Maths Problem(7)

12345679x9
=111111111
Always remember tricky Maths
ABCDx4=DCBA
A＜3
A≠1(n4=even number)
A=2
D=8
Bx4＜10
B≠2
B=1
C=7
A+B+C+D=2+1+7+8=18

12345679 x 9
= 12345679 * (10 - 1)
=123456790
- 012345679
-----------------
= 111111111
(1000A + 100B + 10C + D) * 4 = (1000D + 100C + 10B + A)
4000A + 400B + 40C + 4D = 1000D + 100C + 10B + A
3999A + 390B = 60C + 996D
To balance the equation A cannot be too great.
If A = 1, then D must be at least 4 otherwise no matter how big C is, the equation cannot be balanced. But then odd number + even number = even number + even number is not possible.
If A = 2, then D = 8, following the balance logic above.
7998 + 390B = 60C + 7968
30 + 390B = 60C
1 + 13B = 2C
when B = 1, C = 7
when B = 2, C = 13.5 (rejected) and also > 9
So A + B + C + D = 2 + 1 + 7 + 8 = 18