I'm back with the solution to last week's tricky exercise!
To get us all on the same page, this was the position with White to move:
First of all, White's queen is under attack, and they have to do something about it. A couple of my students suggested 1.Qxd3??, intending 1...Rxd3 2.Rc8+ and then meeting 2...Kf7 with 3.Ne5+. White would indeed be doing well in that position. But this variation is irrelevant: Black responds to 2.Rc8+ with 2...Rd8, and then answers 3.Rxd8+ with 3...Bxd8, with a totally winning position.
Kids are very used to solving tactics, so they often attempt to treat instructive positions as if they were simple tactical exercises: "Takes, takes, bang". But real life doesn't work that way! Your opponent also has the right to exist, and will try to fight against your ideas. Anybody suggesting the sequence starting with 1.Qxd3?? is playing what the famous teacher Dan Heisman calls "hope chess" - making a move and hoping it works.
Note that every move that saves the queen from being captured has to be analyzed - they are all forcing moves, because they create the threat of capturing the bishop on g5! 1.Qf2! is incredibly strong, for a combination of tactical and positional reasons. If Black plays 1...Qxf2, 2.Nxf2 leaves Black's bishop on g5 and rook on d3 both under attack. This position deserves its own diagram.
Do you see why 2...Bh4 won't save Black? After 3.Nxd3 Bxe1, White recaptures on e1 with the knight, 4.Nxe1, preserving an extra knight. 2...Rd2 is another attempt to counterattack. But then after 3.Ne4, Black's rook and bishop are both under attack. He can try to escape with 3...Bh4, attacking the rook on e1, but then 4.g3 (note that this pawn is protected by the knight on e4) wins material thanks to the rook on d2 and bishop on h4 both being under attack.
That means that Black can't capture White's queen. In the game he retreated his bishop with 1...Be7, bringing up the following position:
Now White shows the other idea behind moving his queen to f2: The exchange of queens, 2.Qxb6 axb6, leaves White with an incredibly strong passed pawn on a6. By this point there are multiple ways to win, but I really like how Pavlo Vorontsov continued: 3.Ne5 simultaneously attacked the rook on d3 and prepared to jump to c6. After Black's rook retreated, 3...R3d6, he played 4.Nc6. This move attacked the rook on d8 and the bishop on e7, as well as preparing to help the passed pawn. Black moved 4...Re8, saving the rook and protecting the bishop, leading to this position:
It may look like Black is barely holding things together, but now the passed pawn takes another step: 5.a7. It is simply impossible to defend against White's threats. One idea is to play Nb8, blocking the rook on e8 from controlling the promotion square. Another idea is to play Nxe7+, when the rook on e8 will not be able to recapture without losing control of a8. Black tried 5...Rd7, but this undefended the pawn on e6. After 6.Rxe6 (threatening to take the bishop on e7 - note that the rook on e8 would not be able to recapture, since it has to stop the pawn from promoting) 6...Kf7, White finished things off with 7.Rxe7+ Rdxe7 8.Nxe7, and Black resigned. If he captured the knight with the rook, the pawn would promote. If he captured with the king, Re1+ followed by Rxe8 would queen the pawn.
I hope you found this instructive! It wasn't necessary to see all of this in the original position in order to find the move 1.Qf2! You just have to see that trading queens on f2 loses material for Black, which means that he has to withdraw his bishop and allow white to exchange queens on b6, thereby allowing White to create an incredibly strong passed pawn on a6. This is a simple example of the type of thinking you need to do in a real game: Integrating concrete calculation with positional ideas.