cyclic refutations

Three black moves appear in three tries in pairs: one as a defence, the other as a refutation. In the solution all of them are variations with new mates.

Scheme:
1.X? a 2.A, 1…c!
1.Y? b 2.B, 1…a!
1.Z? c 2.C, 1…b!
1.K a 2.D, 1…b 2.E, 1…c 2.F

complete cyclic refutations

Three black moves appear in three tries in triples: two as a defences, the third as a refutation. In the solution all of them are variations with new mates.

Scheme:
1.X? a 2.A, 1…b 2.B, 1…c!
1.Y? a 2.C, 1…c 2.D, 1…b!
1.Z? b 2.E, 1…c 2.F, 1…a!
1.K a 2.G, 1…b 2.H, 1…c 2.I

Barnes, Barry P.
Problemnoter, 1961
1st Prize

mate in 2 moves