Why two IA creates problems? [closed]

IA creates lots of debates about potential problems such as overtaking humans or destroying jobs. I'm not sure about AI but since 1985 Terminator, I know that two IA ("Intelligence Artificielle) surely creates a problem :

  I A
+ I A
-----
P B


But can someone explain why ^^ ?

My attempt

Domains

• $$D(A) = D(I) = \{1,..., 9\}$$
• $$D(P) = D(B) = \{0,..., 9\}$$

Constraints

• $$10(I + I) + (A + A) = 10P + B$$

I tried to use what I believe to be backtrack research.

1. $$A= \{I = 1\} \rightarrow$$ consistant
2. $$A = \{I = 1, A = 0\} \rightarrow$$ consistant
3. $$A = \{I = 1, A = 0, P = 0\} \rightarrow$$ inconsistant
4. $$A = \{I = 1, A = 0, P = 1\} \rightarrow$$ inconsistant
5. $$A = \{I = 1, A = 0, P = 2\} \rightarrow$$ consistant
6. $$A = \{I = 1, A = 0, P = 2, B = 0\} \rightarrow$$ inconsistant
7. $$A = \{I = 1, A = 0, P = 2, B = 1\} \rightarrow$$ inconsistant
8. $$A = \{I = 1, A = 0, P = 2, B = 2\} \rightarrow$$ inconsistant
9. $$A = \{I = 1, A = 0, P = 2, B = 3\} \rightarrow$$ inconsistant car $$A+A = 0 \neq 3$$

... until we change the value from A to 2 (because I already equal to 1) so far I don't know the answer.

• are you expecting a unique solution? Seems like there are many possibilities... – Kate Gregory Jun 26 '19 at 14:32
• @KateGregory Ideally but it's not a constraint – IggyPass Jun 26 '19 at 14:46
• Even with the new constraints, I found 5 answers in no time. – Duck Jun 26 '19 at 15:08
• @Duck, the constraints is logically deduced from the equation – IggyPass Jun 26 '19 at 16:15

$$a,p\in\{1,...,9\},\ b\in\{0,2,4,6,8\},\ i\in\{0,...,4\}$$.