Piet Hein's puzzles

Here are presented a couple of puzzles designed by Piet Hein. Their respective solutions can be found on Solutions to Piet Hein's puzzles.

Puzzle 1
Blue to play and win.



Puzzle 2
Blue to play and win.



Puzzle 3
Blue to play and win.



Puzzle 5
Blue to play and win.



Puzzle 6
On the board of size 3 there are precisely two opening moves such that, with optimal play from both players, the board will be completely filled before the game is over. Which are the two opening moves?

Puzzle 7
Blue to play and win.

R5 C5 Ra2 Ba3 Rb3 Bc3 Rb4 Ba5