An unusual mate in two in that everybody is on the board.
Yes, the position is quite illegal because only captures could have created this position, yet nothing was captured! I plucked this from Edward Winter’s “A Chess Omnibus,” a thoroughly enjoyable and interesting book. The composition is from a master, W.H. Pollack. 1.Nd6 Kf6 [1...Rxb7 2.Nbc4#; 1...f1=Q 2.Nbc4#] 2.Bd4#