Giri vs. Lagrave endgame puzzle
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Rook to g1?
Hint: Both Rg1 and Rh1 result in draw (with optimal play from black). It's not that simple.
Nice puzzle! But I cheated...
The tricky part of this endgame position, and which makes it so unintuitive and difficult even for not-so-beginner players, is that the first instinct is to do something with the rook. The instinct is that the white pawn doesn't matter, just use the rook to capture the two black pawns, and then it's just a completely trivial KR vs K checkmate pattern. The tricky part here is that if you start going after the pawns with the rook, with perfect play from black it will be draw, and this is extremely hard to see.
The real solution, which is quite awesome, and really hard to see, is that you need to walk with the king all the way from c8 to the lower right corner in order to help capturing the pawns. It doesn't look like it, but the white king can get there in time.
(The crucial detail that makes this possible is that the black king cannot move, or else the white pawn will just advance towards promotion and will be unstoppable.)
What makes this even more awesome is that it happened in a real GM level tournament, and it's not just an artificially created position. In the actual game, after Giri moved Kc7, Lagrave resigned, being able to read ahead that far and seeing that there's no way to promote either black pawn because the white king will reach them in time.
The final (well, almost final) position in a recent Anish Giri vs. Maxime Vachier Lagrave game makes a nice little beginner/medium level endgame puzzle. Not so much a "mate in x moves", but merely "white to play and win" (the exact number of moves isn't all that important).
These types of endgame can be quite tricky for beginners (and even not-so-beginners) and they are very easy to misplay.
So, white to play and win the game (with best possible play by black).