Quicker Maths

Beauty of Numbers

admin — Tue, 07 Sep 2010 12:58:37 +0000

In this post I am sharing with some very interesting numerical symmetries. I got it from varied sources but the most interesting is the book from Shakuntala Devi titled Figuring: The Joy Of Numbers. It's a must read for all math lovers.

So here you go -

1 x 8 + 1 = 9
12 x 8 + 2 = 98
123 x 8 + 3 = 987
1234 x 8 + 4 = 9876
12345 x 8 + 5 = 98765
123456 x 8 + 6 = 987654
1234567 x 8 + 7 = 9876543
12345678 x 8 + 8 = 98765432
123456789 x 8 + 9 = 987654321

1 x 9 + 2 = 11
12 x 9 + 3 = 111
123 x 9 + 4 = 1111
1234 x 9 + 5 = 11111
12345 x 9 + 6 = 111111
123456 x 9 + 7 = 1111111
1234567 x 9 + 8 = 11111111
12345678 x 9 + 9 = 111111111
123456789 x 9 +10= 1111111111

9 x 9 + 7 = 88
98 x 9 + 6 = 888
987 x 9 + 5 = 8888
9876 x 9 + 4 = 88888
98765 x 9 + 3 = 888888
987654 x 9 + 2 = 8888888
9876543 x 9 + 1 = 88888888
98765432 x 9 + 0 = 888888888

Brilliant, isn't it?

And look at this symmetry:

1 x 1 = 1
11 x 11 = 121
111 x 111 = 12321
1111 x 1111 = 1234321
11111 x 11111 = 123454321
111111 x 111111 = 12345654321
1111111 x 1111111 = 1234567654321
11111111 x 11111111 = 123456787654321
111111111 x 111111111 = 12345678987654321

In one of my earlier post named cyclic number you will find similar very interesting of numbers. Pay attention to the comments over there.

If you know of any other symmetry of numbers or any interesting fact about numbers, feel free to share in the comment

Mind Boggling Math Puzzles: Millennium Prize Problems

admin — Wed, 01 Sep 2010 10:36:26 +0000

Quicker Maths offers regular tips and tricks for zooming through some arithmetic problems, as well as giving us fascinating puzzles that offer some solid food for mathematical thought. But what if you were given the opportunity to earn one million dollars to solve one math problem? That's exactly the deal that the Clay Mathematics Institute in Cambridge Massachusetts has offered. And pretty much anyone can enter to win.

The Millennium Problems, as they are known, were originally seven math problems that had existed for several years and remained unsolved. Most recently, one problem--the Poincare Conjecture--was successfully solved by Dr. Grigory Perelman of St. Petersburg, Russia. Perelman worked on and solved the problem in 2002 and 2003, and was thereafter awarded the CMI one million dollar prize in 2010, although he ended up turning down the prize money.

The Poincare Conjecture was a problem proposed in 1904 and left unsolved by French mathematician and theoretical physicist Henri Poincare. Although the details of the problem and the process of solving it are quite complex, essentially what Poincare was asking had to do with three-dimensional spheres.

In layman's terms, Poincare wanted to know why one could strap a rubber band around an apple and shrink the band down to a certain point without the band breaking or leaving the surface of the apple, whereas if you were to do the same with a rubber band and a doughnut, either the doughnut or the band would break.

Although several had attempted to figure out the mathematical details of this problem, Perelman successfully connected all the dots, so to speak, by building on the work of Richard Hamilton and his theory of the Ricci flow. Perelman also employed previous work on the spaces of metrics devised over the years by Cheeger, Gromov, and Perelman himself.

When Perelman solved the prize problem, aside from the CMI prize, he also received other accolades, including Science Magazine's 2006 Breakthrough of the Year award and the International Congress of Mathematicians' Fields Medal. As of now, the Poincare Conjecture is the only Millennium Prize problem that has been solved. The remaining six problems--the Birch and Swinnerton Dyer Conjecture, the Hodge Conjecture, the Navier-Stokes Equations, P vs. NP, the Riemann Hypothesis, and the Yang-Mills Theory--are yet to be resolved.

If you think you may want to someday take a crack at these "unsolvables", you can find more information on the CMI website, including the rules and information on each problem. Even though they may seem impossible, just like with any puzzle, it wouldn't hurt to try.

Author:

This guest post is contributed by Lauren Bailey, who writes on the topics of online colleges. She welcomes your comments at her email Id: blauren99 @gmail.com

What’s your favorite equation?

Vineet Patawari — Fri, 27 Aug 2010 12:36:33 +0000

It has been a while since we had a survey on any mathematics topic, so today I’d like to kick one off. What’s your favorite equation, formula, identity or inequality?

Try to keep it to your top 5 so that things don’t get out of hand – but please share which equation, formula, identity or inequality amuse you the most.

So – What’s your favorite equation, formula, identity or inequality in mathematics and if possible tell us why? Over to you!

Take into consideration all the branches of mathematics

Average Number of Arms

admin — Sun, 22 Aug 2010 16:41:32 +0000

Try out this probability question. It may seem very simple but think twice before giving the answer

What is the probability that the next person you meet has an above average number of arms?

Impossible
Unlikely
Likely
Very Likely
Certain

Leave your answers below as comment -

Red Wine Brain Teaser

admin — Fri, 13 Aug 2010 12:42:12 +0000

This question relates to the solution and mixture topic. You have a bucket of red wine and a bucket of white wine. You take a cup of red wine and pour it into the bucket of white wine. After thoroughly mixing, you then take a cup of this mixture and pour it back into the red wine bucket.

Is there more red wine in the white wine or is there more white wine in the red wine?

Feel free to post your answer in the comments section.

Quicker Maths by M Tyra

admin — Mon, 09 Aug 2010 16:06:52 +0000

Today, let me confess something to all of you. I am sure this will help all the readers.

So here I go. This is regarding the name of the website - QuickerMaths.com. It is inspired by the name of the best mathematics books I have ever come across. This book helped me a lot in clearing CAT and reaching to IIM. The inspiration of creating an interactive platform (QuickerMaths.com) came from this book. As a token of appreciation and to do my bit today I will tell you about this book named -

Magical Book on Quicker Maths

Author: M. Tyra

About the book: The book will be a boon for the aspirants of today’s competitive exams irrespective of their background – whether they come from arts, science or commerce stream. Concepts have been clarified so well, that even if one is vaguely familiar with them as in the case of non-mathematics students, understanding will not be a problem. Direct formulae are beneficial for one and all. They save time and time is precious for everyone.

Must for Competitive Preparation

The book is profusely illustrated. Avoiding the temptation for haste and ending up with a cookbook, the author has put in two years of intensive effort and research. Ideas have been taken from available study material, number theory, readers’ suggestions and, finally Vedic mathematics.

Recently I purchased the latest edition of this book from an online book store Flipkart.com

Purchase Online - The list Price is Rs. 250; you get a Discount of 25% (Rs. 62) on Flipkart.com.

So you get it for: Rs. 188 (incl. of all taxes)

Those who have already read this book please give your feedback to help others

Author: Vineet Patawari

Interesting Picture Puzzle – Answer

Vineet Patawari — Thu, 05 Aug 2010 06:19:24 +0000

This post contains answer to the last post named “Interesting Picture Puzzle”.

I decided to post it separately, so that new comers to the website can try first and then look at the answers.

I am posting the same picture with answered marked on it.

Answers inside

Description of above numbers

TOP PICTURE

1. Girls face -- frontal view.
2. Girls face -- right profile.
3. Mans face -- frontal view.
4. Mans face -- left profile.
5. Girls face -- frontal view.

BOTTOM PICTURE

6. Mans face -- left profile.
7. Girls face -- left profile.
8. Girls face -- right profile.

If you wish to post anything on QuickerMaths.com, visit “Write for Us” for instructions or simply mail the article at vineetpatawari@gmail.com

Interesting Picture Puzzle

Vineet Patawari — Tue, 03 Aug 2010 12:48:19 +0000

If you like picture puzzles, this is post is for you. What do you see? The first picture below has faces hidden - but

Where are they?

How many are there?

How Many Faces Can You Find In This Picture? Post your observations in form of comments below-

Click on the image to enlarge

Click here to know the answer

Interesting Logical Puzzle

admin — Thu, 29 Jul 2010 13:18:27 +0000

This one's an interesting puzzle and DOES NOT involve any MECHANICS!

There's a Bridge 2.4 km long with a load handling capacity of exactly 1 tonne and is bound to collapse if load increases by even a single gram than a tonne.

A bus, loaded fully with passengers, of weight exactly a tonne is crossing over the bridge. At exactly 3/4th of the length of the bridge a Crow comes (out of the Blue) and sits on top of the Bus.
But to everyone's surprise, the Bridge doesn't collapse and the bus crosses it safely.

Why?

Leave your answers below -

Is two equals one?

admin — Mon, 26 Jul 2010 13:27:01 +0000

Is 2 = 1?

Today, I will prove that two is equal to one (2 = 1). I will do that in more than one way. You know what you have to do? You have to point out the fallacy in the proofs.

The Fallacious Proof - 1:

Let, a = x

a+a = a+x [add a to both sides]

2a = a+x [a+a = 2a]

2a-2x = a+x-2x [subtract 2x from both sides]

2(a-x) = a+x-2x [2a-2x = 2(a-x)]

2(a-x) = a-x [x-2x = -x]

2 = 1 [divide both sides by a-x]

Hence Proved

The Fallacious Proof - 2:

Let, a = b

a^2 = ab [multiplying ‘a’ both sides]

a^2 – b^2 = ab – b^2 [subtracting b^2 from both sides]

(a+b)(a-b) = b(a-b) [dividing both sides by (a-b)]

a+b = b

b+b = b [since a=b, replacing a by b]

2b = b

2 = 1 [dividing both sides by b]

Hence Proved