Friday 19 July 2013

Multiplication Cryptarithmetic Puzzle - 1

Three Posts you have to check before continuing reading this:

Elitmus pH Test Pattern & Syllabus

Tips For Elitmus Test

Tips To Solve Cryptarithmetic Puzzles

Cryptarithmetic puzzles/problems are as sure as death in Elitmus pH test, and will fetch you around 30-40 marks if you get them right. Most of the people do not solve this or try to solve them and end up wasting their precious time. But hey, do not worry I will let you know how to effectively solve these kind of puzzles.

These problems are accompanied by 3 to 4 questions, so even if you take 20 minutes to successfully solve these kind of problems, I will assure you, you have done a great job. Because getting around 8-9 right in this section i.e. the Reasoning  section, will easily fetch you 85+ percentile in the pH test.

Before continuing with this post make sure you have read the previous post on Cryptarithmetic Puzzles, in which you would find some invaluable tips in how to begin solving these kind of puzzles.

So this was the puzzle asked when I took the test:

E Y E * M A T
--------------
         S Y I A
    G M T A +
 A I R Y +  +
--------------
 A A S M A A

Follow the steps to solve the above puzzle:

Step 1: Look for '0' or '1' in the Multiplier(M A T), sadly we do not find one.

Step 2: Now, look at the product term of E Y E * - A - = G M T A. If you have gone through the previous post, you will guess that 'E' is either 1 or 6. Since it is not 1, it should be 6. And 'A' should be an even number and hence it should be 2,4,8. Considering 'A' as 2 and rewriting the multiplication we get,

6 Y 6 * M 2 T
--------------
        S Y I 2
    G M T 2 +
  2 I R Y  + +
--------------
 2 2 S M 2 2


Step 3: Now looking at the sum in the 2nd column form the right i.e.  'I + 2 = 2', we can conclude that 'I' = 0, since there is no carry. Rewriting it would yield us,

6 Y 6 * M 2 T
--------------
        S Y 0 2
    G M T 2 +
  2 0 R Y + +
--------------
2 2 S M 2 2


Step 4: Further, looking at the sum in the 2nd column form the left i.e. 'G + 0 = 2', we can conclude that 'G' is either 1 or 0, since we already have 'I' = 0, 'G' has to be 1. Rewriting it we would have,

6 Y 6 * M 2 T
--------------
        S Y 0 2
    1 M T 2 +
 2 0 R Y + +
--------------
 2 2 S M 2 2


Step 5: Now looking at the product 6 Y 6 * M = 2 0 R Y, we can conclude that 'M' = 3. since (6 * M + carry) = 20, and the only value that seems to satisfy that equation is 3. Rewriting this would yield us,

6 Y 6 * 3 2 T
--------------
        S Y 0 2
      1 3 T 2 +
  2 0 R Y + +
--------------
 2 2 S 3 2 2

Step 6: If we look at the product term 6 Y 6 * 3 = 2 0 R Y, we can easily figure out 'Y' to be 8, so rewriting the puzzle would give us,


6 8 6 * 3 2 T
--------------
        S 8 0 2
     1 3 T 2 +
  2 0 R 8 + +
--------------
 2 2 S 3 2 2


Step 7: Now, the sum term 8 + T + 8 = 3 helps us to find out the value of 'T', yeah it is 7. How? Well there is no carry and the sum has to be 23, since no number is greater than 9 (You could aslo find out the value of 'T' from the product 686*2 as well.) We will get

6 8 6 * 3 2 7
--------------
        S 8 0 2
     1 3 7 2 +
 2 0 R 8 + +
--------------
 2 2 S 3 2 2


Step 8: This step is just a formality, since we got to know the values of the Multiplicand and the multiplier, it is a piece of cake to find out the rest of the values. And they happen to be,

6 8 6 * 3 2 7
--------------
        4 8 0 2
     1 3 7 2 +
  2 0 5 8 + +
--------------
 2 2 4 3 2 2

This is it. I know these are too many steps, but yeah practice makes man perfect, so do practice and become a pro in solving such kind of puzzles.



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Check out:

Multiplication Cryptarithmetic Puzzle - 2


Also Check out:

Solved Questions asked in eLitmus

7 comments:

  1. Thanks... please post some more examples soon, i have my exam on 4th!

    ReplyDelete
    Replies
    1. sure buddy we will..if you have a question post it we will solve it or wait for some days we wiil be adding some more posts :)

      Delete
  2. P X B
    W Y A
    ___________
    O A Z O
    O N X W
    O X N P
    ______________
    O A N Z N O

    solution for this question will be of great help.

    ReplyDelete
    Replies
    1. Hello zen mano,
      the question does not seem to be correct. Check the question n get back with the correct version, we will definitely solve it...

      Delete
    2. i also thought so.
      but according to 2 sources it was the same question

      Delete
    3. well, the thing with these kind of questions is, even if you forget a single word of shuffle a single line, it turns out something different..

      Delete
  3. puzzle 1
    step 2
    y did u take only 1 and 6 into consideration..y not 5 coz
    oddno*5=_5

    ReplyDelete