*Originally posted by royalchicken*

**There is a solution. **

And that is 381 654 729.

An 'easy' way to find the solution for ABC DEF GHI is to start with the middle part.

E = 5

D and F must be even

D+ E+ F is a multiple of 3

This leaves 4 possibilities (258, 456, 654, 852)

B, D, F, H are all even (2, 4, 6, 8)

? A, C, E, G and I are all odd

CD is a multiple of 4

And C is uneven, but not 5

This leaves for CD 4 possibilities (32, 72, 16, and 96)

This leaves 4 possibilities for CDEF

1654, 3258, 7258 and 9654

A + B + C is a multiple of 3

A and C are odd (not 5)

B is even

This leaves 20 possibilities for ABC (321, 381, 741, 921, 981, 123,183, 723, 783, 963, 147, 327, 387, 927, 987, 129, 189, 369, 729, and 789),

Combined this leaves 10 Possibilities for ABCDEF

(321654, 381654, 921654, 981654, 963258, 147256, 129654, 189654, 729654 and 789654)

Now you can see what is needed for G by dividing ABCDEFG by 7.

That gives 6 possibilities (3816547, 9216543, 1472569, 1296547, 7296541 and 7296548)

FGH must be divisible by 8.

That leaves 38165472

And the last number (I) must be a 9.

Happy New Year

Fjord