that was kinda easy
Improvers POTD #7 (04/19/25)
First one:why does white keep on blundering?
The queen sacrifices aren't blunders as such, it's because black has a mate in one. They're kinda like spite checks to keep the game going for a couple of moves, maybe hoping that black (somehow) messes something up

In the first one, why did white move their king away on the first check, rather than just take the rook with one of the pawns?

In the first one, why did white move their king away on the first check, rather than just take the rook with one of the pawns?
I had the same question. Went to the analysis board and learnt that capturing via hxg5 (pawn) leads to mate in 2, while Kxg5 is mate in 1. Thus, the best move is to take the king out of the check, by Kf3 or Kh3. Kf3 is mate in 3. while Kh3 is mate in 6, which for black is the best move.

On the first puzzle, I wanted to play queen sac on h2, but it said it was incorrect. It would have still lead to mate though.
Use a Sacrifice to Win Material: