Problem solved!

Solution to puzzle 1

You don't really need help with this one, surely?! Oh well . . .
1. d4 b5
2. d5 b4
3. axb4 a3
4. b5 a2
5. b6 a1=Q
6. b7 mate!

Source:
Fox, M. & James, R. (1993) The Even More Complete Chess Addict. London: Faber & Faber.