"Crazy rook" or "how to get a draw in a losing situation"

Having no small opportunity to see how strong chess players play, I sometimes noticed absurd actions that, oddly enough, made sense. So, for example, one can say about the sacrifice of a rook with a check on the king, after which the inevitable devouring of the rook awaits. But if the piece is removed from the chessboard, a draw awaits us. Of course, it depends on the placement of the pieces and especially the king. As we know, you can't just sacrifice pieces, especially the rook without compensation. But this rook gives us this compensation. Without further ado, let's go straight to theory.

Crazy Rook Recipe:

— The king is in a stalemate.

— Only the rook can make a move.

— The rook is at a sufficient distance from the king to check.

— The rook cannot be eaten by pieces that block the king.

It so happens that there is no stalemate, but it is worth attacking the enemy king with a check in order to move the king to the cell we need after eating a piece by the king. This way you can turn the pawn of the queen with a check, I will tell you about this later.

Examples:

1. The game of streamer Yevgeny Novikov of the rank of CM, author of the "ShakhMatKanal Shakhmaty" channel. In this position, he managed to play the game for a draw, due to the opponent's mistakes, and our hero had 3 seconds on the clock, when, like the opponent, he had a minute of time. We recommend that you watch a segment of his party from the stream. Link to the full game.

2. The game between Alexander Grischuk and Sergei Karjakin ended in a draw, in the tournament for the right to own a land plot in the Moscow region. Although it seemed that Grischuk would win, taking the prize for himself and sending his grandmother to the site, Karjakin decided to take the prize for himself and plant strawberries there. In a fight, a lawn or a garden bed, the garden bed won. The fate of the match was decided by an insane rook, thereby giving Karjakin the victory in the tournament. More about the tournament

3. Party of artificial intellects, computer engines LCZero and Komodo MCTS. Note that in this position, all three pieces (bishop and 2 rooks), maddened and attacked the king, during the march, none of the black pieces survived. But they did their job 100%, thereby saving the king. In the game, the white bishop played into Black's hand. After all, he was patronizing the king. Black took advantage of this and got his desired draw. Full batch link

4. The game between Hikaru Nakamura and Boris Shevchenko ended in Black's defeat due to an impossible move, although the game should be a draw. And here you can see the rook sacrifice. I recommend that you review the analysis of the game. As I said earlier, there are crazy rooks without a king stalemate.
I will note in advance: The diagram contained the best moves, not the moves from the game.
Link to detailed game

Tasks for mastering the material:
Difficulty: easy
1.

2.

Difficulty: medium
1.

Difficulty: madness
1.

I don’t like it when my brains are boiling, so the tasks are over. Perhaps now, I can get paid for my work, subscribe to the blog, and wait for new entries, and Nurik was with you, see you soon!

Disclaimer: None of the kamikaze rooks were injured.

If you do not like the Google translator translation, correct me in the comments