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The quants have been performing especially well in this year’s choppy markets.

How do they do it? You won’t hear any of the brainiacs at firms such as Renaissance Technologies and Two Sigma

Investments giving away any secrets. Hedge funds that use largely quantitative strategies are notoriously

secretive about their algorithms.

NEXT STORY >NEXT STORY >MONEYBEAT

Are You Smarter Than a Quant? Here Are 5 QuestionsAre You Smarter Than a Quant? Here Are 5 Questionsfrom the MoMath Masters Contestfrom the MoMath Masters ContestThe 2016 MoMath Masters competition included questions about quadrilaterals, supermodels and Fermat's

Sandwich Theorem

Mar 4, 2016 11:02 am ET

By BRADLEY HOPEBRADLEY HOPE

23 COMMENTS23 COMMENTS

Two Sigma Investments co-founder John Overdeck competes in the 2016 MoMath Masters competition PHOTO: NATIONAL MUSEUM OF

MATHEMATICS

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But a few times a year, the top quants get together to compete over math puzzles for the good of charity or the

National Museum of Mathematics in Manhattan. (Check out the Wall Street Journal’s weekly math puzzle in

conjunction with MoMath here).

Last week, the museum held its 2016 MoMath Masters competition. The overall winner was Po-Shen Loh, a

Carnegie Mellon math professor. In second place was Two Sigma’s Daniel Stronger, a quantitative analyst with a

Ph.D. in computer science, and in third was Ken Perlin, a computer science professor at New York University who

invented something called “Perlin noise” that makes textures look realistic in computer games.

Winner of the Math Classics category – which has famous, old puzzles – was Geva Patz, co-founder of an

automated options trading firm called Android Alpha Fund LLC (and a part-time “pyrotechnician” for Grucci

fireworks, according to his Linkedin page). Patrick Huggins, a quantitative researcher at Citadel Investment

Group, won the “Gardner Greats” category – named after the famous math puzzler Martin Gardner. And the

winner of the Math Pulse category, which has math questions from popular culture, was Satish Ramakrishna,

global head of prime finance risk and pricing at Deutsche Bank.

Think you can compete with the quants? Here are five questions from the competition, followed by the answers.

Scroll down even further to see detailed explanations of the answers, courtesy of Glen Whitney, founder and

president of MoMath.

Question 1Que stion 1 (Math Pulse trivia category)

Fields Medalist Manjul Bhargave competes in the 2016 MoMath Masters competition PHOTO: NATIONAL MUSEUM OF MATHEMATICS


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Fermat’s Sandwich Theorem reveals what mathematical fact?

A) A function between two others that have the same limit has that limit as well.

B) 26 is the only number immediately between a square and a cube.

C) A bounded increasing sequence has a limit.

D) 152 is the largest number immediately between a prime and a triangular number.

E) Any sandwich can be cut so that both pieces have the same amount of bread and the same amount of filling.

Question 2Ques ti on 2 (Gardner Greats based on the work of Martin Gardner)

Which of the following must be true about the handshaking that occurred at a recent teachers’ convention?

A) The number of teachers who shook hands an odd number of times is even.

B) The number of teachers who shook hands an even number of times is odd.

C) The number of teachers who shook hands an odd number of times is odd.

D) The number of teachers who shook hands an even number of times is even.

E) The number of times teachers shook hands is odd.

Question 3Que stion 3 (Math Classics, easier level)

Given any quadrilateral, connecting the midpoints of consecutive sides will always result in which of the

following shapes?

A) square

B) rhombus

C) rectangle

D) parallelogram

E) kite

Question 4Que stion 4 (Math Pulse pop culture)Who among the following received a scholarship to study Chemical Engineering with Mathematics at

Northwestern University?

A) Heidi Klum

B) Kate Moss

C) Brooke Shields

D) Naomi Campbell

E) Cindy Crawford

Question 5Que stion 5 (From the Finals Round)

Let m be the smallest positive integer such that m²+7m+89 is divisible by 77. What is m?

A) 8

B) 18

C) 52

D) 73

E) 74

AnswersAnswers


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Question 1:Ques ti on 1: B) 26 is the only number immediately between a square and a cube.

Question 2:Ques ti on 2: A) The number of teachers who shook hands an odd number of times is even.

Question 3:Question 3: D) Parallelogram

Question 4:Que stion 4: E) Cindy Crawford

Question 5:Question 5: B) 18

Full e xplanationsFull explanations

Question 1:Ques ti on 1: First, the statement in option D is false; the next time it happens is 230, in that 229 is prime and 231

is triangular. All of the other four statements are true. Statement A is known as the “Squeeze Theorem,”

Statement C is called the “Monotone Convergence Theorem,” and statement E, believe it or not, goes by the

name “Ham Sandwich Theorem.” That leaves option B as the correct answer. 26 is one more than the square 25,

and one less than the cube 27. Another way of stating this theorem is to say that ( ±5,3) are the only solutions to

x² = y³ – 2. The famous Pierre de Fermat is believed to be the first person to have noticed this fact, and it is an

interesting case in which he did have a proof of this statement, which he at first did not reveal and challenged

others to find, stumping them. He in particular taunted the English mathematicians Wallis and Digby for their

inability to find the answer. This pattern, of Fermat claiming the proof of an extraordinary statement and then

backing up his claim even though no one else could reproduce the proof, for years reinforced the notion that

“Fermat’s Last Theorem,” eventually proven by Andrew Wiles, must be true and that perhaps wily old Fermat

really did have a proof.

Question 2:Ques ti on 2: Every handshake that occurred involved two people. Therefore, the number of combinations of aperson and a handshake involving that person must be even. But another way to get that same number is to add

up for each person, how many times s/he shook hands. So we know you get an even number if you do that.

Now think about all of the people who shook hands an odd number of times. If there were an odd number of them,

then all of their odd numbers of handshakes would add up to an odd number. Adding on all of the even numbers of

handshakes from the other teachers would still leave an odd total. But we know the total is even, and so we

conclude that it could not have been an odd number of teachers who shook hands an odd number of times. In

other words, an even number of teachers shook hands an odd number of times, which is option A.

Question 3:Ques ti on 3: It is not hard to see that if you connect the midpoints of the sides of a rectangle, you get a diamond

shape with four equal sides called a rhombus, which rules out choices A (square) and C (rectangle). And if you try

a trapezoid in which the sides are not parallel and one base is much longer than the other, you will find that you

get a quadrilateral in which the sides are not the same, nor are adjacent sides the same, which rules out B

(rhombus) and E (kite). Therefore the answer must be C, parallelogram. The reason that you always get a

parallelogram is that it is not difficult to see, by similar triangles, that each side of this midpoint quadrilateral is

parallel to the diagonal of the original quadrilateral that it does not intersect. Hence, the midpoint quadrilateral is

a parallelogram.

Question 4:Ques ti on 4: In 1984, Cindy Crawford graduated as valedictorian from De Kalb High School, and earned an

academic scholarship to Northwestern University to study chemical engineering. She recalls her first calculus

class thus: “For some reason, I caught the professor’s eye. He was like, ‘Honey, I think you have the wrong

class.’”




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