In the second puzzle, 1. g4! wins, since Black can avoid mate only by desperate measures.
@caveatcanis, sorry, but g4 gives black the opportunity to go Rcb6 and Rb7 and there is not mate at all.
Also, after 1. Rf1 g4 prevents the mate.
However, Kg3 is forced mate.
1. Kg3 g4
2. Kxg4 g5
3.Kh5 and black cannot prevent mate.
THIS ONES A GOOD ONE