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# 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.]

For any questions about eLitmus Cryptarithmetic questions email us at [email protected]