Trick to find out rank of word or word of any rank

Topic -

 Math Trick to find out rank of any word ,Math Trick to find out word of any rank.

Post - 

We know very large number of students facing problem  to find out rank of any word or word of any rank , so here is the solution very easy to use just learn and deploy. 

Example : 

55th word of SHUVANK in dictionary ?

(1)  AHNKSUV 

(2)  AHSNKUV

(3)  AHNKUSV
(4)  AHNKUVS 

Method 1 : ( Hit & Trial ) applicable only if word not repeating

Choose any option 

Suppose we take  (1)  AHNKSUV 

Now  put numbering on each word as given bellow -  

Now move from left to right and put  a number "n" .bellow to every letter.

n ==> number of smaller letter in right hand side of that letter.

Example -

1) For A no any letter smaller in right hand side so n=0

2) For H no any letter smaller in right hand side so n=0

3) For N there is 1 letter smaller (k) in right hand side so n=1

and so on .....

wrong option

( Here 1 added for word itself )

So its wrong option , now doing this is very easy .

Check next option : AHSNKUV

Correct option.

( Here 1 added for word itself )

feel free to comment if any doubt comes in your mind.

Method 2 -  ( For Non-Repeating letter  )

This method is just reverse of 1st but working is very fast , once you understand , you will able to use it very quickly.

Suppose we have to find 42nd word of ADOPT using this method ?

Step 1 :
word rank = 42
we have to count 41 place because at 42nd number word itself lies.
So
find out n as a number less than word rank so n=42-1 ==> 41
So n=41
Step 2 :
since we know adopt have 5 letters.
write it as
n1x(4!) + n2x(3!) + n3x(2!) + n4x(1!) + n5x(0!) 
just like do numbering in method 1 , ok leave that now our task is to move from left to right.
and put values of n1,n2,n3,n4,n5 such thatn1x(4!) + n2x(3!) + n3x(2!) + n4x(1!) + n5x(0!) =41
after solving left to right we can-

write as - 1x(4!)+2x(3!)+2x(2!)+1x(1!) +0x(0!)

Step 3 :

Now write it as -
4    3    2    1     0
?    ?    ?    ?     ?

n1  n2  n3  n4  n5

=====>

4 3 2 1 0
? ? ? ? ?

1 2 2 1 0

Now last step to find out ? values.

Step 4 :
SO Answer will be "D P T O A"

Now you think how can i say it. guess, yes correct by the help of values of n1,n2,n3,n4,n5
just follow this algo :

1) Sort whole word in decreasing order and put rank as

T P O D A
4 3  2 1  0

2) now for 1st place find out value of n1 which is 1 so choose letter which is over 1 and thats D

3) so we got first letter as D so our word is D _ _ _ _  , now again start from (1) with remaining letters TPOA.


Example:

1st Iteration :1)

T P O D A
4 3  2 1  0

2) now for 1st place find out value of n1 which is 1 so choose letter which is over 1 and thats D

3) D _ _ _ _

2nd Iteration :1)

T  P O  A
3  2  1  0

2) now for 2nd place find out value of n2 which is 2 so choose letter which is over 2 and thats P

3) D P _ _ _

3rd Iteration :1)

T   O  A
2   1   0

2) now for 3rd place find out value of n3 which is 2 so choose letter which is over 2 and thats T

3) D P T _ _

4th Iteration :1)

   O  A
   1   0

2) now for 4th place find out value of n4 which is 1 so choose letter which is over 1 and thats O

3) D P T O _ ==> DPTOA

Here we show you each step but once you get it i am sure its very easy to implement  and very less time taking.

Hope you enjoyed this post .
For repeating letter's we will post very soon. All the Best !

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He is a blogger/website designer and developer.he is founder of www.technicalbaba.com and also loves web programming.