Puzzles you will never solve

Hello, I would like to show you some interesting chess puzzles, however not typical like "mate in 4". Hope you'll enjoy them, if you'll be interested in them I'll post more exercises like these. So let's start.

First puzzle by unknown:

Game starts with 1.e4 and finishes in move 5, when Knight takes Rook, and gives checkmate (however it's not said which side wins). This is really hard puzzle because there is no logical way to solve it. Just blind guess, but thinking of possible ending position can help you. If you do it in less than 1 hour, you are chess puzzle expert. For some hint, read what's written in the comment to 1st diagram.

Second puzzle by unknown:

Something similar, but much easier. Game ends in move 5, when one of players mates by underpromotion of pawn into Knight. Hint - ending position will be similar to 1st exercise solution.

Third puzzle by prof. Smullyan:

This is a strange puzzle, where you must find out moves that were made before.

Unfortunately white King fallen out of board. It's Black move. Where he was? And, how did it came to this position (what were the moves before) ?

(Hey chess.com, why I can't make a diagram without King?)

Later or sooner you'll think it's impossible. Then you will be near the solution ;)

Solution:

If it's Black move, what was White's last move? It couldn't be Bishop's move, so they moved King from b3 to somewhere, maybe taking something. But if it moved from b3, was he in so strange double check from Bishop and Rook? It looks impossible, but... it was like this:

That's all. I hope you've liked these not ordinary puzzles. And I hope my English was good (I'm 13 years old and just started learning English). If there are any mistakes, please tell me. I wait for comments :D