2009 October | Quicker Maths

30Oct/0920

Shortcut to find the Cube of a number

Very often we have to find the cube, i.e. third power of 2 digit numbers. Cubes of very large numbers are rarely used.

Cubes of all the single digits should be memorized. Find below the table of cubes of first ten natural numbers -

1³ = 1, 2³ = 8, 3³ = 27, 4³ = 64, 5³ = 125,

6³ = 216, 7³ = 343, 8³ = 512, 9³ = 729, 10³ = 1000

To find the cube of any 2 digit number, we have to take the following steps

First Step: The first thing we have to do is to put down the cube of the tens-digit in a row of 4 figures. The other three numbers in the row of answer should be written in a geometrical ratio in the exact proportion which is there between the digits of the given number.

Second Step: The second step is to put down, under the second and third numbers, just two times of second and third number. Then add up the two rows.

Finding the cube of 12

Or, 12³ = ?

First Step: Digit in ten’s place is 1, so we write the cube of 1. And also as the ratio between 1 and 2 is 1:2, the next digits will be double the previous one. So, the first row is

1 2 4 8

Step II: In the above row our 2^nd and 3^rd digits (from right) are 4 and 2 respectively. So, we write down 8 and 4 below 4 and 2 respectively. Then add up the two rows.

Ex 2: 16³ = ?

Soln:

Explanations: 1³(from 16) = 1. So, 1 is our first digit in the first row. Digits of 16 are in the ratio 1:6, hence our other digits should be 1×6 = 6, 6×6 = 36, 36×6 = 216. In the second row, double the 2^nd and 3^rd number is written. In the third row, we have to write down only one digit below each column (except under the last column which may have more than one digit). So, after putting down the unit-digit, we carry over the rest to add up with the left-hand column. Here,

i) Write down 6 of 216 and carry over 21.

ii) 36 + 72 + 21 (carried) = 129, write down 9 and carry over 12.

iii) 6 + 12 + 12 (carried) = 30, write down 0 and carry over 3.

iv) 1 + 3 (carried) = 4, write down 4.

29Oct/092

The Princess Letters

In ancient times, there lived a prince and a princess who loved each other. They belonged to neighboring kingdoms. But their plans pf happiness together came to a sudden end when the two kingdoms went to war. Their parents locked them up in two towers and had them guarded day and night.

One day the prince bribed the guard so that he would deliver and collect written massages from himself and the princess. The prince however, did not trust the guard not to read the letters. Even if he were to seal the letters, the guard could open, read the reseal them without the princess knowing. The clever prince and princess then devised a way of making it impossible for the guard to read the letters before they were delivered.

How did they do it?

Popularity: 1%

Filed under: Puzzles 2 Comments

28Oct/090

Divisibility Rule of 7, 13, 17, 19, 23, 29, 31, 37, 41, 43 and 47

You might have seen divisibility rules of various numbers. But most of them very conveniently skip the ones which are very difficult and a divisibility rule for which is very much required. Today I’ll show you the divisibility rule for 7, 13, 17, 19, 23, 29, 31, 37, 41, 43 and 47.

Number	Method	Example
7	Subtract 2 times the last digit from remaining truncated number. Repeat the step as necessary. If the result is divisible by 7, the original number is also divisible by 7	Check for 945: : 94-(2*5)=84. Since 84 is divisible by 7, the original no. 945 is also divisible
13	Add 4 times the last digit to the remaining truncated number. Repeat the step as necessary. If the result is divisible by 13, the original number is also divisible by 13	Check for 3146:: 314+ (46) = 338:: 33+(48) = 65. Since 65 is divisible by 7, the original no. 3146 is also divisible
17	Subtract 5 times the last digit from remaining truncated number. Repeat the step as necessary. If the result is divisible by 17, the original number is also divisible by 17	Check for 2278:: 227-(5*8)=187. Since 187 is divisible by 17, the original number 2278 is also divisible.
19	Add 2 times the last digit to the remaining truncated number. Repeat the step as necessary. If the result is divisible by 19, the original number is also divisible by 19	Check for 11343:: 1134+(23)= 1140. (Ignore the 0):: 11+(24) = 19. Since 19 is divisible by 19, original no. 11343 is also divisible
23	Add 7 times the last digit to the remaining truncated number. Repeat the step as necessary. If the result is divisible by 23, the original number is also divisible by 23	Check for 53935:: 5393+(75) = 5428 :: 542+(78)= 598:: 59+ (7*8)=115, which is 5 times 23. Hence 53935 is divisible by 23
29	Add 3 times the last digit to the remaining truncated number. Repeat the step as necessary. If the result is divisible by 29, the original number is also divisible by 29	Check for 12528:: 1252+(38)= 1276 :: 127+(36)= 145:: 14+ (3*5)=29, which is divisible by 29. So 12528 is divisible by 23
31	Subtract 3 times the last digit from remaining truncated number. Repeat the step as necessary. If the result is divisible by 31, the original number is also divisible by 31	Check for 49507:: 4950-(37)=4929. Since 492-(39) is divisible by 465:: 46-(3*5)=31. Hence 49507 is divisible by 31
37	Subtract 11 times the last digit from remaining truncated number. Repeat the step as necessary. If the result is divisible by 37, the original number is also divisible by 37	Check for 11026:: 1102 - (116) =1036. Since 103 - (116) =37 is divisible by 37. Hence 11026 is divisible by 31
41	Subtract 4 times the last digit from remaining truncated number. Repeat the step as necessary. If the result is divisible by 41, the original number is also divisible by 41	Check for 14145:: 1414 - (45) =1394. Since 139 - (44) =123 is divisible by 41. Hence 14145 is divisible by 41
43	Add 13 times the last digit to the remaining truncated number. Repeat the step as necessary. If the result is divisible by 43, the original number is also divisible by 43. This process becomes difficult for most of the people because of multiplication with 13.*	Check for 11739:: 1173+(13*9)= 1290:: 129 is divisible by 43. 0 is ignored. So 11739 is divisible by 43
47	Subtract 14 times the last digit from remaining truncated number. Repeat the step as necessary. If the result is divisible by 47, the original number is also divisible by 47. This too is difficult to operate for people who are not comfortable with table of 14.	Check for 45026:: 4502 - (146) =4418. Since 441 - (148) =329, which is 7 times 47. Hence 45026 is divisible by 47

Notes: In applying the above methods, stop repeating the step of adding or subtracting (as the case may be) from the remaining truncated number as soon as you realize that the truncated number is divisible by the given number.

Popularity: 14%

Filed under: Speedy Calculation No Comments

26Oct/092

There are 9 coins.

There are 9 coins. 8 are of 1 gm and 1 is of 2 grams. How will you find out the heavier coin in minimum number of weighing and how many weighing it will need?

Popularity: 1%

Filed under: Puzzles 2 Comments

24Oct/091

Drop An Egg

If you standing on a pavement, how can you a raw egg to the ground for 1 metre without breaking it, without trying to cushion its fall?

Popularity: 1%

Filed under: Puzzles 1 Comment

22Oct/092

Solve a Dilemma

What is wrong with this proof?

2 = 1

a = b

a² = ab

a² – b² = ab – b²

(a + b) (a – b) = b (a – b)

a + b = b

2b = b

2 = 1

Popularity: 1%

Filed under: Puzzles 2 Comments

22Oct/094

A Puzzle Of Cultural Groups

My club has five cultural groups. They are literary, dramatic, musical, dancing and painting groups. The literary group meets every other day, the dramatic every third day, the musical every fourth day, the dancing every fifth day and the painting every sixth day. The five groups met, for the first time on the New Year’s day of 1975 and starting from that day they met regularly according to schedule.

Now, can you tell how many times did all the five meet on one and the same day in the first quarter? Of course the New Year’s day is excluded.

One more question-were there any days when none of the groups met in the first quarter and if so how many were there?

Popularity: 1%

Filed under: Puzzles 4 Comments

20Oct/092

Entrance Test

As an entrance test for a particular university, you are given a corked bottle with a very small coin in it. Your task is to remove the coin without taking the cork out of the bottle or breaking the glass, or boring a hole in the cork or glass.

How do you pass the test and get the coin out?

Popularity: 2%

Filed under: Puzzles 2 Comments

20Oct/093

Selling Eggs

The egg vendor calls on his first customer and sells half his eggs and half an egg. To the second customer he sells half of what he had left and half an egg and to the third customer he sells half of what he had then left and half an egg.
By the way e didn't break any eggs. In the end three eggs were remaining.

How many did he start out with?

Popularity: 1%

Filed under: Puzzles 3 Comments

19Oct/090

Vedic Multiplication by 9, 99, 999 and so on

When any number has to be multiplied by a series of 9s, like 9, 99, 999, 9999 and so on than we can apply this very simple vedic maths technique to increase your speed of calculation.

Multiplication with 9/ 99 / 999 and so on.

we know, 789 × 999 = 788,211

You will get the answers in two parts,

The left hand side of the answer: subtract 1 from 789, which is 788
The right hand side of the answer subtract 789 from 1000 = 1000-789= 211

Thus, 999 x 789 = 789-1 | 1000-789 = 788, 211 (answer)

{for the right hand side of the answer, 789 should be subtracted from (999+1)}

or, 99999 x 78 = 78-1 | 100000 - 78

= 7799922

{78 should be subtracted from (99999+1)}

Another example:

1203579 × 9999999 = 1203579-1 | 10000000- 1203579

=120357887964 21

Number in red is 1 less than 1203579. Number in blue is (10000000-1203579). Hence the answer.

This method has to be altered a little bit when number of 9s are lessers than the number of digit in the divisor.

1432 x 9 = 1432 (10 – 1) = 14320 – 1432 = 12888

So for multiplication with 9, put a zero after that number and subtract the number itself from that.

Likewise for 99 put two zeroes after that number .

3256 x 99 = 325600 – 3256 = 322344

Older Entries »

Quicker Maths Learn Vedic Maths Tricks | Enjoy Puzzles, Brainteasers & Riddles

Shortcut to find the Cube of a number

The Princess Letters

Divisibility Rule of 7, 13, 17, 19, 23, 29, 31, 37, 41, 43 and 47

There are 9 coins.

Drop An Egg

Solve a Dilemma

A Puzzle Of Cultural Groups

Entrance Test

Selling Eggs

Vedic Multiplication by 9, 99, 999 and so on

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