Carrying over is a concept taught to us at a very early stage of our life. However, it has never been an easy thing to do. In adding two or more numbers, most of us face problem while “carrying over”. Larger the digits, involved in the numbers to be added, more likely it is to involve carrying.   More the carrying over involved, more likely are we to make mistakes.

Friends, remember the most basic and effective rule of making arithmetic fast and quick is to break difficult calculations into simpler, easily manageable small calculations.

Any digit when added to 9 (except 0) makes carrying over mandatory.  On the contrary, anything added to 0 can’t produce a two digit number.  Even if 9 is added to 0, no carrying is needed.

So, to make things simpler let us create some zeroes.

Example:

Add 38 + 86

First make 38 to 40 by adding 2.  Now obviously adding 86 to 40 is definitely easier than adding 86 to 38.

86 + 40 = 80 + 40 + 6 = 126

I am sure you must be concerned about the 2 we added out of nowhere.  Well you must be, but if you can balance out this extra 2 by subtracting 2 from the answer (126), the final answer will be the same.

You can create 0 towards the end of both the numbers to be added.  Try to understand this with an example,

187 + 139

Add 140 (=139+1) to 190 (=187+3)

140 + 190 = 330

Now deduct back ‘1’ and ‘3’ added to the respective numbers. Hence to balance out subtract 1 and 3 from 330 = 330 – 1 – 3 = 326 is the final answer.

The effect of the above trick can be remarkable. Like any other quick calculation tricks, this also requires a lot of practice to master it.

Check out yourself by adding the following numbers -

37 +54 =?

79 + 23 =?

While adding decimals, this can be a very powerful trick. Try these questions -

12.97 + 1.34 = ?

14.95 + 11.60 = ?

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Your grandfather, determined to start the year 1900 off right, went to bed at 7 p.m. on December 31, 1899, setting his alarm clock to wake him at 8 the next morning. He slept like a log. How many hours sleep did he get?

Ancient Coin Puzzle

A thief went to a shop that sold antique coins. He stole a coin from Emperor Alexander’s time that had 326 B.C. inscribed on it. These rare coins were worth $ 100 for every year of their age (years from date of minting till now). So how much did the thief get for his stolen coin?

Both the puzzles above have some similarity. There is a clue hidden in the title of the post itself.

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Three friends check into a hotel. They pay $30 to the manager and go to their room. The manager suddenly remembers that the room rate is $25 and gives $5 to the bellboy to return to the people.  On the way to the room the bellboy reasons that $5 would be difficult to share among three people so he pockets $2 and gives $1 to each person. Now each person paid $10 and got back $1. So they paid £9 each, totalling $27. The bellboy has $2, totalling $29.

Where is the missing $1?

leave your answers below.

The above  missing dollar riddle is a famous problem that illustrates problems of confusion and misdirection in conversation. It illustrates how misdirection and irrelevant facts and questions can foil a person's clear understanding of a problem. Apply your mind and explain the logic behind the missing dollar.

Follow-up to the above problem - An interesting resolution is often cited as the solution to the above problem. Just read the following paragraph and post a comment whether you agree or not the given resolution to the above mystery.

A few months later, two of the original three guests check into a hotel room in the same hotel. The clerk says the bill is $20, so each guest pays $10. Later the clerk realizes the bill should only be $15. To rectify this, he gives the bellhop $5 to return to the guests. On the way to the room, the bellhop realizes that he cannot divide the money equally. As the guests didn't know the total of the revised bill, the bellhop decides to just give each guest $1 and keep $3 for himself.

Now that each of the guests has been given $1 back, each has paid $9, bringing the total paid to $18. The bellhop has $3, so $18 + $3 = $21, and the guests originally handed over $20, so that's where the missing dollar from the original problem is!

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Timing Puzzle 1
Having 2 sand-glasses: one 7-minute and the second one 4-minute. How can you time correctly 9 minutes ?

Timing Puzzle 2
A teacher of mathematics used an unconventional method to measure a 15-minute time limit for a test. He just used 7 and 11-minutehourglasses. During the whole time he turned sandglasses only 3 times (turning both hourglasses at once count as one flip).

Explain how the teacher measured 15 minutes.

Leave your answers below

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Age by Chocolate - Mathematics Trick

Step 1. Choose the number of times a week that you would like to have chocolate between 1 and 10.

Step 2. Multiply this number by 2. Add 5. Multiply it by 50.

Step 3. If you have already had your birthday this year add 1761. If you haven't, add 1760.

Step 4. Now subtract the four digit year that you were born. You should end up with a three digit number.

The first digit is the number of times you like chocolate in the week.

The last two digits is your age!
Let me explain this to you using my date of birth as an example. You can try with yours.

Step 1. I choose to eat chocolate 6 times in a week. I love chocolates

Step 2. 6*2=12+5=17*50=850

Step 3. My birthdate is 5^th April 1983 and my birthday in 2011 is yet to come. It will be there tomorrow

So we have to add 1761 to 850 = 2611

Step 4. Subtracting 1984 from 2611 gives 627.

Here 6 is the number of time I would like to have chocolate and 27 is my age. Isn’t it fun?

So for those who just want to have fun, go and do the trick with your pals. Those who want to exercise their grey cells, try and tell me what’s going on here.

Vineet Patawari

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During the latest round of a game, Kamal was fourth. Ramesh is not the oldest, but is older than Sujan, who was not second. The child who was next in age to the youngest, finished second. The child who finished in third place is older than the child who finished first. Bimal is younger than the child who finished in third place. Can you determine who finished where and place the children in order of age?

Leave your answers below -

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Grid Puzzle

Below is a very special grid, around each shaded number are 8 white squares. However, each white square should have a number from 1 to 7. Once filled in, these 8 numbers will sum to the shaded number. In addition, once completed correctly, no row nor column will contain a duplicate number within a white square. For example, the top row may be 5 6 4 2 3 1 7, etc. hence no digit repeated (similar to Sudoko)

Try to fill all the blank spaces. Leave your answers below by writing the numbers row-wise.

If you like the stuff here on QuickerMaths.com, you can share it with your friends on FaceBook using the Like it button.

Answer (posted on September 17, 2010)

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After quite a few days I am posting a riddle. I assure you it's very interesting. Though it may seem a little difficult when you first read it, maintain your cool and ponder over it again.

Suppose you have ten threads and a lighter. If a thread is lighted, it will burn for exactly one hour. The threads do not burn at constant speed, in other words it can happen that the first half of the thread is burned in 15 minutes, while the remaining part will take three quarters. How can you measure exactly 45 minutes using these threads, and what is the minimum of threads you need for this?

If you need any clarification, leave your queries as comment.

Leave your asnwers below as comments.

Try your hand at another interesting time keeping puzzle

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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 online book store Flipkart.com

Purchase Online

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

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Here I am giving a small mathematical problem, which can be solved as soon as you finish reading it if you know the simple trick to answer it. In my next post I will explain this very helpful trick of finding the change in area of 2-dimensionals figures and volume of 3-dimesionals figures if their dimensions changes. Also relationships between surface area and volume of cube, sphere, pyramid, etc. will be explained. These tricks come very handy in competitive examinations.

Geometric Puzzle
I have a miniature Pyramid of Egypt. It is 6 inches in height. I was invited to display it at an exhibition. I felt it was too small and decided to build a scaled-up model of the Pyramid out of material whose density is 1/8 times the density of the material used for the miniature. I did some calculation to check whether the model would be big enough.
If the mass (or weight) of the miniature and the scaled-up model are to be the same, how many inches in height will be the scaled-up Pyramid?
Now it’s upto you to answer this and figure what could be the trick to solve such questions.
Leave your answers and comments below:

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