### Dictionary Rank of a Word | Permutations & Combinations

PERMUTATIONS & COMBINATIONS Rank of the word or Dictionary order of the English words like COMPUTER, COLLEGE, SUCCESS, SOCCER, RAIN, FATHER, etc. Dictionary Rank of a Word Method of finding the Rank (Dictionary Order) of the word  “R A I N” Given word: R A I N Total letters = 4 Letters in alphabetical order: A, I, N, R No. of words formed starting with A = 3! = 6 No. of words formed starting with I = 3! = 6 No. of words formed starting with N = 3! = 6 After N there is R which is required R ----- Required A ---- Required I ---- Required N ---- Required RAIN ----- 1 word   RANK OF THE WORD “R A I N” A….. = 3! = 6 I……. = 3! = 6 N….. = 3! = 6 R…A…I…N = 1 word 6 6 6 1 TOTAL 19 Rank of “R A I N” is 19 Method of finding the Rank (Dictionary Order) of the word  “F A T H E R” Given word is :  "F A T H E R" In alphabetical order: A, E, F, H, R, T Words beginni

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Maths Magic, Interesting Mathematical Concepts

Mathematics is full of magic, It is the game with numbers. A person with the knowledge of mathematical tricks can use it as a magic. Here you learn many tricks and magics which make you different from others.

Maths Magic, Interesting Mathematical Concepts
Maths Magic, Interesting Mathematical Concepts

Magic 1 : Method of finding day from the date of birth

In order to find the day from the date of birth we should have the knowledge of two tables which are given as follows.

 Table of days Name of the day Day Code Sunday 1 Monday 2 Tuesday 3 Wednesday 4 Thursday 5 Friday 6 Saturday 0

 Table of Months Name of the Month Month Code January 1 February 4 March 4 April 0 May 2 June 5 July 0 August 3 September 6 October 1 November 4 December 6

Start from the date of birth let it is   03 – 08 – 1977
Step 1:-  1977 – 1900(Nearest century less than or equal to the  year of birth) = 77

Step 2:-  77 divide by 4 (leap year factor)    = 19 (leap years) + 1 (year extra)

Step 3:-  77(subtraction result of first step) + 19 (no. of leap years) = 96

Step 4:-  96 + 03 (no. of days from the date of birth) = 99

Step 5:-  99 + 03 (month code of August from the above table )=102

Step 6:-  102 divide by 7 (no. of days in one week) = 14 (quotient) and  4(remainder)
4 means Wednesday (from 2nd table of day codes.
In this way we can find the day from any date of birth.

Magic 2 : Getting three digit integer written twice
Consider any three digit number and multiply it by 1001. Now the result is the original number written twice.

For example:  456 x 1001 = 456456
678 x 1001 = 678678 and so on
This is true for all the three digit numbers.

Magic 3 : Always get answer 7

 Back to the same number seven (7) S No Steps Results 1 Select any number, Let it is 15 2 Double it we get 30 3 Adding 17 to it we get 47 4 Subtracting 3 from it we get 44 5 Dividing  44 by 2 we get 22 6 Subtract original number from 22 we get 07

Magic 4 : Magic Number 142857

When we divide 1000000 by 7 the then quotient is 142857. This number is a magic number because of the following reasons.
This number shows a cyclic property (clockwise) as follows

142857 x 1 = 142857  Start from 1 and go clockwise direction
142857 x 2 = 285714  Start from 2 and go clockwise direction
142857 x 3 = 428571 Start from 4 and go clockwise direction
142857 x 4 = 571428 Start from 5 and go clockwise direction
142857 x 5 = 714285 Start from 7 and go clockwise direction

142857 x 6 = 857142 Start from 8 and go clockwise direction

Magic 5 : Predicted table of 1089

Tell your friend to write any three digit number. It should be such that the left hand digit exceeds right hand digit by at least 2.
 Let the number be 981 Its reverse order is 189 Subtract 981 from 189 792 Reverse order of 792 297 Add 792 and 297 we get 1089

The result is always same with all three digit numbers with above condition.

Magic 6 : Get a series of two

Write natural number from 1 to 9 in ascending order in first row.
Write natural number 9 to 1 in descending order in second row.
In third row repeat the digits of first row.
In fourth row repeat the digits of second row.
In fifth row write only 2 and add vertically.
Result : We get a series of 2.
 First Row 1 2 3 4 5 6 7 8 9 Second Row 9 8 7 6 5 4 3 2 1 Third Row 1 2 3 4 5 6 7 8 9 Fourth 9 8 7 6 5 4 3 2 1 Fifth Row + + + + + + + + 2 Total 2 2 2 2 2 2 2 2 2

Magic 7 : Prove that  2 = 1 which is not generally true
To Prove  2 = 1
It is well known fact that 2  is not equal to 1 but we can prove that 2 = 1 by using the following algorithms
Let us consider the expression   a2 – a2

 a2 – a2 (a + a)(a – a) a(a - a) (a + a)(a – a) Dividing both side by (a-a) a a + a a 2a 1 2

Magic 8 : Prove that 3 = 4 which is generally not true

It is well known fact that 3 is not equal to 4 but we can prove it as follows

Magic 9 : Magic Number  12345679

12345679 is a magic number because of the following reasons
12345679 x 9 (1 x9) = 11111111
12345679 x 18(2 x 9) = 22222222
12345679 x 27 (3 x 9) = 33333333
12345679 x 36 (4 x 9) = 44444444
……………………………………………..
……………………………………………..
12345679 x 81 (9 x 9) = 99999999

Magic 10 : Magic of Number 152207

152207 is a magic number because if we multiply it by 73 then we get eight times one.
If we multiply it by 73 X 2  then we get eight times two.
If we multiply it by 73 X 3  then we get eight times three and so on...
Example :
 152207 x 73 (73 x 1) 11111111 152207 x 146 (73 x 2) 22222222 152207 x 219 (73 x 3) 33333333 152207 x 292 (73 x 4) 44444444 152207 x 365 (73 x 5) 55555555 ………………….. …………. 152207 x 657 (73 x 9) 99999999

Magic No 11 : Always getting Answer

Think of a number. Double it. Add six to it. Make its half. Take away the number you started with. Your is is always 3

Magic No. 12: Story of a Mathematician

Once a math. teacher lend Rs 15000 from a rich person, after few days he again lend Rs 25000 from the same person and then forget to return the money. After many days the rich person went to the Math. Teacher and ask for the money. Math. Teacher replied as he returned the money many days back. He explains the concept as follows.

 15000+25000 40000 A + B C (A +B)(A+B) C(A + B) A2 + AB + AB + B2 AC + BC A2 + AB - AC BC – AB - B2 A(A + B - C) -B(A + B - C) Cancel (A +B – C) on both side we get A - B A + B 0

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