final presentation v 1dot 1

8/14/2019 Final Presentation v 1dot 1

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Round 1Marathon

(TheoreticalMathematics)

4 Questions


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Question 1

10


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How many elements are therein the rotation group of a

soccer ball (having 20hexagonal faces and 12

pentagonal faces) ?


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Solution

60Explain the

solution here -

ANKUSH


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Question 2

15


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If you have N envelopes (Nbeing very large) and each

has its unique recipient . Youdont know which one is to be

sent to whom. Sending all

them randomly what is theprobability that more thanperson receives a correct

envelope.


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Solution

n

n

)11(1


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Question 3

20


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Assume that the random variableX1 and X2 are normally distributed

.Mean Standard

deviation

X1 : u1 s1

X2 : u2 s2

The co-relation between X1 andX2 is -1 .

How can you choose constants 'a'and 'b' such that (a*X! + b*X2)has minimum variance

Mean StandardDeviation

X1 u1 s1

X2 u2 s2


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Solution

a+b = 1 , 0


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Question 4

15


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Q2 : Label the four chairs on a table as1,2,3,4 clockwise . Let there are threeoperations possible on the chairs :

i) switching 1 and 3

ii)switching 2 and 4iii)rotating 2,3 and 4 clockwise without

moving 1

How many different possibleoperations can be done on the chairswith the combination of these threeoperations ?


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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

15


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CompleteMetric Spaces

Compact

Metric Spaces

Totally Bounded

Metric Spaces

Draw the relation

between the three sets

Universal

Set


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The solution

Universal

Set

CompleteTotally

Bounded

Compact


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Question 2

15


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Join these with 4straight lines without

lifting your pen


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The solution


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Question 3

10


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Connect the threehouses to water,

electricity and gassuppliers without any

lines crossing-


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Solution

It is not possible because K3,3 is not planar.

If it were, m


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Question 4

10


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1 1 1 = 6

Insert operators to make

the following statementtrue

Hint: Dont constrain yourself to basic operators


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Solution

(1 + 1 + 1 )! = 6


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Round 3

(History/Trivia)

Buzzer Round12 Questions

Cross

Country


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Question 1

Identify X3

Hints25 2

0 15 1

0


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Hint3

Hint1

Hint2

Ques2

5

2

0

1

5

1

0


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Solution

Paul Erdos


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Question 2

2Hints25 2

0 15


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Hint1

Hint2

Ques

25

20

1

5 PTO


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Hint

215


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Solution

Alan Turing


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Question 3

NO

HINTS10


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X (December 7, 1823 December 29,1891) argued that arithmetic and analysismust be founded on "whole numbers",

saying, "God made the integers; all else isthe work of man".


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Solution

Leopold Kronecker


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Question 4

NO

HINTS10


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He at the age of nineteen proved that a

regular polygon with 17 sides cannot bedrawn by compass and straightedge. Hewas so pleased by this result that herequested 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

HINTS10


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X wrote only one paper in number theory

but the ideas introduced in it wereastonishing and the conjecture made isstill one of the biggest open problem in

mathematic. Whom are we talking about?

Identify X.


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Solution



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Question 6

NO

HINTS10


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X died at young age of twenty but not

before he proved a long time unsolvedproblem that there exists no generalmethod for solving polynomial equationsof fifth degree or more by the method of

radicals. Identify X.


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Solution



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Question 7

10


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X famously proposed 23 problems at the

international congress of Mathematicsheld in Paris in 1900. Most of theseproblems have been proved to be

influential in developing mathematics inthe last century and most of them have

been solved. Identify X.


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Solution



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Question 8

10

Dutch graphic artist


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Dutch graphic artist.

He is known for his often mathematicallyinspired woodcuts, lithographs andmezzotints. These feature impossibleconstructions, explorations of infinity,architecture and tessellations.


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Solution

M.C. Escher


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Question 9

15

________curves to have been described


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curves to have been described.

It can be created by starting with anequilateral triangle. At each step, eachside is altered recursively as follows:

1. Divide the line segment into threesegments of equal length.

2. Draw an equilateral triangle that hasthe middle segment from step 1 as itsbase 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

15

poss e s a es, or . very ce n erac swith its eight neighbours which are the


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with its eight neighbours, which are thecells that are directly horizontally,vertically, or diagonally adjacent. At eachstep in time, the following transitionsoccur:

1. Any A cell with fewer than two Aneighbours or more than three A

neighbours goes to state B.2. Any A cell with two or three Aneighbours stays in state A.

3. Any B cell with exactly three Aneighbours comes to state A.


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Solution

The Game of Life


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Question 11

15

_________ ______

cryptographic attack, so named becausef it l ti t th bl


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of its relation to the ___________ problemin probability theory.

Given a function f, the goal of the attackis to find two inputs x1,x2 such that f(x1)= f(x2).

Inputs are chosen randomly until such apair is obtained.

This method can be rather efficient.

Say a function f(x) yields any of Hdifferent outputs with equal probability.

Then it is expected that the required pair

will be obtained after testing 1.25*sqrt(H)


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Solution

Birthday attack


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Question 12

10

n c ass ca og c, _______ ___________(Latin: mode that affirms by affirming) is


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(Latin: mode that affirms by affirming) isthe name given to an form of argumentsometimes referred to as affirming theantecedent or the law of detachment.

An example of an argument that fits theform for _____ _________:

If today is Tuesday, then I will go towork.

Today is Tuesday.Therefore, I will go to work.


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Solution

Modus ponens


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Rapid FIRE3 questions120 seconds

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