I have a pawnless game with a rook, knight, and king against just a king. Can I checkmate from this position?
[FEN "8/8/8/8/1n6/8/2rk4/1K6 w - - 0 1"]
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Yes, since K+R is an easy beginner checkmate. In fact, the Knight will get in the way. The only value of the Knight will be to get White into Zugzwang quicker (easier?), which helps Black push the king to an edge.
To answer the specific question, from above, assuming Black to move:
1... Kc3 2. Ka1 Rc1#
Assuming White to move:
1. Ka1 Kc3 2. Kb1 Kb3 3. Ka1 Rc1#