This is a quick and dirty walkthrough for Fourbyfouria normal and hard modes, without any explanations.

Knight stalemate:
place n/s/place k/a1/place k

Bishop stalemate, normal mode:
w/place b/se/place k/a1/place k
Bishop stalemate, hard mode:
place k/s/place b/s/place k

Knight vs. knight checkmate, west:
s/place k/nw/place n/sw/place n/s/place k
Knight vs. bishop checkmate, southwest:
s/place n/s/place k/a2/place b/s/place k
Bishop vs. bishop checkmate, north:
place b/s/place k/a2/place b/s/place k
Bishop vs. knight checkmate, northeast:
s/place k/w/place b/w/place n/s/place k.

There are several alternate solutions below. I'll go with the ones I used in my Inform sanity-test code.

Two knights checkmate, south, normal:
place n/w/place n/w/place k/a1/place k
Two bishops checkmate, east, normal:
place b/s/place b/a3/place k/a5/place k
Bishop and knight checkmate, southeast, normal:
place b/w/place k/w/place n/a5/place k

Two knights stalemate, south, hard:
place k/sw/place n/d2/place n/sw/place k
Two knights checkmate, south, hard:
w/place n/sw/place k/e3/place n/c1/place k

Two bishops stalemate, east, hard:
place b/w/place b/a1/place k/c1/place k
Two bishops checkmate, east, hard:
e/place b/a3/place k/se/place b/s/place k

Bishop and knight stalemate, southeast, hard:
a3/place n/a1/place b/e1/place k/c1/place k
Bishop and knight checkmate, southeast, hard:
place k/e/place n/sw/place b/s/place k

