Mathopolis 2020: A Mathematics Quiz by St Stephens College

MATHOPOLIS 2020
FINALS
Proctored by
Agastya Pulapaka and Shayanak Kundu
The Mathematics Society in
collaboration with the Quiz Club of
St. Stephen’s College presents

RULES
● The Finals will contain 24 Questions.
● Scoring is +10/0 on Bounce, +10/-10 on Pounce.
● QM’s decision is final.

Q1.
In a paper released in 1950, X introduced the field of using computers for a
certain game. What he basically found was a lower bound for the number
of possible games of 40 moves that can be played, and hence the number
was named after X. The exact number of such games is not known yet due
to the enormous and ever increasing no. of subgames that are possible
after each move. The game recently gained a lot of attraction in India due
to YouTube streaming.
ID X, or the number, and the game in question.

A1.
Claude Shannon/Shannon’s Number
Chess

Q2.
After a visit to the Russian city of Kaliningrad, Peter Taylor wrote an
article for the Australian Mathematical Trust. In the article, he wrote that
only five of the original ones still remain (as of 2000), however only a
couple are from Euler’s time. Two of them were destroyed in the Soviet
bombing of the city in WW2. The others were demolished and rebuilt.
What is being talked about?

Q3.
In 1956, Nobel Prize winning Economist Herbert Simon made three predictions
regarding the capabilities of computers. Two of them were that computers
would prove mathematical theorems and compose aesthetically satisfying
music. His third prediction came true 40 years later, which the IBM
supercomputer ‘Deep Blue’ was responsible for, and this event was the subject
of the 2004 documentary The Man vs The Machine.
What was the other prediction Simon made?

A3
A computer would defeat a World Champion in a game of chess

Q4
X was one of the few mathematicians who were awarded a Nobel Prize because of the
fact that his greatest mathematical contribution in the field of Y serves as a great
advance in some other subject.
X was strictly against communism and once thought that all men wearing red ties
were in a communist conspiracy against him. X attempted a proof of the Riemann
hypothesis in his 1959 American mathematical society lecture but the lecture soon
became incomprehensible to the listeners.
In 2011, the National Security Agency declassified letters written by X in the 1950s, in
which he had proposed a new encryption–decryption machine. The letters show that
X had anticipated many concepts of modern cryptography, which are based on
computational hardness.
ID X

A4
X: John Nash
Y: Game Theory

Q5
Xs were used symbolically in ancient Greece and Babylonia, and are used today as a symbol
of faith by many Wiccans, akin to the use of the cross by Christians.
Christians once commonly used the X to represent the five wounds of Christ.
An inverted X is used as the symbol for a particular religious group, whose beliefs can be
assumed from the very nature of their symbol in relation to the groups X is used for.
ID X, and the religious group in question.

Q6
Lateralus is the titular song from Tool’s 2001 album. This song in particular has interesting
mathematical significance in the way the lead singer, Maynard James Keenan, sings the verse.
"Black, then, white are, all I see, in my infancy. Red and yellow then came to be, reaching out to me.
Lets me see.
As below so above and beyond I imagine. Drawn beyond the lines of reason. Push the envelope.
Watch it bend. There is, so, much, more and, beckons me, to look through to these, infinite
possibilities.”
What is the mathematical significance, which also helps derive one of the famous constants in
Mathematics?

A6
The number of syllables per word are in the Fibonacci
Sequence

Q7.
X was a French mathematician whose remarkable work in the field was eclipsed by tragedy. X
failed to gain admission in any mathematical school due to his poor expositional ability, failure to
state proper reasonings. While still in his early teens, he was able to determine a necessary and
sufficient condition for a polynomial to be solvable by radicals, thereby solving a problem standing
for 350 years. While submitting his paper to the French Academy of Science, Augustine Cauchy lost
his manuscript. He rewrote the paper that had been lost and presented it again to the Academy—
but for a second time the manuscript went astray. Jean-Baptiste-Joseph Fourier took it home but
died a few weeks later, and the manuscript was never found. Hence X had no significant work
published in his name.
ID X

Q8.
The following lines were written by a soldier, referring to
himself in the third person.
However, in this extreme distress, he was not destitute of his usual sagacity; but trusting himself to the providence of God, he put his life
into hazard: "And now," said he, "since it is resolved among you that you will die, come on, let us commit our mutual deaths to
determination by lot. He whom the lot falls to first, let him be killed by him that hath the second lot, and thus fortune shall make its
progress through us all; nor shall any of us perish by his own right hand, for it would be unfair if, when the rest are gone, somebody should
repent and save himself." This proposal appeared to them to be very just; and when he had prevailed with them to determine this matter by
lots, he drew one of the lots for himself also. He who had the first lot laid his neck bare to him that had the next, as supposing that the
general would die among them immediately; for they thought death, if X might but die with them, was sweeter than life; yet was he with
another left to the last, whether we must say it happened so by chance, or whether by the providence of God. And as he was very desirous
neither to be condemned by the lot, nor, if he had been left to the last, to imbrue his right hand in the blood of his countrymen, he persuaded
him to trust his fidelity to him, and to live as well as himself.
Who is X? Or, what famous permutation problem did this story create?

A8.
Flavius Josephus/Josephus Problem

Q9.
The origin of X’s logo dates back to 1989, and it was introduced to
commemorate the 50th year anniversary of the company. This
distinctive logo includes three ellipses that are combined in a
horizontally symmetrical configuration. The two perpendicular
ellipses inside the larger ellipse represent the heart of the customer
and the heart of the company. They are overlapped to represent a
mutually beneficial relationship and trust between each other.
ID X

Q10.
The logo is stylized to resemble a sine wave, and the last two
letters to resemble the binary digits 1 and 0, the combination
representing the merging of analogue and digital signals. The
sound some models make when starting up is derived from the
melody created when typing the keys that would spell out the
name on a phone keypad.
ID the logo

Q11.
Though the X and Y signs now seem familiar, the Egyptian hieroglyphic
sign for X resembled a pair of legs walking in the direction in which the
text was written with the reverse sign indicating Y. German
mathematician Johannes Widmann first referred to the X and Y in his
1489 treatise. However they were not used for their modern indication,
rather used to indicate surplus and deficit.
ID X and Y

Q12.
X developed a version of Z but didn't publish his work at the time. Ten years later,
Y formulated his own version of Z, publishing his work a decade later. X later
charged that the Y had plagiarized his unpublished writings after documents
summarizing it circulated through the Royal Society. In an effort to defend
himself, Y eventually appealed to the Royal Society and X, who’d served as the
organization’s president , agreed that an impartial committee would be assembled
to look into the issue. Instead, he packed the committee with his supporters and
even penned the group’s report, which publicly credited him with discovering Z.
Identify the rivals X and Y and the work Z they argued on.
ID X,Y, Z

A12.
X: Newton, Y: Leibniz, Z: Calculus

Q13.
X and Y were two of the greatest French mathematicians in the world.
However, they had very contrasting philosophies.
While X thought our mind and body are separate, and man lives by mind, Y
argued that human mind and body are connected and unified.
In 1647, a 51-year-old X visited the 24-year-old prodigy Y. Their meeting
quickly devolved into a heated argument over the concept of a Z. X said it
was impossible; Y disagreed. After the falling out X wrote a public letter that
said that Y had “too much Z in his head,” basically saying Y had an empty
head.
ID X, Y, Z

A13.
X: Descartes Y: Pascal Z: Vacuum

Q14.
Recently, X conceived an astute way of using its branding to lead commuters
into its outlets, by sharing bits of its famous arches upon select outdoor ad
buys.
Originally, X sold its Y in packs of 9 and 20. Math enthusiasts were curious to
find the largest number of Y that could not have been bought with these
packs, thus creating the Y Theorem.
ID X and Y

A14.
X - McDonald’s
Y - Chicken McNugget Theorem

Q15.
The short story 'A Sound of Thunder', set in 2056 in a time where time travel has become
exceedingly popular, wealthy citizens can pay a hefty sum to go back in time and hunt
currently extinct creatures, subject to certain restrictions. One of these restrictions is to
follow a specific path while hunting in the past, lest they alter too many events. In the story,
our protagonist veers off this path due to losing his nerve on seeing the T-Rex they were
hunting, and this leads him to accidentally do something on this path.
This particular action of his has far reaching implications in his present, and on inspecting
his footwear, he finds what is a very literal hint for the concept that this story hinges on,
which is a smaller part of a larger concept
What did he do, and what is the concept here?

A15.
He stepped on a butterfly
Butterfly Effect (Accept Chaos Theory)

Q16.
The following is an audio clip of a parody song. Listen to the
clip, then make suitable adjustments to give us the punny
name of the parody.

Q17.
Given on the next slide is a series of ten figures, all part of the
same family. They are the solution to a particular problem that
came into the public eye in 1997, from a rather unpredictable
place.
The mathematical name for these figures are homeomorphically
irreducible Xs, with X being a real world object that we see
everyday, which bears physical similarities to these figures, and
also due to what their constituting parts are called.
Fill in X, and also where did these figures come into the public
eye?

A17.
X: Trees
One of the questions solved in Good Will Hunting.

Q18.
X is a 1998 American psychological thriller film written and directed by Darren Aronofsky in his feature
directorial debut. The film explores themes of religion, mysticism, and the relationship of the universe to
mathematics. The story, about a mathematician with an obsession to find underlying complete order in
the real world, contrasts two seemingly irreconcilable entities: the imperfect, irrational humanity and the
rigour and regularity of mathematics, specifically number theory.
The protagonist was shown to program his computer named Y, to make stock predictions. Some argue that
Y was one of the first mathematicians to have hinted at the possibility of X being a constant.
At the end of the film, the protagonist is asked to do several calculations, including 748 ÷ 238. He smiles
and says that he does not know the answer.
ID X, Y.

Q19.
X’s Law is a law that deals with the frequency distribution of certain things,
specifically a certain way in which these things deviate from what the
uniform distribution would be. The law finds a large number of applications,
including (but not limited to) population, social media followers, stock prices,
values of constants, etc. Some examples of these datasets are included in the
next slide.
Give the funda behind this law.

Q19.
Population of some
countries
India- 1.3 billion
Russia - 0.145 billion
China- 1.4 billion
Japan - 0.126 billion
USA - 0.33 billion
Philippines - 0.109 billion

A19. Benford’s Law states that in many naturally occurring
collections of numbers, the leading digit is likely to be
small.

Q20.
There have been several discussions and theories regarding this particularly strange
exclusion from a certain list/group. Some theories include the creator of this group had
a bad personal experience with someone related to the sphere of the excluded item,
and hence refused to include it. Another theory suggests the creator simply did not
care much for it, and hence didn't deem it important enough to include.
This has led to several alternatives for people in the sphere of this excluded item to
receive recognition, the most famous of which came about in 1928, and has been called
the equivalent of the aforementioned list for this particular sphere.
What was this exclusion? What was the alternative that came about?

A20.
Nobel excluding Math from the Nobel Prizes
Fields Medal

Q21.
Once, the school of X, an occult team of early mathematicians that pushed mathematical
knowledge forward, like all cults, was based on some fundamentalistic beliefs.
They were so astonished by the applicability of a certain mathematical concept to almost
everything that they considered it to be 'divine'. Hence they concluded that everything can be
expressed in terms of that. Their beliefs were however shattered when Hippasus, one of the
thinkers discovered that this is not true by observing a regular closed geometric figure. The school
was so frightened by the discovery that they drowned Hippasus in order to ensure that the
remarkable discovery doesn't come out!
Identify X, whose famous theorem was used in the discovery, and the 'divine' concept that was
proved wrong with this discovery.

A21.
X: Pythagoras
The concept of ratios

Q22.
Somewhere around 2011-12(which coincided with a particular culmination
related to what he made), a high school teacher decided to make his mathematics
class a little more enjoyable for his students, since he felt they not only needed
this, but deserved it. He did so by working out an extremely ugly and complicated
looking equation for a particular image/logo, one which we are all familiar with,
and one which may cause his students to be awestruck by it, considering the
person the image represents. In order to create the the necessary equation, he
used a combination of straight lines, curves and ellipses.
Tell us what the equation is for, i.e, what iconic image it creates.

A22.
This is the Batman Equation.

Q23.
The original X took the world by storm since its introduction in the 20th
century. There are 8! ways to arrange the __. 7 of the 8 __ can be oriented
independently in 3 ways, with the orientation of the 8th depending on the
preceding ones, giving 3⁷ possibilities.
There are 12!/2 ways to arrange the __. 11 of the 12 __ can be flipped
independently, with the flip of the 12th depending on the preceding ones,
giving 2¹¹ possibilities.
ID X

Q24.
_______ (1895), by Alphonse Allais, is a collection of absurdist short stories about anti-
intellectualism as politics.
Almost half a century later, a justifiably paranoid protagonist character uses the above title to
establish a contrast with the obvious, but politically undesirable truth.
Fast forward almost a century and a half, a political themed short film is released, drawing
inspiration from the above.
FITB and ID where the character is from
Video is included in the next slide

A24.
2+2 makes 5
1984, by George Orwell

THANK
YOU!
Set made by Agastya Pulapaka, Shayank Kundu, Athak
Chaudhary, Joseph Philip and Chaitanya Varma

Mathopolis 2020: A Mathematics Quiz by St Stephens College

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Mathopolis 2020: A Mathematics Quiz by St Stephens College