Question

Calculate the Product of the DigitsAyush uses different letters to represent different digits. He writes a number N as follows:- A, BCC, CCC, CCC. Ayush notes that the successor of N can be written as follows:- A, DDD, DDD, DDD. He also notes that the sum of the digits of N is 82. Can you calculate the product of the digits at the following places in N: hundred crores, hundred millions, ten millions and millions?

Answer 1

Is there some mistake in the given problem?

   A, B C C, C C C, C C C  
+                                     1
= A, X D D, D D D, D D D

Here  X cannot be B or D..  Perhaps it is A? or C ?  Surely C = 9  and D = 0. That is the only way we have carry  =1.

   A B99  999 999
+                        1
= A X00 000 000

X = B+1

(1) If X = A, then  B = A-1.
      sum of digits of N : 8*9 = 72   so   A+B= 10
       B cannot be 0.
       If B = 1,  X =2 and A = 9;
          B=2, X =3., A = 8
          B=3, X =4..  A = 7
            :
         if  B = 7,  X = 8 ,  A = 3
         if  B = 8, X = 9 = C,    A = 2

So N = A B 9 9,9 99,999

Answer :  A * B * 9 * 9  = 81 * A * B
    If X = 9 = C then:   Answer = 1,296
    if    = 8,                               = 1,701
          = 7                                = 1,944
          :
             2                  answer  = 729