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Cryptarithmetic Problem-3

Ayush Agarwal | 08:17 | 2 comments

Multiplication

            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 1Look 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 and S A SF, 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, ifyou 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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2 comments:

  1. In first step why s can't be 6 and FBI all even? How we can correctly guess s as 1?

    ReplyDelete
    Replies
    1. yes siva..i have also tried using 6. but cant sole..
      its difficult to pedict.

      Delete