, including the Interactive Stories series and the SMS experiment. It was also a nice surprise to find Karen Crouse’s story about Bruce Gemmell, an old college teammate of mine and current coach of swimmer Katie Ledecky.
The Same Court Time
Patrick Mills of Australia lays up in the men’s basketball preliminary round match between Australia and Spain during the London 2012 Olympic Games. Our puzzle this week was suggested by Marco Moriconi, a regular Numberplay contributor who makes his home in Rio, site of the upcoming Olympic Games. Basketball is one of the most popular team sports in this summer’s Olympic Games.
Dodging 9s - NYTimes.com
Our puzzle this week was suggested by Sam Vandervelde, head of Proof School, a secondary school in San Francisco for kids who love math. The problem, which Sam created for his Algebra II class, offers a terrific way to engage kids in deeper thinking about mathematical ideas, and proving that a complete solution is a fun challenge for any mathematician. Let’s try — The goal is to find the longest arithmetic progression of positive integers, none of whose terms contain the digit 9.
U.S. Team Wins First Place at International Math Olympiad
Photo U.S. International Mathematical Olympiad team members Ankan Bhattacharya, Allen Liu, Ashwin Sah, Michael Kural, Yuan Yao, Junyao Peng, and coach Po-Shen Loh. The United States has won the 57th International Mathematical Olympiad, the world’s most prestigious problem-solving competition for high school students. The competition, held July 6-16 in Hong Kong, included teams from over 100 countries.
Four Fractions - NYTimes.com
Our puzzle this week was suggested by Fred Gluck, a frequent Numberplay contributor whose seemingly simple problems can challenge both children in the classroom as well as more experienced math lovers. In this week’s problem there’s more than one solution. Can you find them all? Find four different fractions, in each of which the numerator is one less than the denominator, so that when all four fractions are added together, their sum will be a whole number. There is more than one solution.
America! - NYTimes.com
Our puzzle this week was suggested by Daniel Finkel of Math for Love, the Seattle-based team out to transform math education through games and teacher workshops. With the Brexit campaign making headlines, the words “Independence Day” have never felt more loaded. Here are a pair of July 4 puzzles to celebrate American Independence. Take the digits 7, 4, 1, and 6 from the date (7/4/16) and build an equation that uses each digits exactly once, and that equals 240, the number of years since 1776.
Jordan Ellenberg: The Lottery Scheme
This week’s challenge was suggested by Jordan Ellenberg, a math-world superstar and current professor of mathematics at the University of Wisconsin. Jordan is the child prodigy who turned out well. After teaching himself to read at age 2, he attained a perfect 800 on the math portion of the SAT at age 12, won two gold medals in the International Math Olympiad (with perfect scores), and was a two-time Putnam Fellow at Harvard.
Hockey Problems - NYTimes.com
This week’s challenges were suggested by Po-Shen Loh, a math professor at Carnegie Mellon University as well as the national coach of the USA International Mathematical Olympiad team. Po is also the founder of Expii, a platform for free personalized learning and adaptive math practice, built upon algorithmic analysis of openly licensed lessons and problems. Among Expii’s offerings is a series of short challenges built around real-world themes, such as sports contests.
Travel Problems - NYTimes.com
This week’s challenges were suggested by Laura Feiveson, an M.I.T.-trained economist at the Federal Reserve and regular Numberplay contributor. Laura’s an expert at bringing out unexpected twists in classic puzzles, and I’m looking forward to seeing what emerges this week. Let’s join Laura with — When recently on a road trip up the coast of the Southeast, my husband and I found ourselves stuck in a small Airbnb apartment with our two sick toddlers while it poured rain outside.
The Candy Store - NYTimes.com
This week’s challenge was suggested by Sunil Singh, a regular Numberplay contributor and math consultant with Scolab, an educational technology laboratory based in Montreal. Sunil’s challenge seems impossible at first, but has a beautiful solution. Let’s try — There is a retired mathematician who owns a candy store in your town. Not only does she sell amazing sweets, but she is also known to give challenging puzzles to all her customers.
A Brief Introduction to Infinity by Edward Frenkel
The concept of infinity has perplexed thinkers since the dawn of civilization. Everything we observe in the physical world around us is finite; even the number of atoms in the observable universe, though it is unimaginably large, is still finite. Does infinity really exist? If so, how do we find it?
The Fiftieth Number
Sixteen, of course, if we’ve counted right, or 16. But that’s just base-10, inspired by our 10 fingers. But we could also write the quantity in base 16 (10) or base 17 (G). Although this different representations look a little weird, using something besides base-10 can sometimes be used to flush out otherwise hidden patterns.
Two Heads in a Row
Our puzzle this week was suggested by Mike O’Connor, a retired software engineer. “The puzzle was given to me by my friend Jon Stein,” explained Mike by email. “I stumbled on it for a little bit and it reminded me of a puzzle you had last year by Steve Humble [see “Steve Humble’s Neighbor Problem”]. Both puzzles sent me down wrong paths of realizing my logic didn’t anticipate events that weren’t actually independent. It seems like an easy question but the solution actually isn’t obvious.
Two Sides of the Same Coin
Our puzzle this week was suggested by Joe Fendel, a regular Numberplay contributor whom we most recently encountered At the Video Store. Joe specializes in original puzzles based on everyday situations, but this week’s is a bit different, inspired by Dan Faley’s Coined Phrases. As Joe suggests, it’s helpful to start small with this one. Let’s give it a try.
The Ship and the Boiler
The Titanic, with its four giant smokestacks, leaves Southampton, England, on its doomed journey across the Atlantic. Are you as smart as a fifth-grader? Find out this week with a pair of challenges suggested by Fred Gluck, a retired engineer and math educator who works mainly with grade-school children. The challenges can be solved with simple algebra, but how would you take them on as a fifth-grader, without algebra in your mathematical toolkit? Two hens were squawking one day.
The Polka Dot Puzzle
This week’s puzzle was suggested by Daniel Finkel of Math for Love, the Seattle-based team out to transform math education through games and teacher workshops. Math for Love’s latest creation is the game Tiny Polka Dot, which was just launched on Kickstarter (check it out here). Let’s get a feel for the game with — Take the numeral cards from 0 to 10.
Jo Boaler: Mathematical Mindsets
Finnish markka, the currency of Finland until the markka was replaced by the euro in 2002. The thing I love about Numberplay — the bit that really defines it — is that it’s not about correct answers. Instead, it’s about insight and exploration. During our weeklong discussion, did we discover something new — maybe a nice visual or analogy? Did we come up with a nice twist on the problem — something a bit different (and more interesting) than the original challenge?
The Wedding Ring
This week’s challenge was suggested by regular Numberplay contributor Sunil Singh, a math consultant with Scolab, a creative and effervescent educational technology laboratory based in Montreal. The puzzle is a seemingly simple question about a would-be bride. Is marriage in her near future? Let’s find out. Here’s Sunil: One of the old textbooks I used to teach from for a course called Geometry and Discrete Mathematics had the following wonderful historical probability problem.
The Average Puzzle
A giant 16 covered in light bulbs that was used to ring in the new year in Times Square. This week’s puzzle was suggested by a regular contributor to Numberplay, Daniel Finkel, a Seattle-based educator out to transform the way math is taught and learned. (Check out Math for Love for more.) Daniel’s challenges often hinge on a key insight that makes the complicated simple. Let’s give it a try.
Martin Gardner’s Favorite Funny Quickies
Happy April Fools Week! Let’s celebrate this ancient tradition with a sampling of favorite foolish puzzles by the late recreational mathematician Martin Gardner. The series was originally featured in Issue 28 (April 1983) of the The Four Star Puzzler and is used with generous permission of the publisher. (Check out Games World of Puzzles at their website here.) And before jumping in — what’s your own favorite foolish puzzle? Or favorite April Fools Day prank? Share as a comment.
Certainty Despite Randomness
Cheers! This week we toast the arrival of spring with three beverage-glass challenges. We'll start with Laura Feiveson, an M.I.T.-trained economist at the Federal Reserve Board and regular Numberplay contributor. Here's Laura with two problems that may surprise even the most experienced puzzle-solver: These two problems have always been linked in my mind since I first heard them many years ago.
The Rajah’s Pearls
This week’s puzzle was suggested by Fred Gluck, a math educator who works mainly with grade-school children. I really enjoy Fred’s challenge because there’s more than one way to crack it. How many can we come up with? Let’s find out by trying on — A rajah, in his will, left his daughters a certain number of pearls with the instructions to divide them as follows: The oldest daughter was to receive 1 pearl plus 1/7 of what was left.
Adam Kucharski: The Perfect Bet
For this week’s challenge we continue with Adam Kucharski, the award-winning author of “The Perfect Bet: How Science and Math Are Taking the Luck Out of Gambling.” We met Dr. Kucharski last week with the St. Petersburg Lottery, in which we were playing directly against a house with infinite resources. This week we take on a different kind of gamble: one in which the winning value is determined by other players in the game.
The St. Petersburg Lottery
This week’s challenge was suggested by Adam Kucharski, a lecturer in mathematical modeling at the London School of Hygiene & Tropical Medicine, where he studies the dynamics of infectious diseases, particularly emerging infections. Adam is also an award-winning writer, and author of “The Perfect Bet: How Science and Math Are Taking the Luck Out of Gambling,” the story of the mathematicians who make millions by doing the impossible: cracking the code of gambling.
The Unexpected Sequence
恭禧发财! Today we welcome the Year of the Monkey with a mischievous challenge suggested by Sunil Singh, a math consultant with Scolab, an education technology laboratory in Montreal. The best puzzles — including crosswords, of course — will often contain a bit of purposeful misdirection, and Sunil has offered up a challenge that’s beyond tricky. Fortunately, he promises to help us out with few hints (left as comments) if needed.
Google Artificial Intelligence Beats Expert at Go Game
Tremendous news last week: Google announced that it had created a computer program that defeated a professional player at Go – an event that many thought was still a decade away. This week we celebrate this victory with a simple strategy challenge suggested by our friends at Brilliant.org, the online community for students and professionals looking for tantalizing problems, like-minded peers, and mentorship. Our discussion will be moderated by Brilliant’s Zandra Vinegar.
Round Robin - NYTimes.com
Zhang Shuai of China serves to Madison Keys of the United States during their fourth round match of the Australian Open tennis tournament in Melbourne, Australia. This week’s challenge — timed to coincide with the final few days of this year’s Australian Open tennis tournament — was suggested by Marco Moriconi, a regular Numberplay contributor and professor of physics at the Universidade Federal Fluminense, in Niteroi, Rio de Janeiro.
The Switch - NYTimes.com
This week’s puzzle was suggested by Daniel Finkel of Math for Love, a Seattle-based math education consultancy. It’s a beautifully simple puzzle with plenty of room to explore. Let’s try: Imagine a switch that changes all the addition signs in an expression to multiplication signs, and all the subtraction signs to division signs. For example, if you had the expression 4 + 6 − 2, and you threw the switch, it would change to 4 × 6 ÷ 2.
Beyond Monty Hall
This week’s puzzle is twist on a stunning, counter-intuitive classic — the Monty Hall Problem, made famous by Marilyn vos Savant in her “Ask Marilyn” column in Parade Magazine. Here was the problem in its original form as sent in by a reader to Ms. vos Savant: Suppose you’re on a game show, and you’re given the choice of three doors: Behind one door is a car; behind the others, goats.
The Doubly Good Year
A delivery man takes balloons to two different birthday parties. Some years there is more to celebrate. This week’s main feature was suggested by Dana Mackenzie, the regular Numberplay contributor, chess champion, hula enthusiast and award-winning mathematics writer.
The Gift Exchange
This week’s puzzle was suggested by Henk Tijms, a Dutch mathematician and emeritus professor at the VU University Amsterdam. Dr. Tijms, the author of the acclaimed Understanding Probability, told me that he is often asked to give a light-heartened presentation on probability to a general audience. Sometimes people in the audience come up themselves with interesting probability questions.
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