We're a student who's about to be expelled over a very poor showing on a physics test; but we have fifteen minutes in the science lab while our professor goes to get the principal. Fifteen minutes alone with a time machine. I think it's pretty obvious what happens next.
The whole thing is a puzzle, requiring a bit of coordination and note-taking and careful behaviour. It's a class of IF that, taken in moderate doses, actually rather appeals to me. I also found the voice and the writing to be appropriately amusing.
I don't know if this has been fixed in updates, but it appears that there are at least two environmental details that do not "revert" when you make your first time jump. The first is the location of the test paper: if it has not on the floor when your second iteration arrives, the game ends in paradox. This kind of requires you to know what your future self is going to see when he arrives in your present, and adjust the present accordingly. Which is in itself a paradox. The second is the state of the secret compartment: if you leave it open when you make that first jump, it will be open when you arrive in the past which is totally not what you remember and therefore paradox.
If that last paragraph was a little hard to get one's head around, well, that's time travel for you.
The business with the pen -- your future self gives it to you, and later you give it to a past self -- is, as the game notes, a bit of a head-breaker. Yet, not a paradox. It feels to me as though the author had meant there to be another puzzle to obtain the pen in the first place, but ran out of time and/or energy.
It was, I think, a very neat complication that the sequence of future-self appearances is not perfectly chronological: that is, you meet the arrivals from jump #5 and #6 before you meet the arrival from the jump #4. This requires just a little bit more thinking than if all the arrivals came in the same order as departures. But there are far more jumps than really necessary for you to do everything, so that some of these jumps are really just complications, hoops to jump through. I can't help but think, "what will I have been thinking?"
Warm blueberry muffins with melting butter, and an endless supply of strong black tea.