White to move and win
I've solved it: Qxa7+ Kxc6; Na5+ Kb5(the only move); a4#
You are right. Try to find one more variation.
or
1. Qxa7+ Kb52. a4 Kc43. Qa6#
The black king doesn't move to 2...Kxc6 because there is no way to live.


At last, you got it!!! c4+ is a quite hard to think.
But. only first solution of your 2 solutions is right.
1. Qxa7+ Kb5 2. c4+! Kxc4 3. Qa6#.
The white move 3. Na5# in your second solution is not a checkmate
because the black king can move to Kd3 to avoid checkmate.
Don't forget that the white pawn at c2 has been already caught.
Thank you for participating in this puzzle.