It depends on the individual problem, some have a smaller problem space than others so unique inputs would be tricky for everyone.

But there are enough possible inputs that most people shouldn't come across anyone else with exactly the same input.

Part of the reason why AoC is so time consuming for Eric is that not only does he design the puzzles, he also generates the inputs programmatically, which he then feeds through his own solver(s) to ensure correctness. There is a team of beta testers that work for months ahead of the contest to ensure things go smoothly.

(The adventofcode subreddit has a lot more info on this.)