doesn't just bringing king back to e4 and getting in front of the pawns draw in the second puzzle?
Pawn Endgame Study 2

doesn't just bringing king back to e4 and getting in front of the pawns draw in the second puzzle?
Kc6 Kd8 Kd5 Kxd7 Ke4 Kd6 and the king heads to e5 with zugzwang ideas

nice
yeah i thought that study was a pretty cool because the stalemating idea was very nice

yeh i recognized it, i would have never found it unless i have a board to analize with but i was lucky to remember it

More dvoretsky nice
Nah this is from one of the calculation books Im reading, 1234 Endgame Studies
i found kc6, kd8 kd5 which is correct, i didn't calculate whole line though. i think the idea is that if black king ever steps to f6 white king steps to g4 right away and wins pawn.
The idea is actually a stalemating idea