# Unit Digit Method for Cryptarithmetic Problems ## 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-

• Break the problem in to subcomponents for eg -If it is a 3 x 3 Cryptarithmetic Problem, then you have to convert it into 3 x 1 problem.
• After dividing the problem in three parts, analyse all the parts very closely and try to collect some clue. Now, you have to choose one among 3 which has maximum number of clues.
• You have to start hit and trial with the possible values of  the variable which is present at the unit digit. {0,  1,  2,  3,  4,  5,  6,  7,  8,  9}

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.]
```

### One comment on “Unit Digit Method for Cryptarithmetic Problems”

• Atulya PrepInsta

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