When one has eliminated the impossible, then whatever remains, however improbable, must be the truth.
This is what Sherlock Holmes used to say, who was a great master in retrograde chess.
You can learn more about it from a great book with retrograde puzzles:
The Chess Mysteries of Sherlock Holmes by Raymond M. Smullyan.
Highly recommended.
PS Well done, k-man

The description of game Set in Wikipedia contains the following statement:
If 26 Sets are drawn from a collection of 81 cards, the remaining 3 cards form a Set too.
Can you provide a nice and smooth proof for it?

1. The difference of two real numbers numbers always exists and is also a real number.
2. A real number cannot be "infinitesimally small".
3. Please don't answer "thanks for the explanation, but I'll stick to... "