Here are a few unusual chess problems:- answers at the bottom of the page.

 

1:This is White to move an mate in 6 moves, it has an easy answer even though it may seem difficult to mate in 6.
2:How does White win with only a King and pawn against the World? Mate in 2 for White.
3:the ten king problem, how does White mate all ten Kings at once? in 1 move?

1 just make the only available moves for both sides ie 1 d4 b5 2 d5 b4 3 axb4 a3 4 b5 a2 5 b6 a1=Q 6 a7#.

2 underpremote to a Knight ie 1 d8=N d1=Q 2 Nf7#.

3 1 Ne5 delivers the coup-de-gras .