[superprismatic]

In the following puzzle, each of the capital

letters A, B, C, D, E, F, G, H, and I stands

for a unique digit from 1 to 9. Concatenated

capital letters stand for the appropriate

contatenated digits, so, for example, if A=7

and B=3, then AB would equal 73. The powers

of x in the following polynomials are not

necessarily written in decreasing order.

If the polynomial Cx^G - AAx^D + ABx^C + AEx^B - A

is divided by Ax^A + Fx^G + Bx^B - D, the quotient

would be Ex^H - Ix^A + G and the remainder would

be BDx^E + AFx^H - HHx^A + AA. Find the values

of A, B, C, D, E, F, G, H, and I.

[Guest]

Very nice puzzle superprismatic! I solved it twice and both times I ended up eliminating all the options. I was about to write to you to verify if all the alphabets were right, but then thought I might as well give it another shot and guess what, they are all correctly placed. The solution I did was rather long and it was all about eliminating the possibilities at each step, so I wont post the complete solution but just the answer.

A 1

B 5

C 9

D 6

E 3

F 8

G 2

H 4

I 7

Start with the terms that have x⁰; you get D.G = 12A

That gives you sets of possibilities for A, D and G. Then eliminate whatever is not possible and go to next step for terms with power x¹ and so on

Keep eliminating and eventually you will narrow down to one possibile solution!

[superprismatic]

Very nice puzzle superprismatic! I solved it twice and both times I ended up eliminating all the options. I was about to write to you to verify if all the alphabets were right, but then thought I might as well give it another shot and guess what, they are all correctly placed. The solution I did was rather long and it was all about eliminating the possibilities at each step, so I wont post the complete solution but just the answer.

A 1

B 5

C 9

D 6

E 3

F 8

G 2

H 4

I 7

Nice Job! I'm glad you didn't write me to verify because it was quite difficult to make up this puzzle without mistakes. It was even harder to insure that there was only one solution!

Start with the terms that have x⁰; you get D.G = 12A

That gives you sets of possibilities for A, D and G. Then eliminate whatever is not possible and go to next step for terms with power x¹ and so on

Keep eliminating and eventually you will narrow down to one possibile solution!