Its actually a fun question to do. The answer is:
5286143709
This is how we figure it out. From equation 1 we deduce:
1. Neither D nor F is zero, F is 3 or greater than 3.D is 3 or less than 3 otherwise F will be greater than 9 which is not possible.
From equation 2:
2. B/H is an integer. H is not 1 as if H=1, B = K which is not possible. B, H and K aren't 0. K is not 1. Possible values are:
B= 6
H= 2
K= 3
B= 6
H= 3
K= 2
B= 8
H= 2
K= 4
B= 8
H= 4
K= 2
So, B=6,8; H=2,3,4; K=2,3,4
3. H can only be 2,3 or 4, so B can only be 4,6 or 8. As we determined before, B cannot be 4, so B is 6 or 8.
Maximum value of H is 4 and maximum value of D is 3, so maximum value of D X H is 12. It is also the only way in which the product can be 2 digit i.e. either H is 4 or D is 4 and the other one is 3. As we know D cannot be greater than 3, H = 4 and D = 3.Also, K = 2 and C = 1.
As H = 4, B = 8. As D =3, F = 9.
4.
Writing the equation with the values we already have:
G + 8 + E = 9 + A + 1
G + E - A = 2
One of G or E must be Zero, the other one is definitely 7 as A can only be greater than or equal to 5. As neither G, nor E can be greater than 7, A must be 5. So A = 5; Zero is either G or E. As neither G, nor E can be 6, by elimination, J = 6.
5. A X H = KE
Writing it with information we have:
5 X 4 = 2E
It is clear now that E= 0. Thus G =7 by elimination.
Now we have values for all the numbers.
A=5 ;K=2; B=8; J=6; C=1; H=4; D=3; G=7; E=0; F=9
The rest of the equations confirm our solution.
The code is:
5286143709