>Just from considering hint 5, we know that the sum of the first three digits must be 8: any other value leaves either no solution or multiple solutions. Knowing that, we can answer hints 2 and 3 any way except "no, no" and get a single solution each way.
I think this is where both our reasonings are "the other way round": With this being a Constraint Satisfaction Problem without an a priori fixed set of constraints, you're instead treating this more like an iterative deduction based problem?
Also sorry if you've already stated that elsewhere and I didn't catch that, but what exactly is your actual problem with this puzzle? I mean it clearly has a single unique solution (ie. exactly 1 set of answers that results in exactly 1 pin) which you can proof by just bruteforcing all permutations of pin numbers and answers.