The following table represents addition of two sixdigit numbers given in the first and the second rows, while the sum is given in the third row. In the representation, each of the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 has been coded with one letter among A, B, C, D, E, F, G,H, J, K, with distinct letters representing distinct digits.
Question 1:
Which digit does the letter A represent?
Question 2:
Which digit does the letter B represent?
Question 3:
Which among the digits 3, 4, 6 and 7 cannot be represented by the letter D?
Question 4:
Which among the digits 4, 6, 7 and 8 cannot be represented by the letter G?
F + F = F.
This implies that F has to be 0. Since all the digits are less than 10, the maximum sum of any two letters will be 17 (i.e. 9 + 8).
Therefore, a maximum of 1 can be carried over to the digits place on the left. In the ten thousands place, either the units digit of H + H = F or the units digit of H + H + 1 = F.
It cannot be H + H + 1 because 2H + 1 is an odd number and the units digit of that cannot be 0. From this, we can infer that the units digit of 2H must be 0.
This implies that H = 5. Sum of both the 6digit numbers is a 7digit number. This implies that the leftmost digit in the 7digit number has to be 1. Therefore. A = 1.
Since H = 5, H + H = 10. This means that B + A + 1 = AA = 10A + A. A = 1. Therefore. B = 9.
In the hundreds place the units place of the sum A + F is C. Now A = 1 and F = 0.
But C cannot be 1. Hence, C has to be A + 1, i.e. C = 2. Therefore, G + K should be greater than 10.
The units digit of the sum of G + K is 1. This implies that G and K are either 3 and 8 or 4 and 7. not necessarily in that order.
We now have the following:


9 
5 
1 
1 
G 
0 


1 
5 
J 
0 
K 
0 

1 
1 
0 
G 
2 
1 
0 
Since G is a single digit, J + 1 is less than 9.
If J = 3. G = 4 and K = 7. In that case. D and E will be 6 and 8. not necessarily in that order.
If j = 4. G = 5. which is not possible because H = 5 and each letter has a distinct number.
If J = 6. G = 7 and K = 4. In that case. D and E will be
3 and 8. not necessarily in that order.
If j = 7. G = 8 and K = 3. In that case, D and E will be
4 and 6 not necessarily in that order.
If J = 8, G = 9, which is not possible because B = 9 and each letter has a distinct number.
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