Showing posts with label Math Puzzle. Show all posts
Showing posts with label Math Puzzle. Show all posts

Saturday, July 25, 2015

IAS Questions

IAS is one of the toughest exams to crack. People who have studied for it, or better still, cleared it, would tell you how competitive it can get, and how tough the whole process of getting through really is.
It's nothing like giving the boards where you mug up everything and vomit it out on a paper. You actually need to an incredibly smart person here. Once you have cleared the written examination, you are called in for an interview session, so only the very best of the best make the cut.
We found 19 really quirky questions (and answers) that were asked in the two stages of the examination process. These questions don't check how well you know the subject, but how knowledgeable you really are, and how witty you can get. Check them out, see if you can solve them without checking out the answers (given at the end of the article). I instantly answered 11 out of 19, let see your scores.

Q1: How can you drop a raw egg onto a concrete floor without cracking it?

Q2: What looks like half apple?

Q3:  What will you do if I run away with your sister?

Q4:  ( ) + ( ) + ( ) + ( ) + ( ) = 30
This is what you have for the equation. The following are the numbers that you can use to fill in the brackets: 1, 3, 5, 7, 9, 11, 13 and 15. You can repeat the numbers if required. The resulting sum should be 30.

Q5: Jamie looked at his reflection on the window mirror of the 45th floor. Driven by an irrational impulse, he made a leap through the window on the other side. Yet Jamie did not encounter even a single bruise. How can this be possible if he neither landed on a soft surface nor used a parachute?

Q6: By using only one straight line, can you make the equation correct. 5+5+5=550?

Q7: A murderer is condemned to death. He has to choose between three rooms. The first is full of raging fires, the second is full of assassins with loaded guns, and the third is full of lions that haven't eaten in 3 years. Which room is safest for him?

Q8: Can you name three consecutive days without using the words Wednesday, Friday, or Sunday?

Q9: This is an unusual paragraph. I'm curious as to just how quickly you can find out what is so unusual about it. It looks so ordinary and plain that you would think nothing was wrong with it. In fact, nothing is wrong with it! It is highly unusual though. Study it and think about it, but you still may not find anything odd. But if you work at it a bit, you might find out. Try to do so without any coaching!
Q10: What if one morning you woke up and found that you were pregnant?

Q11: Twins (Adarsh and Anupam) were born in May but their birthday is in June. How's this possible?

Q12: The peacock is a bird that does not lay eggs. How do they get baby peacocks?

Q13: If two's company, and three's a crowd, then what is four and five?

Q14: A cat had three kittens: January, March and May. What was the mother's name.

Q15:  James bond was pushed out of an airplane without any parachute. He survived. How?

Q16: If it took eight men ten hours to build a wall, how long would it take four men to build it?

Q17: How can a man go eight days without sleep?

Q18: Bay of Bengal is in which state?

Q19: Where would Lord Rama have celebrated his “First Diwali”?

(Answers are after the jump) 

Monday, July 20, 2015

Integrating your Deluxe Car

A guy is travelling in a deluxe car in the desert. He wants to take a bath. But he has no soap and there is no water.

What does he do?

He will integrate his ‘d(lux)’ car to get ‘lux + c’. Using the ‘lux’ soap he will bath in the ‘c’.

Can you murder math more than this?

Sunday, July 12, 2015

How to prove √i + √(-i) = √2

We have, √i + √(-i)

= √{ √i + √(-i) }2
= √{ i + (-i) + 2i(-i) }
= √( i - i - 2i2 )
= √(-2i2)
= √2

Simple, yet tricky.

Wednesday, July 18, 2012

What Equals 100%?


What does it mean to give MORE than 100%?
Ever wonder about those people who say they are giving more than 100%?

How about ACHIEVING 101%?

What equals 100% in life?

Here’s a little mathematical formula that might answer these questions:

If
A B C D E F G H I J K L M N O P Q R S T U V W X Y Z
represent
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26
then,

KNOWLEDGE = 11+14+15+23+ 12+5+4+7+ 5 = 96%
HARDWORK = 8+1+18+4+23+ 15+18+11 = 98%

But, ATTITUDE = 1+20+20+9+20+ 21+4+5 = 100%
And, LOVE OF GOD = 12+15+22+5+15+ 6+7+15+4 = 101%

Therefore, one can conclude with mathematical certainty that,
While "Knowledge" & "HardWork" will get you close
and "Attitude" will get you there,
It’s the "Love of God" that will put you over the top!


But there is always a debate on the presence of GOD.

Something from Nothing

0! = 1

Proof of 6 Weeks = 10! Seconds

6 Weeks
= 6 x 7 Days
= 6 x 7 x 24 Hours
= 6 x 7 x 24 x 3600 Seconds
= 6 x 7 x (3 x 8) x (4 x 9 x 100) Seconds
= 6 x 7 x (3 x 8) x (4 x 9 x 5 x 2 x 10) Seconds
= 1 x 2 x 3 x 4 x 5 x 6 x 7 x 8 x 9 x 10 Seconds
= 10! Seconds

Monday, April 30, 2012

Proof of 0 = 1

ʃ tan(x) dx = ʃ sin(x) / cos(x) dx
ʃ tan(x) dx = ʃ sec(x) sin(x) dx [taking sec(x) as the 1st function]
ʃ tan(x) dx = - sec(x) cos(x) + ʃ sec(x) tan(x) cos(x) dx
ʃ tan(x) dx = - 1 + ʃ tan(x) dx
0 = - 1

0 + 1 = - 1 + 1
1 = 0

Nine Nine Nine Nine

Using only four 9s and standard arithmetic operations, it is possible to produce each of the numbers from 1 to 20.


For example,
1 = (9 + 9) / (9 + 9)
2 = (9 + √9) / (9 - √9)


Can you do the others?


(Kevin Hinks, Plymouth, MI)

Is 0.999 ... = 1 ?

Let C ...

We have,
1/3 = 0.333 ...
3 * (1/3) = 0.999 ...
1 = 0.999 ...

What do sin, cos, tan stand for?

Sin stands for Sine Function
Cos stands for Co-Sine Function
Tan stands for Tangent Function
Cot stands for Co-Tangent Function
Sec stands for Secant Function
Cosec or Csc stands for Co-Secant Function

Wednesday, February 1, 2012

Friday, November 11, 2011

The All 11

What is the time now? It’s 11:11:11
What is the date? It’s 11.11.11
Hour, Minute, Second & Day, Month, Year. It’s all ‘11’
11:11:11 on 11.11.11

This will happen again after 100 years on 11th Nov 2111!

Saturday, October 22, 2011

The Answer is 22

Select any 3-digit number with all digits different from one another. Write all possible 2-digit numbers that can be formed from the 3-digits selected earlier. Then divide their sum by the sum of the digits in the original 3-digit number.

e.g.    Consider a 3-digit number 365.
         All possible 2-digit numbers are 36, 35, 63, 65, 53, 56.
         Their sum is 36+35+63+65+53+56=308
         Sum of the digits of original number is 3+6+5=14
         Then 308/14=22

Wednesday, October 5, 2011

Knock-out Cricket Tournament

A single elimination (knock out – one loss & out) cricket tournament has 16 teams competing. How many games must be played to get one champion?

Typically, the majority problem solvers will do something like this –
i) Taking 2 groups of 8 teams, playing 1st round. In each group there are 4 matches, eliminating 4 teams. Total 8 matches & 8 teams remaining in the tournament.
ii) Now 4 Quarter-final matches to get the top 4 teams of the tournament. (8 + 4 = 12 matches so far)
iii) 2 Semi-finals & a final to get the champion. (12 + 2 + 1 = 15 matches total)

A much simpler way to solve this problem is to focus only the losers, not the winners.
“How many losers must be there in a tournament of 16 teams to get one winner?” The answer is simply 15.
“How many games must be played to get 15 losers?” Naturally 15.
That’s the answer.

Saturday, October 1, 2011

No Nobel for Mathematics

Nobel prizes were instituted by the will of Alfred Nobel, a Swede who was a chemist, an industrialist and the inventor of dynamite. Since 1901, prizes have been awarded for achievements in Physics, Chemistry, Physiology or Medicine, Literature and Peace – but not in Mathematics. Legend says that Nobel ignored mathematics because his wife rejected him for a mathematician, named Gosta Mittag Leffler. Furthermore, Nobel didn’t consider mathematics a “practical” science that had much impact on society.

That’s why Able prizes have been awarded for achievements in Mathematics.

Tha value of Pi

In 1844, Johann Dase (aka Zacharias Dahse) computed π to 200 decimal places in less than 2 months.

π = 3.14159 26353 89793 23846 26433 83279 50288 41971 69399 37510 58209 74944 59230 78164 06286 20899 86280 34825 34211 70679 82148 08651 32823 06647 09384 46095 50582 23172 53594 08128 48111 74502 84102 70193 85211 05559 64462 29489 54930 38196

To get this result Dase used the equation,
π/4 = arctan (1/2) + arctan (1/5) + arctan (1/8) + … with a series expansion for each arctangent.