#1

White to play and mate in two.
Solution

#2

White to play and mate in two.
Solution

#3

White to play and mate in two.
Solution

#4

White to play and selfmate in two. White has to force black to checkmate on the second move, while black aims to avoid doing so! White move, black move, white move, black mates.
Solution

#5

Oops! Someone has pointed out to me that this is an illegal position. It is not possible for a Bishop to get to B8 with black pawns on A7 and C7. The intellectual challenge is not affected but it is generally agreed that chess problems should begin from legal positions. Sorry.

White to play and mate in three.
Solution

#6

White to play and mate in three.
Solution

#7

Black to play and helpmate in three. Black plays and co-operates with white so that white mates on the third move. Moves: black, white, black, white, black, white mates.
Solution

#8

White to play and mate in two.
Solution