How do you respond when students submit the wrong assignment, but you only notice after the deadline has passed? I occasionally get students who submit their assignments, but I only notice that they've submitted the wrong assignment when I begin grading. I can think of three possibilities to explain this:

They made an honest mistake
They are trying to buy some time to submit their assignment by making it seem like an honest mistake
They didn't do the assignment at all and are trying to get some kind of credit

Sometimes I allow students a few hours or 24 hours to resubmit the correct assignment (is 24 hours too long?). If they don't, then I usually assume they haven't actually completed it. Other times, I'm just tempted to give them a zero.
The student in question submitted an assignment that was submitted previously in the semester.
Is there a better way that you know of to confirm whether they're being honest or not?
By the way, I'm looking for a general answer that can apply across multiple situations. In this specific situation, due to many different factors, I decided to allow the student to resubmit. She resubmitted right away, which seems to demonstrate it was an honest mistake.
The fact that you're left guessing at unknowable motivations suggests a deeper problem to me.  I always found guessing games like this very frustrating when assignments are due; giving students the benefit of the doubt sounds harmless... unless you're a student who scrambled to meet the deadline, while your peers took advantage of the professor's good will.  This is especially true if the class is curved.
The policy I use now leaves my opinions completely out of it:

Give clear due dates and turn-in proceedures
Give students a &quot;budget&quot; for late assignments.  I like to give three 12-hour tokens they can use at their discretion, no questions asked.  If they turn something in late, I automatically use whatever tokens they have left to cover the time.
Anything beyond that requires an issue serious enough that we're probably involving academic affairs as well.  Things like serious illnesses and hospitalizations, for example.
Anything turned not turned in on time, or within the scope of one of their &quot;late tokens&quot;, gets a daily penalty added onto the score.

That way you're never faced with trying to ascribe motivations to what students are doing, and the rules are laid out clearly for them, which I find students like.