possible or impossible?

I'm very impressed, Adrian! A lot of funky extra moves towards the end, but I since I didn't actual play through a game for the position, I can't really complain. :D

I'm very impressed, Adrian! A lot of funky extra moves towards the end, but I since I didn't actual play through a game for the position, I can't really complain. :D
Thanks JamieKowalski. I also did alot of wrong moves and had to redo some couple of times. But it was a brain scratcher indeed!!
~~ Adriandmen ~~

OKay, this is an anti-puzzle. White to AVOID checkmating black !!!
Three possible solutions:
1. Offer a draw.
2. If Black is stupid enough to decline the offer, let your time run out. The arbiter has to declare the game a draw, since ALL moves are forced and lead to mate for white (which means, Black has no winning chances).
3. Resign (fastest, but costliest).

how about this one
Impossible because in order for Ke7, the king would have had to travel through squares defended by pawns and of course the king can't move through check.
Please be relevant, helpful and nice