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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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( Click here to receive the Morning MoneyBeat newsletter via email.)
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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