Could someone explain the logic behind this puzzle.. I don't get it!

https://www.chess.com/puzzles/problem/1926080

I don't understand why opponent would just sack a queen ever like that...

Thanks in advance.

White has Rh3 mate and is ahead a rook and two passed pawns that are about to queen.

The point of the puzzle is avoiding a draw, so you have to choose between Kh1 and Kf1 (Kf1 is a draw).

It's a very bad puzzle since Kh1 is a natural move that most people will play without thinking, and Rh3 mate is an uncommon pattern, and the reason why Kf1 draws is not super obvious (Qa6-a1-a2 wins the rook, and since white's king has little cover and white's queen is out of play for a moment, there's a perpetual check or both sides queen).

Anyway, a better version of the puzzle would end after Kh1.

Since puzzles are mined from a database of games by a program, what the puzzle mining program is looking for is moves where only 1 move wins... as long as white wins no matter what, it will choose a move for black that has only 1 way to win, even if that move is really bad... and that's the technical reason why the queen sac happens.

Another way to put it: black's last move ..Qb6?? was awful when ..Qa1+ would have salvaged half a point. Responding with .Kh1! keeps black from getting a second bite at the cherry!

You're correct. The second move by Black is nonsensical. The situation of the game is that Black must keep checking the White King to avoid a Mate in 1 with Rh3#. So, the White Queen should have checked with Qa1+. However, many of these puzzles start with a blunder. Chess.com must have an algorithm that creates a blunder and then run a few moves to create a puzzle. However, this puzzle doesn't fit any themes except Queen Sacrifice. But this Queen Sacrifice doesn't offer any compensation. It doesn't prevent or delay checkmate. As soon as the Black Queen is taken the puzzle ends. It's assumed that White will complete the forced mate starting with Rh3#. Terrible puzzle.

I'd like to know why the White King doesn't capture the Black Bishop on move #3 in this puzzle: https://www.chess.com/puzzles/problem/1222159 ? Once again, the puzzle starts with a blunder. Every puzzle seems to start with a blunder.

Yes, but doesn't the King advance to the pawn in the same number of moves regardless of taking the Bishop or not? Also, logically you'd take the Bishop to increase your chances of surviving.

It's a 'spite check'. Black cannot avoid mate, so he gives up the Queen to delay it one move.