Look at the problem first!
Rewriting the problem once again,
ABCB - DEFC = GAFB
: + -
DH x AB = IEI
-------------------------
GGE + DEBB = DHDG
We have 6 equations from above -
(1) A B C B - D E F C = G A F B
(2) G G E + D E B B = D H D G
(3) G A F B - I E I = D H D G
(4) D E F C + A B = D E B B
(5) A B C B : D H = G G E
(6) D H x A B = I E I
Steps :
1. From (1), we have B - C = B. That's possible only when C = 0.
2. If C = 0 then in (1), for tens' place subtraction i.e. C - F = F the carry need to
be taken from B. And that subtraction looks like 10 - F = F. Obviously, F = 5.
3. From (3), we see D in result seems to be carry and carry never exceeds 1
even if those numbers are 999 + 9999. So, D = 1.
4. From (1), since C = 0, at hundreds' place (B - 1) - E = A and from (4),
we have F + A = B (since first 2 digit of first numberremain same in result
indicating no carry forwarded in addition of FC + AB = BB.
So placing F = B - A in (B - 1) - E = A gives, F = E + 1. Since, F = 5, then E = 4.
5. In (3), G at the thousands' place converted to D without actually subtraction
of digit from IEI. Since, G and D are different numbers some carry must have been
taken from G.
As D = 1 then G = 2.
6. From (1), A - D = G and D = 1 and G = 2 then A = 3 since if carry had been taken
from A then A = 4 which is impossible as we already have E = 4.
7. From (2), E + B = G i.e. 4 + B = 2 only possible with B = 8.
8. With that, in (2), carry forwarded to G + B = D making it
1 + G + B = 1 + 2 + 8 = 11 = 1D i.e. carry 1 forwarded to G + E = H making it
1 + G + E = H = 1 + 2 + 4 = 7.
Therefore, H = 7 and no carry forwarded as digit D in second number remains
unchanged in result.
9. Now (6) looks like - 17 x 38 = 646 = IEI = I4I. Hence, I = 6.
To sum up,
A = 3, B = 8, C = 0, D = 1, E = 2, F = 5, G = 3, H = 7 and I = 6.
Eventually, all above 6 equations after replacing digits in place of letters look -
1. 3808 - 1450 = 2358 ✅
2. 224 + 1488 = 1712 ✅
3. 2358 - 646 = 1712 ✅
4. 1450 + 38 = 1488 ✅
5. 3808 : 17 = 224 ✅
6. 17 x 38 = 646 ✅
Rewriting in the given format,
3808 - 1450 = 2358
: + -
17 x 38 = 646
-----------------------------
224 + 1488 = 1712
