Mathopolis 2020: A Mathematics Quiz by St Stephens College

The Mathematics Society and Quiz Club of St Stephens College present Mathopolis, a Mathematics Quiz (no actual calculations, just questions on math)

1. 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

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

3. 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.

4. A1. Claude Shannon/Shannon’s Number Chess

5. 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?

6. A2 The Bridges of Konigsberg

7. 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?

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

9. 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

10. A 4 X: John Nash Y: Game Theory

11. 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.

12. A5 Pentagram Church of Satan

13. Q 6 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?

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

15. 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

16. A7. Evariste Galois

17. 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?

18. A8. Flavius Josephus/Josephus Problem

19. 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

20. A9. Toyota

21. 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

22. A10. Vaio

23. Q 11. 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

24. A11. X: ‘+’ , Y: ‘-’

25. Q 12. 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

26. A 12. X: Newton, Y: Leibniz, Z: Calculus

27. 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

28. A13 . X: Descartes Y: Pascal Z: Vacuum

29. Q 14. 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

30. A 14. X - McDonald’s Y - Chicken McNugget Theorem

31. Q15. T he 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?

32. A 15. He stepped on a butterfly Butterfly Effect (Accept Chaos Theory)

33. Q 16. 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.

34. A 16. All About That Base

35. Q 17. 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?

36. Q 17.

37. A 17. X: Trees One of the questions solved in Good Will Hunting.

38. Q 18. 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.

39. A 18. X: Pi, Y: Euclid

40. Q 19. 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.

41. Q 19. 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

42. A 19. Benford’s Law states that in many naturally occurring collections of numbers, the leading digit is likely to be small.

43. 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?

44. A20 . Nobel excluding Math from the Nobel Prizes Fields Medal

45. Q 21. 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.

46. A21 . X: Pythagoras The concept of ratios

47. Q 22. 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.

48. A22. This is the Batman Equation.

49. Q 23. 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

50. A 23. Rubik’s Cube.

51. Q 24. _______ (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

52. Q 24.

53. A 24. 2+2 makes 5 1984, by George Orwell

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