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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.

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  • 3
    $\begingroup$ are you expecting a unique solution? Seems like there are many possibilities... $\endgroup$ – Kate Gregory Jun 26 at 14:32
  • $\begingroup$ @KateGregory Ideally but it's not a constraint $\endgroup$ – IggyPass Jun 26 at 14:46
  • $\begingroup$ Even with the new constraints, I found 5 answers in no time. $\endgroup$ – Duck Jun 26 at 15:08
  • $\begingroup$ @Duck, the constraints is logically deduced from the equation $\endgroup$ – IggyPass Jun 26 at 16:15
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I'm not at all sure what the question is. Here's some info based on what I think is the question

There are 27 solutions. Among these,
$a,p\in\{1,...,9\},\ b\in\{0,2,4,6,8\},\ i\in\{0,...,4\}$.
Here's some code that generates the possible solutions

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  • $\begingroup$ A good puzzle is, "Alice gives Bob [this equation]. Bob does not know the answer. Alice tells Bob what A is. Bob now knows the answer." $\endgroup$ – RShields Jun 26 at 15:15

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