Pentagram - The mathematics society of BMSCE, hosted its first event on 9th March, 2013.

2. Final Round
Answers

3. Q1. Connect
• P versus NP problem
• Hodge conjecture
• Poincaré conjecture
• Riemann hypothesis
• Yang–Mills existence and mass gap
• Navier–Stokes existence and smoothness
• Birch and Swinnerton-Dyer conjecture

4. • Millennium Prize Problems
These are seven problems in mathematics that were
stated by the Clay Mathematics Institute in 2000.
A correct solution to any of the problems results in a
US $1,000,000 prize.

5. Q2. Identify all the curves present in the figure.

6. • Circle
• Ellipse
• Parabola
• Straight line
• Rectangular Hyperbola

7. Q3. Identify the curve given parametrically as x =
acos³θ , y = asin³θ

8. Astroid

9. Q4. Is the series
1 + 1/4 + 1/9 + 1/16 + 1/25 + ….
convergent(sum is finite) or divergent(sum is
infinite) ?

10. • This is a convergent series. The sum of this
series is finite and equal to π²/6
This is also famously known as the Basel
problem and was first proved by Leonhard
Euler.

11. Q5. Connect

12. • Golden ratio, phi

13. Q6. Which step is wrong and why?
a=b
a²=ab
a²-b²=ab-b²
(a+b)(a-b)=b(a-b)
a+b=b
2b=b
2=1

14. • 4th step is wrong.
• Since a = b, cancelling (a-b) on both sides is
wrong because 0/0 is undefined.

15. Q7. Find the total number of common
tangents to these two circles.

16. • 4 common tangents.

17. Q8. Decode it and rewrite the complete
sentence.

18. • I ate some pie ……. and it was yummy!!!

19. Q9. Identify the logo.

20. • This is the logo of the International
Mathematics Olympiad(IMO) to which Google
donated 1 million Euros to help cover the
costs of the next five global events (2011-15).

21. Q10. Identify this famous mathematician.

22. • Gottfried Leibniz

23. Q11. Draw the graph of x² - y² = 0

25. Q12. Decipher the code
• Sherlock, the detective who was mere days from
cracking an international smuggling ring has
suddenly gone missing.
• While inspecting his last-known location, you find
a note:
710 57735 34 5508 51 7718
• Currently there are 3 suspects: Bill, John, and
Todd. Can you break the detective's code and find
the criminal's name?

26. • Bill is the criminal. Rotating the image by 180 degrees
clockwise, we get :
Here 8 resembles ‘B’, 1 resembles ‘I’, 7 resembles ‘L’ and so
on…

27. Q13. Twin statistics
• Suppose that 3% of births give rise to twins.
What percentage of the population is a twin :
a. 3%
b. <3%
c. >3%

28. c. >3%
Out of 100 births, 97 are single and 3 are twins.
That’s 103 babies in total, 6 of which are
twins, which represent 5.8% of the total population.

29. Q14. Which figure will come next in the
series?
M
8
?

31. Q15. Identify
• It is often described as the "Nobel Prize of Mathematics"
for being traditionally regarded as the most prestigious
award in the field of mathematics.
• It is awarded two, three, or four mathematicians not over
40 years of age at each International Congress of
the International Mathematical Union (IMU), a meeting
that takes place every four years.

32. • Fields Medal

33. Bonus Problem.
Q16. Using only four 4s and any mathematical
operation/function, form all numbers from 1 to 10.

34. • 1=4÷4+4−4
• 2 = 4 −(4 + 4)÷ 4
• 3 = (4 × 4 − 4)÷ 4
• 4 = 4 + 4 ×(4 − 4)
• 5 = (4 × 4 + 4)÷ 4
• 6 = 4 +(4 + 4)÷ 4
• 7=4+4−4÷4
• 8=4÷4×4+4
• 9=4÷4+4+4
• 10 = 4 + 4 + 4 −√4