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I know you’re joking, but apparently it was given as a programming problem in a contest on at least one occasion.

Here’s another more recent case where it appeared in a coding contest: https://discuss.codechef.com/questions/133115/wrong-problem-...

It has been asked in real interviews

That’s a different (rather easier) problem: note that the safe combination can contain the same digit more than once.

The solution to this problem is given by de Bruijn sequences: https://en.wikipedia.org/wiki/De_Bruijn_sequence

Ah, I see. Thanks