Final Presentation V 1dot 1

Round 1 Marathon (Theoretical Mathematics) 4 Questions 2

Question 1 1 0

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How many elements are there in the rotation group of a soccer ball (having 20 hexagonal faces and 12 pentagonal faces) ?

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Solution

60 Explain the solution here ANKUSH

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Question 2 1 5

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If you have N envelopes (N being very large) and each has its unique recipient . You don’t know which one is to be sent to whom. Sending all them randomly what is the probability that more than person receives a correct envelope. 7

Solution

1 n 1 − (1 − ) n

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Question 3 2 0

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• Assume that the random variable X1 and X2 are normally distributed . Mean Standard Deviation Mean Standard X1 u1 s1 deviation u2 X2 s2 X1 : u1 s1 X2 : u2 s2 • The co-relation between X1 and X2 is -1 . • How can you choose constants 'a' and 'b' such that (a*X! + b*X2) has minimum variance 10

Solution

a+b = 1 , 0
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Question 4 1 5

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Q2 : Label the four chairs on a table as 1,2,3,4 clockwise . Let there are three operations possible on the chairs : i) switching 1 and 3 ii)switching 2 and 4 iii)rotating 2,3 and 4 clockwise without moving 1 How many different possible operations can be done on the chairs with the combination of these three operations ? 13

Solution

Explain the solution here ANKUSH

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Round 2 Shot Put (Audio/Visual Round) Buzzer Round

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Question 1 1 5

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Draw the relation between the three sets Complete Metric Spaces

Universal Set

Compact Metric Spaces

Totally Bounded Metric Spaces

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The solution Compact Complete

Totally Bounded

Universal Set

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Question 2 1 5

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Join these with 4 straight lines without lifting your pen

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The solution

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Question 3 1 0

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Connect the three houses to water, electricity and gas suppliers without any lines crossing-

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Solution It is not possible because K3,3 is not planar. If it were, m<= 2n-4 (for bipartite) 9 <= 2*6 – 4 9 <= 8 Contradiction

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Question 4 1 0

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Insert operators to make the following statement true

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1

1 =6

Hint: Don’t constrain yourself to basic operators 26

Solution

(1 + 1 + 1 )! = 6 27

Cross Round 3 Country (History/Trivia) Buzzer Round 12 Questions 28

Question 1 Identify X 3 Hints 2 5 2 0 1 5

1 0 29

Ques 2 5 Hint 1 2 0 Hint 21 5 Hint 31 0

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Solution

Paul Erdos

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Question 2 2 Hints 2 5 2 0 1 5

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Ques 2 5

Hint 1 2 0

Hint 2 1 5

PTO 33

Hint 2 1 5

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Solution

Alan Turing

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Question 3 NO HINTS 1 0

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X (December 7, 1823 – December 29, 1891) argued that arithmetic and analysis must be founded on "whole numbers", saying, "God made the integers; all else is the work of man".

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Solution

Leopold Kronecker

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Question 4 NO HINTS 1 0

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He at the age of nineteen proved that a regular polygon with 17 sides cannot be drawn by compass and straightedge. He was so pleased by this result that he requested that a regular 17-gon be inscribed on his tombstone.

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Solution

Maggo - PUT SOLUTION HERE

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Question 5 NO HINTS 1 0

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X wrote only one paper in number theory but the ideas introduced in it were astonishing and the conjecture made is still one of the biggest open problem in mathematic. Whom are we talking about? Identify X.

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Solution

Maggo - PUT SOLUTION HERE

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Question 6 NO HINTS 1 0

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X died at young age of twenty but not before he proved a long time unsolved problem that there exists no general method for solving polynomial equations of fifth degree or more by the method of radicals. Identify X.

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Solution

Maggo - PUT SOLUTION HERE

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Question 7 1 0

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X famously proposed 23 problems at the international congress of Mathematics held in Paris in 1900. Most of these problems have been proved to be influential in developing mathematics in the last century and most of them have been solved. Identify X.

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Solution

Maggo - PUT SOLUTION HERE

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Question 8

1 0

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X (17 June 1898 – 27 March 1972) was a Dutch graphic artist. He is known for his often mathematically inspired woodcuts, lithographs and mezzotints. These feature impossible constructions, explorations of infinity, architecture and tessellations.

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Solution

M.C. Escher

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Question 9

1 5

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The X is one of the earliest ________ curves to have been described. It can be created by starting with an equilateral triangle. At each step, each side is altered recursively as follows: 1. Divide the line segment into three segments of equal length. 2. Draw an equilateral triangle that has the middle segment from step 1 as its base and points outward. 3. Remove the line segment that is the base of the triangle from step 2.

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Solution

Koch snowflake

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Question 10 1 5

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possible states, A or B. Every cell interacts with its eight neighbours, which are the cells that are directly horizontally, vertically, or diagonally adjacent. At each step in time, the following transitions occur: 1. Any A cell with fewer than two A neighbours or more than three A neighbours goes to state B. 2. Any A cell with two or three A neighbours stays in state A. 3. Any B cell with exactly three A neighbours comes to state A.

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Solution

The Game of Life

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Question 11 1 5

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cryptographic attack, so named because of its relation to the ___________ problem in probability theory. Given a function f, the goal of the attack is to find two inputs x1,x2 such that f(x1) = f(x2). Inputs are chosen randomly until such a pair is obtained. This method can be rather efficient. Say a function f(x) yields any of H different outputs with equal probability. Then it is expected that the required pair will be obtained after testing 1.25*sqrt(H) 61

Solution

Birthday attack

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Question 12 1 0

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In classical logic, _______ ___________ (Latin: mode that affirms by affirming) is the name given to an form of argument sometimes referred to as affirming the antecedent or the law of detachment. An example of an argument that fits the form for _____ _________: If today is Tuesday, then I will go to work. Today is Tuesday. Therefore, I will go to work.

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Solution

Modus ponens

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Sprint Rapid FIRE !!! 3 questions 120 seconds

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