I had to hammer-hand this one -- basically eliminating everything that was impossible and doing trial and error on what was left.
First there is one possibility and one exclusion that you missed. C = 4, D = 2 is possible. G can be no larger than 7 because the largest E * F can be is 72. (Although in the final analysis neither of these facts had any bearing on the results)
I started by saying "Let A = 0, then B is 2. Then C can't be 2 or 4 (if 4, D = 2), so if C is 6, D is 3. Then I examined all of the possibilities of E*F given the constraints of neither E nor F nor the resulting GH containing 0, 2, 3, or 6 and E or F not equal to 1. For the very few possibilities I got, I listed A through F against a list of the 10 digits to see if the two remaining unused digits were adjacent (so that I and J could differ by 1).
Then I tried A=0, B=2, C=8, D=4. Then A=1, B=3, C=4, D=2 (C=2, D=1 repeats 1), and so on.
In point of fact, unless you missed including some criteria that wasn't considered, there are 4 answers.
A = 7
B = 9
C = 6
D = 3
E = 5 or 8
F = 8 or 5
G = 4
H = 0
I = 2
J = 1
A = 7
B = 9
C = 8
D = 4
E = 5 or 6
F = 6 or 5
G = 3
H = 0
I = 2
J = 1
There is probably a better way to go about this, and I'm going to chew on it for a couple of days. Write back early next week and I'll let you know if I discovered anything new. Thanks for the interesting challenge.
John
My calculator said it, I believe it, that settles it
