Determine the quotient, divisor and the dividend from this incomplete division:

                 
                          
         
                  H * B
            +-----------
         A B| * G C D *
              * * I
             ---------
                F F *
                  G *
             -----------
                  A H F
                  A H F
                --------
                 

a) F must be 1, because of the 2nd subtraction
b) B must be 9, because B*B ends in 1
c) A must be less than 5, because the 2nd multiplication is a two digit product
d) Consider the 3rd multiplication
   A9 * 9 = AH1
   A*9 + 8 = A*10 + H
   8 = A + H
   
   Because A < 5, {A,H} is either {2,6} or {3,5}
   
   But H cannot be 5, because A9 * H ends in I
   
   So A = 2 and H = 6
e) First multiplication is 29 * 6 = 174
g) So, from the first subtraction, G = 8
h) So, the 2nd multiplication must be 29 * 3 = 87
i) So, the divisor is 29 and the quotient is 639, so the problem is solved.

We never needed to use C or D.

The problem could have been
                  H * B
            +-----------
         A B| * G * * *
              * * I
             ---------
                F F *
                  G *
             -----------
                  A H F
                  A H F
                --------

Posted by Steve Herman on 2024-02-08 08:49:51