[VadeRetro]

While I cannot think of an example of this problem in our universe...

Three jars are brought into a vacuum chamber. One vial is full of air. The other two are empty. All are opened.

Very quickly, the gas from the one vial disperses throughout the chamber. Can you determine which vial held the gas?

Yes and no. If you really knew the position and velocity of every molecule in the chamber, you could still model it all back to its origin. The information is somehow still there.

But of course you could never really do that.

[VadeRetro]

We're making it too hard. There is a bowl with three holes in the lid through which a ball can be dropped. A ball is lying in the bottom of the bowl.

Which hole did the ball drop through? Or did someone cheat and lift the lid?