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

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.]