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

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Also Check out:

Multiplication Cryptarithmetic Puzzle - 3

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