Solutions to Piet Hein's puzzles
No matter what Red does, Blue can connect via either g5 or g8. Both blue stones at the right are connected to the right (see the Strategy guide for details). The stone at d8 is connected to the left because of the ladder breaker at c2.
Using twice edge template III 2b
Blue 1 is connected to the right via Template IIIa and threatens to connect directly to the left. The only possibility to prevent this connection is to play out the ladder:
Since the cells for the ladder and those for the edge template do not overlap, Red cannot do anything against the connection.
Not posted yet...
The two blue pieces are connected to the right using edge template III2a. Red must block the connection to the left at B2
And now blue can connect with either E2 or E1. Had red played 4. E3 blue could respond with D4 with a similar outcome. Had red played 2. D3 to block the future ladder, blue could respond with 3. C4, keeping the connection to the right and connecting to the left in two different ways (via B2 and B5).