cryptarithmetic SoLuTiOn For CrYpTs by (M.R Kartheek & Bhanu Chander)

Multiplication Problem 1

01.25.2013 · Posted in Multiplication Problem's

PROB 1

This type of problems can be solved by back-tracking technique after finding one letter (number).

Approach (Method):

The best method which I follow is from bottom to top multiplication (You can do in vice-verse), but I found it was easy.

If you see the question, start from bottom to top like D*(ABC) and E*(ABC)

It is given that E * C = C this happens only with numbers of 5 & 6 let’s see how?

Explanation:

1 * 5 = 5

3 * 5 = _5 (Actually 15 but concentrate on last digit)

7 * 5 = _5 (35) I am not using 5 * 5 because it’s already assigned to C we should not repeat.

9 * 5 = _5 (45) so, from this don’t conclude C = 5 & E= (1, 3, 7, 9).

Because there is another number with these properties Ex: – number (6)

6 * 2 = _2 (12)

6 * 4 = _4 (24)

6 * 8 = _8 (48)

From this don’t conclude E = 6 & C = (2, 4, 8).

Let, note all the possible cases and try. For Example take C = 5 and E = odd number (1, 3, 7, 9)

 A  B  C
     D  E
   F  E  C
 D  E  C  
 H  G  B  C

Now Replace C with 5 and redraw the following table.

And also place E as odd number (3, 7, 9) I didn’t write 1 here because it’s not going to be 1 Let’s take first E = 3 and fill the table.

 A  B  5
     D  3
   F  3  5
 D  3  5  
 H  G  B  5

If you see the colored portion then sum 3 + 5 = B (8) lets assign 8 to B

And redraw the table, if u put B = 8, let’s check from first

3 * 5 = 5 (carry 1)

3 * 8 = 24 + 1 = 5 (carry 2) but in the table it is showing 3 it is contradictory, then we can understand that E! = 3.

So Next I will take E = 7 and again fill the table.

 A  B  5
     D  7
   F  7  5
 D  7  5  
 H  G  B  5
 A  2  5
 D  7
 F  7  5
 D  7  5
 H  G  2  5

If you see the red color portion

Sum of 7 + 5 = 2 (carry 1) so we got B = 2.

Assign B = 2 and fill the table.

Now see the row which I highlighted and think what value we can keep for D after clear Observation we can get D = 3 satisfy the given condition and put D = 3.

 A  2  5
 3  7
 F  7  5
 3  7  5
 H  G  2  5
 1  2  5
 3  7
 8  7  5
 3  7  5
 4  6  2  5

To get 375 in second row the value of A is

A = 1 so put value of A in table

If you keep A = 1 it’s very simple

F = 8, G = 6, H = 4.

solution 1

Hope everyone can understand the solution…… Thanks for spending your valuable time to read this :-)

48 Responses to “Multiplication Problem 1”

  1. sirisantosh says:

    Got it without seeing ur solution
    A=1,B=2,C=5,D=3,E=7,F=8,G=6,H=4

  2. Pranay Das says:

    Sm people r born with Intellignce….and some keeps on figuring it out through out their life..Gud one.:)

  3. rrrrrrrrrrrrrrr says:

    please tell me a simpler way…………

  4. Ravindra says:

    I got a doubt regarding the explanation of the problem, at the beginning of the solution you considered E*C=C and you told that it would happen only with 5 &6 but what about 1*3=3,1*4=4,1*6=6,1*7=7,1*8=8,1*9=9
    can u explain why you eliminated them..
    Thank u in advance :)

  5. Ravindra says:

    HI
    In the starting of your explanation for E*C=C why you excluded the options 1*2=2,1*3=3,1*4=4,1*6=6,1*7=7,1*8=8,1*9=9..

  6. Ashfaque Ahmed says:

    A small addition i would like to make : take ABC X E = FEC and ABC X D = DEC
    now we can directly see that C has to be = 5 ..why??? because D and E both can’t be = 6 at the same time , and from this we can also that D & E lies in { 1,3,7,9 } but D & E can’t be =1 & 0 so D & E lies in { 3,7,9}. now we can proceed further….

    • yash.bhanu says:

      Yes Mr.Ashfaque Ahmed,
      what you told is exactly correct you can proceed in that way also, Every person has their own way. But we took it as simple and easily understandable by normal person who is not having any idea up-on like this problems. So we are elaborating the explanation.
      You can do it in another way in one(1) minute also by practice…
      Good Luck For the exam….

    • ravindra says:

      HI Ahmed,
      I have a doubt in the problem…why can’t we take these possibilities
      1*2=2,1*3=3,1*4=4,1*6=6,1*7=7,1*8=8,1*9=9…

  7. wow… nice.I understood such problems how to solve for the first time..Thank you!!!

  8. in choice With Choosing E=7,c=5 ..
    u said that by observing marked position,value of d=3.
    How it come.?

  9. Rashmi T says:

    now understood how to solve this problem very well….. thank u… :)

  10. plz solve this problm:
    DSP
    LIE
    —–
    SPSS
    PETA
    PODE
    —————–
    PLEADS

  11. How did u get the value of D=3 ??

  12. can u pls elaborate back tracking technique and pls provide more information about the this cryptarithmetic problems??? and i m the beginner..

  13. chandra shekhar narayan says:

    it is too easy

  14. thanks for the great site it helps me alot

  15. nice work get

  16. Please mail the detail solution

  17. $$vishal$$ says:

    I would like know to know the solution of 4*4 multiply problem

  18. Why you assumed b=(5+3)
    or b=(7+5) in above cases???????????//

  19. good explanation…

  20. is it compulsory that all digits have value among 1 to 9 which are multiplied like abc*def(a,b,c,d,e,f all are nonzero)

  21. How did you add 5+3=8(B)
    (“If you see the colored portion then sum 3 + 5 = B (8) lets assign 8 to B”)

  22. When you multiplay (C*E) with values 5 & 7 i.e 5*7=35 and carry is 3… but you are not consodering this 3 carry for next addition.. you are telling the next addition will make 7*2 = 14 with D value 3 then its going to be 17 and hence E value equals 7.. but where does the carry from 5*7 = 35.. 3 goes ???

  23. can any one tell me how will be the verbal questions?

  24. Good Explanation my friend

  25. can u solve in easier way …. wid full illustration plz…
    WPD
    *GKI
    ——
    KFPP
    GGZM-
    FGFI–
    ——
    GDWDFP

  26. harsh saini says:

    ya it is understandable but some practice is required to get pretty handy at this

  27. please suggest me some addition problems on this crypo…….i wany some websites also on this type of questions ……….send asap…….

  28. WPD
    *GKI
    ——
    KFPP
    GGZM-
    FGFI–
    ——
    GDWDFP

    its 943 *678

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