Saturday, 12 November 2016

Cryptographical Tutorial for eLitmus

Fundamental Rules
1.Each Variable should have unique and distinct value.
2.Each Letter, Symbol represents only one digit throughout the problem.
3.Numbers must not begin with zero  i.e.  0123 (wrong) , 123 (correct).
4.You have to find the value of each letter in the Cryptarithmetic.
5.There must be only one solution to the problem.
6.The Numerical base, unless specifically stated , is 10.
7.After replacing  letters by their digits, the resulting arithmetic operations must be correct.
Example of Cryptarithmetic Problem
Detailed Explanation
1.Suppose if you are considering  A=2, then  other variable in problem cannot have value equal to 2.
i.e.  In the given problem above, B≠2, M≠2, R≠2, Y≠2 etc.
2.You cannot take someplace A=2 and someplace A=3 in a single problem.
i.e. If you are getting  A=2 and A=3 in same problem, solution is wrong.
3.Numbers must not begin with zero.i.e. In the given problem above, Value of M≠0, B≠0. 
Fundamental rules
Rule-1
If  A + B = A  then the possible value of B={0, 9}
Case I 
i.e. K + A = A (K=0)
Example Supporting Case-I 
                      P  A  S
                   x  R  B  Q
                   S  B  K  W
                A  S  A  A 
             S  E  P  B      
             S  Q  S  K  A  W
Here, you can easily predict the value of K = 0

Case II 

If A + B = A
When B = 9  9 + A = A   [9 + A + 1(carry) = _A]
When you have 1 carry from the previous addition.
Example supporting Case-II
                                                3  5 
                                               +9  7
                                             1  3  2
Example:

                      A  I  D
                      x  A  D
                   R  I  A  D
                D  D  C  D      
                D  I  C  E  D

Here, you can take I=9 as I + C = C

Rule-2
If A * A = _A  then the possible value of A={1, 5, 6}
Case I 
      1.    When A=1   1 * 1 = _1  

Case II
      1.    When A=5   5 * 5 = _5 (25) [consider last digit only]
      2.    When A=6   6 * 6 = _6 (36) [consider last digit only]

Example supporting Case-II
 
                       T  E  A
                    x  H  A  D
                    L  D  T  R
                 H  R  S  A
              E  W  D  A        
              L  E  S  S  E  R


In this problem, you can easily predict value of A={5, 6}

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

                 
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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