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Unit Digit Method for Cryptarithmetic Problems

Elitmus Unit Digit

Cryptarithmetic Unit Digit Method

When to use Unit Digit Method?

  • When you don’t know how to solve the problem and just can’t get started.
  • You think the problem is really tough to solve.
  • In this case you have to start hit and trial with the possible values of unit digit of the multiplication problem.

Time to solve whole problem – 10 mins

Suggestion – You must know how to solve Basic Crypt arithmetic questions firsts

The Cryparithmetic methods discussed below are developed by PrepInsta only and available on 2 PrepInsta owned websites only. Anyone copying the method will be legally sued as these are not open source but are PrepInsta’s Proprietary methods.

Steps to Solve-

At each step, you have to check, whether the values satisfies Basic Cryptarithmetic Rule

Example

                       W  B  A
                    x  B  P  W
                    ----------
                    C  X  R  F
                 F  X  A  X
              A  A  C  C      
              -----------------
              A  P  C  A  B  F
Firstly divide the problem in three parts. As,
 

(1)      W  B  A             (2)     W  B  A        (3)      W  B  A
            x  W                        x  P                    x  B
     -----------                   ---------               ---------
      C  X  R  F                  F  X  A  X              A  A  C  C
 
Now, you have to select one from three which has maximum number of clues.i.e. maximum number of variables getting repeated.
In this case take,
(3)          W  B  A
                x  B
          ----------
          A  A  C  C
Now, you have to start hit and trial with the possible values C i.e.
 
C={1, 2, 3, 4, 5, 6, 7, 8, 9} 
  
Firstly take  C=1 and check further

Possible ways of getting 1 as Unit Digit

(3)                                  W  B  A 
                                        x  B
                                  ----------
                                  A  A  C  C 

then
Case 1     C=1  A=1  B=1   Rejected As A = B = C [violates the Basic Cryptarithmetic Rules.]
Case 2     C=1  A=7  B=3   Needs to be checked further
Case 3     C=1  A=3  B=7   Needs to be checked further
Case 4     C=1  A=9  B=9   Rejected As A = B  [violates the basic Cryptarithmetic Rules.]
Now check for Case 2 and Case 3 only.
(3)     W  B  A
            x B
     ----------
     A  A  C  C 

        W  3  7
           x  3
     ----------
     7  7  1  1
Rejected as,  even after taking the value of W=9, You will never get 77.
        W  3  7
           x  3
     ----------
     7  7  1  1
Now, you have to check with case 3
C=1, A=3, B=7
       W  B  A
          x  B
    ----------
    A  A  C  C

       W  7  3
          x  7
     ---------
    3  3  1  1 
Here you can easily predict the value of W=4
Hence W=4, C=1, A=3, B=7 put these values in main problem
              4  7  3
           x  7  P  4
           ----------
           1  X  R  F
        F  X  3  X
     3  3  1  1      
     ----------------   
     3  P  1  3  7  F
Now, you can see
              4  7  3
                 x  4
           1  8  9  2 [ 1  X  R  F]
If you compare side by side you will get X=8, R=9 and F=2
Put these values in main problem, and rewrite again
              4  7  3
           x  7  P  4
           ----------
           1  8  9  2
        2  8  3  8
     3  3  1  1       
     ---------------- 
     3  P  1  3  7  2
Now, you can easily predict the value of P=6
Hence,
              4  7  3
           x  7  6  4
           ----------
           1  8  9  2
        2  8  3  8
     3  3  1  1      
     ----------------
     3  6  1  3  7  2
[Relax - it's going to take some time to understand the whole concept. 
If you are facing any difficulty. Please go 
through the Cryptarithmetic Tutorial.]

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