Friday 16 August 2013

Multiplication Cryptarithmetic Puzzle - 3

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 * Q 6 8

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

          6 A 3 6
      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

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