ElitmusZone » How To Solve Cryptarithmetic Problems 03

How To Solve Cryptarithmetic Problems 03

Fundamental Rules

Rule-3
If  A x B = _ A then possible values of A and B
Case I 
When A = 5 and B = {3, 7, 9}
A x B = _ A
5 x 3 = _ 5  [15]  (consider last digit)
5 x 7 = _ 5  [35]  (consider last digit)
5 x 9 = _ 5  [45]  (consider last digit)

Case II 
When A = {2, 4, 8} and B = {6}
A x B = _ A
2 x 6 = _ 2  [12]  (consider last digit)
4 x 6 = _ 4  [24]  (consider last digit)
8 x 6 = _ 8  [48]  (consider last digit)

Example Supporting Case-I and Case-II
               T  H  E
            x  P  E  N
            S  N  T  I
         P  I  A  E
      H  B  N  E      
      S  H  A  A  H  I

Complete Solution
                 
In this problem, P x E= _E [H  B  N  E]

Case 1   E={5} and P={3, 7, 9}

Case 2   P={6} and E={2, 4, 8}

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Cryptarithmetic Tutorial 01
Cryptarithmetic Tutorial 02
Cryptarithmetic Multiplication Problems
Introduction to  Cryptarithmetic
Logical Reasoning Problems

5 comments

    1. Abhishek

      Since the initial expression is AxB=_A and not AxB=A, we are looking for 2 digit product such that the unit’s digit (A) is same as the first multiplier (A).

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