Junior Quiz Finals

8/3/2019 Junior Quiz Finals

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JUNIOR QUIZThe Mathematical Crusade 2011


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PROBLEMSRound 1


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Q1.How many primes p are there,

such that p2 + 20 is also prime?


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Q2.Using the digits 1, 2, 3, 4, 5, 6, 7, and

9, form 4 two-digit prime numbers,using each digit only once. What isthe sum of the 4 prime numbers?


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Q3.Both roots of the quadratic equation

x2

63x + k = 0 are primenumbers. Find the value of k.


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Q4.How many numbers between

1 and 2005 are integer multiplesof 3 or 4 but not 12?


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Q5.What is the maximum number of

points of intersection of5 lines and 1 circle?


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Q6.Compute the value of:


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Q7.In the city of Funkytown, the following facts are true:

No two inhabitants have exactly the same number of

hairs.No inhabitant has exactly 483,207 hairs.

There are more inhabitants than there are hairs onthe head of any one inhabitant.

What is the largest possible number of inhabitants ofFunkytown?


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Q8.Compute:


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TRIVIARound 2


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Q1.Known as the Prince of Mathematicians, this late18th century mathematician is counted among the

three greatest mathematicians of all time, along withNewton and Archimedes. In reminiscence ofArchimedes, when he discovered that every positiveinteger can be expressed as the sum of at most

three triangular numbers, he famously wrote in hisdiary, "! num = + + ". Who is he?


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Q2.Connect the following:

Riemann Hypothesis

P vs NP Poincare Conjecture

Hodge Conjecture

Birch and Swinnerton-Dyer conjecture

Yang-mills existence and mass gap problemNavier-Stokes existence and smoothness


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Q3.This award, officially known as the International Medal forOutstanding Discoveries in Mathematics is commonly called theNobel Prize of mathematics, due to the lack of a Nobel Prize

in the field. Unlike the Nobel Prize, however, It is awarded onlyonce every four years at the International Congress ofMathematicians and further is awarded only to mathematiciansbelow the age of 40; the rationale behind this, given by the John,

the man who instituted the prize, is that while the medal wouldbe a recognition of work already done, it would also be anencouragement for further achievement on the recipients part.What is this award colloquially known as?


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Q4.Edward Kasner, an Americanmathematician, is best remembered forintroducing a piece of notation inventedby his then 9-year old nephew Milton

Sirotta. What is this invention?


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Q5.As Euclid is known as the father of Geometry, another Greekmathematician, Diophantus, is known as the father of Algebra.This title however, is strongly contested by a 12th century Islamic

mathematician, who, among other things, introduced the decimalsystem to the western world. His influence on medievalmathematics runs so deep, that the word Algebra is taken fromal-Jabr, a word for an operation he used to solve quadratic

equations and the word Algorithm is taken from the latinizedversion of his name, Algoritmi. Name him.


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Q6.The Fields Medal is only awarded to mathematiciansbelow the age of 40. However, when a

mathematician named Andrew Wiles proved theTaniyama-Shimura conjecture, over the course of 7years culminating in a proof over a 100 pages long,he was 41, but his achievement was deemed worthy

enough that he was presented a Silver Plaque inplace of the Fields Medal by the InternationalMathematical Union. What was his achievement?


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Q7.Charles Dodgson, a British mathematician of theVictorian era, once reportedly sent his mathematical

paper An Elementary Treatise on Determinants tothe Queen Victoria when she expressed interest inone of his earlier manuscripts. Dodgson, who wrotethe earlier manuscript, himself claimed that all such

stories of him sending her his paper were in factfallacious. Identify the earlier manuscript.


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Q8.X, a British philosopher, physicist, astronomer andmathematician was also an alchemist and theologian. As amatter of fact, he wrote more on Biblical hermeneutics andoccult studies than on the science and mathematics he isremembered for. He was also the warden of the British RoyalMint, and was personally involved in the prosecution, andeventual hanging of 28 counterfeiters. He also served a short

stint in the Parliament of the country, during which heapocryphally spoke only once: to request that the windowsbe closed due a cold drafty wind. Who is X?


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PROBLEMS IIRound 3


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Q1.What is the sum of all positive

numbers which are less than 37and are co-prime to it?


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Q2.What is the last digit of

6767?


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Q3.Three integers are randomly chosen

from the set {1,2,3,4} withoutrepetitions. What is the probabilitythat the chosen set may be the sides

of the same triangle?


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Q4.All of Karanveers and Sakshis facebook friendsare members of the Mathematical Society. The

Mathematical Society has 2011 members,Karanveer has 777 friends and Sakshi has 1729friends. What is the minimum number of mutual

friends that Karanveer and Sakshi will have?


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Q5.Give any one solution of the

Diophantine Equationx2 7y2 = 1


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Q6.If the price of one pencil and one

eraser is the same as that of a pen,and buying 4 pencils, 4 erasers and 6pens cost 50 bucks. How much does

it cost to buy 3 pencils, 3 erasersand 2 ens?


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Q7.A rope burns non-uniformly for

exactly one hour. How do youmeasure 45 minutes, given two

such ropes?


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Q8.At a family reunion were the following people:one grandfather, one grandmother, two fathers,

two mothers, four children, three grandchildren,one brother, two sisters, two sons, twodaughters, one father-in-law, one mother-in-law,

and one daughter-in-law. But not as many peopleattended as it sounds. How many were there,and who were they?


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VISUAL / CONNECTRound 4


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Q1.

Connect


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Q2.

Identify


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Q3.

Connect

Now I will haveless distraction upon the loss of

his left eye


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Q4.

Connect


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Q5.

Connect


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Q6.

Connect


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Q7.

Connect


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Q8.

Identify


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ENDJunior Quiz,

The Mathematical Crusade, 2011

Junior Quiz Finals

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