Solutions to puzzles

Piet Hein

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Claude Berge

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Bert Enderton

Puzzle 1

The unique winning first move is Red b4. (Blue can easily defend the bridges at e3/e4 and g2/g3. Red d3 is defeated by blue b5, red b5 is defeated by blue d3, and all other red moves are defeated by blue b4).

Notice that the red stone at a6 is already connected south via the ladder escape at e5. Also, red threatens to connect north via a double threat at b3 and d3; each of these would connect to the northern edge via Template IIIa. The two templates overlap at d1, but blue d1 is defeated via the following sequence of forcing moves:

Puzzle 2

A winning move is Red e3. This connects to the top edge via Template IIIa, and to the bottom edge via Template J5. The two templates overlap at one point d3, but if Blue plays there, Red can reply f3 to seal the connection up and down.

Puzzle 3

The unique winning first move is Red c3! (e2 is defeated by e3, d3 is defeated by e1, e3 is defeated by e2, and b4 is defeated by d3).

The following seem like horizontal's (Blue's) best tries from the above position.

1. d2	e2	2. d5	c5	3. d4	b3	4. c4	a5
1. d3	b3	2. b5	e3
1. e1	d2	2. d1	d1	3. c4	b3	4. e3	a5	or	4. b5	e3
........	....	2. c4	b3	3. c5	e3	4. e4	f3	5. e6	d5
1. d5	b3	2. d2	b2	3. c4	a5	4. a6	c5	5. b5	e3	6. d5	f5
........	....	........	....	3. b5	c5	4. c4	e3
........	....	........	....	3. b6	a6	4. b4	c5	5. c4	e3	6. e6	d4
1. c4	e3	2. e2	b3	3. d3	a5
1. b5	d4	2. d3	f2	3. f1	d2	4. c4	e2	5. e4	e3	6. c5	e5
........	....	2. e1	d2	3. d1	f1	4. e2	f2...
1. b4	d2	2. d5	c5	3. c4	e3	4. d4	e5

Other authors

Puzzle 1

Not posted yet...

Puzzle 2

Note that Red is connected upwards by Template J5. The only way to prevent Red from connecting downwards is to play in the cell marked *.

Therefore, the only possible move for Blue is 1.b6. Perhaps surprisingly, it is also a winning move. If Red responds as expected at 2.c5, Blue's response is to intrude Red's upward connection at 3.b4. This leaves Blue in a strong position.

If Red instead plays 2.g4, Blue can respond with 3.d5, again leaving Blue in a strong position.

,

Other possible moves by Red also have a strong response, for example 2.c6 3.c4, or 2.d4 3.d5, or 2.d5 3.c4, or 2.e4 3.e5.

Puzzle 3

Puzzle 5

part 1:

part 2:

part 3:

See Also

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