View source for Solutions to Piet Hein's puzzles

== Puzzles ==
=== Puzzle 1 ===
<hex>
R11 C11 Q1
Vd1 Vd2 Vd3 Vd4 Vd5 Vd6 Vd7 Vd9 Vd10 Vd11 Vh6 Vh7 Hc2 Hd8 Hh9 Hi4
H1f7 +g5 +g8
</hex>

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#General strategy guide|Strategy guide]] for details). The stone at d8 is connected to the left because of the ladder breaker at c2.

=== Puzzle 2 ===
<hex>R3 C3 Q1 Ha1 Va2 Vb3 N:on Hb2</hex>

=== Puzzle 3 ===
<hex>R6 C6 Q1 Vc3 Vf3 Vd5 Hb1 Hb5 N:on He2</hex>

=== Puzzle 4 ===
<hex>R4 C4 Q1 Vd1 Va4 Hc2 N:on Hb3</hex>
Using twice [[Edge templates with two adjacent pieces|edge template III 2b]]
=== Puzzle 5 ===
<hex>R4 C4 Q1 Va4 Ha1 N:on Hb3</hex>

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:

<hex>R4 C4 Q1 Va4 Ha1 N:on Hb3 Va3 Hb2 Va2 Hb1</hex>

Since the cells for the ladder and those for the edge template do not overlap, Red cannot do anything against the connection.

=== Puzzle 6 ===

We interpret "optimal play" to mean that the winning player tries to win in as few moves as possible, and the losing player tries to postpone the loss as long as possible.

The unique opening move for which the board will be completely filled is Red a2 (or equivalently on the other side of the board, Red c2).  It leads to the following sequence of forced moves:

<hexboard size="3x3"
   coords="show"
   contents="R 1:a2 R 3:c2 B 2:a3"
   />

At this point, Red has already won (due to the double threat at b2 and c1). To postpone the loss as long as possible, Blue should play c1, which forces Red b2, followed by 4 more moves to fill in the edge templates.

<hexboard size="3x3"
   coords="show"
   contents="B 4:c1 R 1:a2 R 5:b2 R 3:c2 B 2:a3"
   />

No other opening move fills the board completely. If Red opens at b2, they win in at most 4 more moves. If Red opens at a1 or b1, Blue plays b2 and wins in at most 4 more moves. If Red opens at c1, optimal play proceeds as follows:

<hexboard size="3x3"
   coords="show"
   contents="R 1:c1 B 2:b3 R 3:a3 B 4:b2 R 5:a2"
   />

This ends with a win for Red in at most 2 more moves. The remaining opening moves are symmetric to the ones already discussed.

=== Puzzle 7 ===
Blue's unique winning move is c2:
<hexboard size="5x5"
  contents="R a2 B a3 R b3 B c3 R b4 B a5 B 1:c2
            S area(d1,c2,c3,e3,e1)"
  />
The two blue pieces are connected to the right using [[Edge templates with two adjacent pieces|edge template III2a]]. If Red tries to block the connection to the left at b2, Blue responds as follows:
<hex>R5 C5 Q1
 Ra2
  Ba3 Rb3 Bc3
       Rb4
    Ba5 Bc2 R2b2 B3b5 R4c4 B5c5 R6e4 B7d4 R8e3 B9d3</hex>
And now Blue can connect with either e1 or e2.
If Red instead tries to intrude into Blue's template in the red-shaded area, Blue responds at c4:
<hexboard size="5x5"
  contents="R a2 B a3 R b3 B c3 R b4 B a5 B 1:c2 B 3:c4 E +:(e1,d3,d5) E *:(b2,b5)
            S red:area(d1,d3,e3,e1)"
  />
Note that Blue is now connected to the left edge by double threat "*", and to the right edge by three independent threats "+". Therefore, no matter where Red's piece is in the shaded area, Blue still has at least two ways of connecting right.

== See also ==
* Back to [[Piet Hein's puzzles]].
* Main page: [[Puzzles]].

[[category:puzzle]]