A three-mover as a problem for Arbiters

The problem of this post has a postulation [White plays and mates in 3 moves].
The composer Nikita Plaksin has produced more than 50 similar works of art with retroanalysis.
See here.
The solution is published in many places of the web, but please refrain from searching for it right away.

Suppose that you observe the position of a chess game.
Someone has whispered to you that White can mate in three moves.
By simple examination you see that there is an easy mate in two moves :
first the Queen checks and then the Rook gives the final blow (let say [1. Qf1+ Kxh2 2. Rh3#] ).

1) Why can not the Queen give check in the first move, and drive the White to an easy win?
2) What will the Black ask from the Arbiter after the check by the Queen in the first move?
3) Which are the correct three moves for the solution of this problem?

	(Problem 322) Nikita Plaksin, 1st and 2nd prize, Die Schwalbe, 1971 Dedicated to Dr K. Fabel Mate in 3. #3 retro ( 15 + 14 )
[1b1K3s/2pppprp/1p4p1/1p6/b1P2B2/RP2P1R1/r1PPQPPP/SB5k]

The solution follows. If you can solve the problem without seeing the solution, send a comment stating your solution.

	(Sketch for Problem 322)
[rb5s/2pppp1p/1p4p1/1p5Q/bkP3K1/4P1R1/BPPP1PPP/SrB4R]

We start from a position (see the sketch exactly above and the source here) which can be reached from the initial placement of the pieces without special difficulty. The black Rook can go to b1, the black King can come out in the middle, the black Knight can leave from g8 allowing the other Rook to move to a8, then the black Bishop returns to b8 and the Pawn moves b7-b6, and the Knight goes to h8 and the Pawn moves g7-g6. Similarly with the white pieces, the white Rook goes from a1 to g3 and then the black Rook can reach b1, etc..
Now we show the moves from the last move of a Pawn (allowing the passage of the black King) and on :

1. b3 Ra7 2. Bb2 Rf1 3. Be5 Ka3 4. Bd6+ Kb2 5. Rg1 Kc1
6. Rh1 Kd1 7. Rg1 Ke2 8. Rh1 Rb1 9. Rg1 Rb2 10. Bb1 Ra2
11. Rh1 Ra3 12. Ba2 Ra8 13. Rb1 Ra7 14. Rb2 Kf1 15. Kf3 Kg1
16. Ke2 Kh1 17. Kf1 Ra8 18. Rb1 Ra7 19. Re1 Ra8 20. Re2 Ra7
21. Ke1 Ra8 22. Kd1 Ra7 23. Kc1 Ra8 24. Kb2 Ra7 25. Bb1 Ra2+
26. Kc3 Rb2 27. Ba2 Rb1 28. Kd3 Rf1 29. Ke4 Ra8 30. Kf4 Ra7
31. Kg5 Ra8 32. Kh6 Ra7 33. Kg7 Ra8 34. Kf8 Ra7 35. Ke8 Ra6
36. Kd8 Ra8 37. Kc8 Ba7+ 38. Kb7 Rg8 39. Re1 Rg7 40. Rb1 Rg1
41. Rb2 Rf1 42. Bb1 Re1 43. Ra2 Bb8 44. Ra3 Kg1 45. Ba2 Rb1
46. Kc8 Rb2 47. Bb1 Ra2 48. Kd8 Rb2 49. Qe2 Ra2 50. Bf4 Kh1

So, the last move of a pawn (or a capture) was the move [1. b3], at least 49.5 moves ago. Black is ready to use the 50-moves rule! (See FIDE rules, articles 5(e), 9.2).

The correct solution to the Problem-322 by Plaksin is :

Key : 1. Rxg6! (the capture interrupts the series of the 50 moves) Rg8+
2. Rxg8 Sg6
3. Qf1#