COMPUTER ANORAK

Three Posts you have to check before continuing reading this:

Elitmus pH Test Pattern & Syllabus

Tips For Elitmus Test

Tips To Solve Cryptarithmetic Puzzles

The puzzle that we will be solving today looks something like this,


W H Y * N U T
--------------------
        O O N P
      O Y P Y +
  O U H A + +
--------------------
 O N E P O P


Follow the steps to solve the above puzzle:

Step 1: The term (W H Y)* U = O Y P Y, we can guess that U=6 and Y=2,4,8. Whenever there are more than one occurence of the same character in these kind of problems, Y is usually 4(No all the times though). So let us take y=4 as proceed to see if the assumption is correct.

 W H 4 * N 6 T
--------------------
        O O N P
      O 4 P 4 +
  O 6 H A + +
--------------------
 O N E P O P

Step 2: Looking at the sum term, O+6=N, and also since there is no carry from this sum to the next term, we conclude that N<=9, and as a result O could be 1/2/3. Considering O=1 as proceeding we get,

 W H 4 * N 6 T
--------------------
        1 1 N P
      1 4 P 4 +
  1 6 H A + +
--------------------
 1 N E P 1 P


Step 3: Now looking at the term N+4=1, we can easily guess that N=7, since there is no carry being carried to this term from P(which is the previous term). Rewriting with N=7 would yield,

 W H 4 * 7 6 T
--------------------
         1 1 7 P
      1 4 P 4 +
  1 6 H A + +
--------------------
 1 7 E P 1 P


Step 4: Looking at the product term (W H 4)*7, we can guess that, A=8. And since the last term in all the sum term of individual products (i.e. "1 1 7 P", "1 4 P 4", "1 6 H A") is always 1, the minimum value W can take is 2. So considering W=2, we get

  2 H 4 * 7 6 T
--------------------
         1 1 7 P
      1 4 P 4 +
  1 6 H 8 + +
--------------------
 1 7 E P 1 P

Step 5: Looking at the product term, (2 H 4)* T = 1 1 7 P, we can guess that T=5, since (2 H 4)*T = 1 1 7 P. And, further it is safe to assume P=0, since (2 H 4)*T(=5). Rewriting we get,

  2 H 4 * 7 6 5
--------------------
         1 1 7 0
      1 4 0 4 +
  1 6 H 8 + +
--------------------
 1 7 E 0 1 0

Step 6: Now, (2 H 4)*5=1 1 7 0, we find H to be 3, and hence E turns out to be 9 (1+4+3+carry_of_1=E). This gives us the solution of,

2 3 4 * 7 6 5
--------------------
         1 1 7 0
      1 4 0 4 +
  1 6 3 8 + +
--------------------
 1 7 9 0 1 0

which is the required result.


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More to come soon...


Also Check out:

Solved Questions asked in eLitmus

Three Posts you have to check before continuing reading this:

Elitmus pH Test Pattern & Syllabus

Tips For Elitmus Test

Tips To Solve Cryptarithmetic Puzzles

The puzzle that we will be solving today looks something like this,


S U J * Q M N
---------------
        M A T M
      J Q  J  J +
  U T S U +  +
---------------
 U M S T A M


Follow the steps to solve the above puzzle:

Step 1: Look at the individual product term (S U J) * M = J Q J J. If you would have gone through the previous posts, you would guess the value of M=6 and J=2 or 4 or 8. Considering J as 2 and rewriting the puzzle we get,


S U 2 * Q 6 N

---------------

          6 A T 6
      2 Q 2  2 +
  U T S U +  +
---------------
  U 6 S T A 6

Step 2: Now (S U 2) * N = 6 A T 6, hence, N=3, 8. Let us assume N=3. Looking at the sum term 2+T=6, it is safe to assume that T=3 since a carry is most probably generated. But T cannot be 3, since N is already 3. So the assumption of N=3 is wrong.
Now assume N= 8 and T=3(as explained above) and rewriting we get,


S U 2 * Q 6 8

---------------

          6 A 3 6
      2 Q 2  2 +
  U 3 S U  +  +

---------------

  U 6 S 3 A 6

Step 3: It is easy to note that A = 3+2 =5, also A+2+U = 3  i.e. 5+2+U=3, hence U=6. However, M is already 6. Hence the assumption of J=2 is not correct. Now assume J=4 as rewriting the equation we get,


S U 4 * Q 6 N

---------------

          6 A T 6
      4 Q 4  4 +
  U T S U +  +
---------------
  U 6 S T A 6

Step 4: (S U 4)*N = 6 A T 6, gives N=9. And the sum term 4+T+carry=6. Hence T=1. And T+4=A, i.e. A=5. Rewriting, we get



S U 4 * Q 6 9
---------------
           6 5 1 6
       4 Q 4 4 +
   U 1 S U + +

---------------

  U 6  S 1 5 6

Step 5: The sum term, 5+4+U=1, which gives U=2. Therefore,

 S 2 4 * Q 6 9

---------------


           6 5 1 6
       4 Q 4 4 +
    2 1 S 2 + +

---------------

    2 6 S 1 5 6

Step 6: Now, (S 2 4)*9 = 6 5 1 6, gives S=7. And 6+Q+S=S i.e. 6+Q+7=7, gives Q=3. Therefore,



 7 2 4 * 3 6 9

---------------
           6 5 1 6
       4 3 4 4 +
    2 1 7 2 + +

---------------

    2 6 7 1 5 6

is the required solution.


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Also Check out:

Multiplication Cryptarithmetic Puzzle - 4

Solved Questions asked in eLitmus

Three Posts you have to check before continuing reading this:

Elitmus pH Test Pattern & Syllabus

Tips For Elitmus Test

Tips To Solve Cryptarithmetic Puzzles

The puzzle that we will be solving today looks something like this,


G A S * F B I
---------------
         F T B I
     S S T B +
 S A S F +  +
---------------
 S R I S T I


Follow the steps to solve the above puzzle:

Step 1: Look for '0' or '1' in the Multiplier(F B I), sadly we do not find one.

Step 2: Now look at the last terms in each of the individual products of this puzzle, F T B I, S S T B and S A S F, it is clear that 'S=1' (Because, any other odd number will not give the same value when multiplied to it.) Now our cryptarithmetic problem will look something like this(I've bolded the I's just to differentiate from the 1's),

G A 1 * F B I
---------------
         F T B I
     1 1 T B +
 1 A 1 F +  +
---------------
 1 R I 1 T I


Step 3: This step is the most important step in this problem, if you recognize this, you have done a great job. In the product term, G A 1 * F - -, F*1=F and there will be no carry which is a well known fact. Now, if you look at the product (- A -) * F = 1 A 1 F, you will guess that, F * A leads to a product of 21(because there is 1 in the second term of the resulting product of the considered section of the puzzle, and of course no carry from the previous product term.). Now, it is not a Rocket Science to guess that F, A should be 3, 7 or 7, 3. Let us assume that F=3 and A=7, and proceed,

G 7 1 * 3 B I
---------------
        3 T B I
     1 1 T B +
  1 7 1 3 +  +
---------------
 1 R I 1 T I


Step 4: Now, looking at the term (G 7 1) * 3 = 1 7 1 3, we can easily make out that G=5. Hence our puzzle will look like,

5 7 1 * 3 B I
---------------
        3 T B I
     1 1 T B +
  1 7 1 3 +  +
---------------
 1 R I 1 T I

Step 5: Notice that R=8, which is pretty straightforward, since there is no carry coming through. I, will either be 5 or 6, depending on whether a carry is coming through or not. Since, A is already 5, I is 6. Hence the puzzle will look like,

5 7 1 * 3 B 6
---------------
        3 T B 6
     1 1 T B +
  1 7 1 3 +  +
---------------
 1 8 6 1 T 6

Step 6: Looking at the product term (5 7 1) * - - 6 = 3 T B 6, we find that 5 7 1 * 6 = 3 4 2 6, we can easily say that, T=4 and B=2. And hence, we have completed solving this cryptarithmetic problem.

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


Follow us on G+, Twitter. Or you chose to get updates of the new posts by entering your email in the Follow By Email field as well.

Feel free to share if you found this helpful.


Also Check out:


Multiplication Cryptarithmetic Puzzle - 3


Solved Questions asked in eLitmus

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.