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 :-)

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