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(Puzzle 5)
(Puzzle 4: Additional explanation - perhaps this could be generalised?)
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== Bert Enderton ==
 
== Bert Enderton ==
 
=== Puzzle 1 ===
 
=== Puzzle 1 ===
Not posted yet...
+
 
 +
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).
 +
 
 +
<hex>R7 C7 Q1
 +
  Sd1
 +
    Sb3 Hc3 Sd3 Hf3
 +
    V1b4 Vc4 Hd4
 +
      Hc5 Ve5
 +
Va6</hex>
 +
 
 +
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:
 +
 
 +
<hex>R7 C7 Q1
 +
  H2d1
 +
  H4b2 V7c2 V5e2
 +
    V3b3 Hc3 H6d3 Hf3
 +
    V1b4 Vc4 Hd4
 +
      Hc5 Ve5
 +
Va6</hex>
 +
 
 
=== Puzzle 2 ===
 
=== Puzzle 2 ===
Not posted yet...
+
 
 +
A winning move is Red e3. This connects to the top edge via [[Template IIIa]], and to the bottom edge via [[Edge template J5|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.
 +
 
 +
<hexboard size="7x7"
 +
  coords="show"
 +
  contents="B c3 E *:d3 R 1:e3 B f5 R b6"
 +
  />
 +
 
 
=== Puzzle 3 ===
 
=== Puzzle 3 ===
  
Line 40: Line 67:
 
| 1. b4 || d2 || 2. d5 || c5 || 3. c4 || e3 || 4. d4 || e5
 
| 1. b4 || d2 || 2. d5 || c5 || 3. c4 || e3 || 4. d4 || e5
 
|}
 
|}
 +
 +
=== Puzzle 4 ===
 +
 +
<hexboard size="7x7"
 +
  contents="B f4 e4 d4 R f5 f2 1:c4"
 +
  />
 +
 +
Red 1. c4 is the only way to prevent Blue from connecting immediately by b5, c3 or c4. Red threatens to connect c4 to the top and bottom edges with assistance from the [[ladder escape]]s at f2 and f5.
 +
 +
Blue 2. c5 is met by Red 3. a6, which connects to the bottom edge with assistance from the ladder escape at f5 and threatens to connect to c4 or [[climbing|climb]] to  a4 and then connect to the top edge with assistance from the ladder escape at f2.
 +
 +
Blue may attempt a [[ladder escape fork]] by playing in the [[edge template]] between c4 and the top edge, but 2. c3 is met by 3. b4 and 2. c2 is met by 3. b3, which maintain the connection to the top edge and block Blue's ladder escape.
  
 
== Other authors ==
 
== Other authors ==
Line 47: Line 86:
  
 
=== Puzzle 2 ===
 
=== Puzzle 2 ===
Not posted yet...
+
Note that Red is connected upwards by [[Edge_template_J5|Template J5]]. The only way to prevent Red from connecting downwards is to play in the cell marked *.
 +
<hexboard size="7x7"
 +
  coords="show"
 +
  contents="R b2 B e3 R b5 E *:b6"
 +
  />
 +
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.
 +
<hexboard size="7x7"
 +
  coords="show"
 +
  contents="R b2 B e3 R b5 B 1:b6 R 2:c5 B 3:b4"
 +
  />
 +
If Red instead plays 2.g4, Blue can respond with 3.d5, again leaving Blue in a strong position.
 +
<hexboard size="7x7"
 +
  coords="show"
 +
  contents="R b2 B e3 R b5 B 1:b6 R 2:g4 B 3:d5"
 +
  />,
 +
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 5 ===
+
=== Puzzle 3 ===
  
 +
<hexboard size="10x10"
 +
  coords="show"
 +
  contents="R a3 e3 f3 g3 a4 b4 c4 e4 g4 h4 c5 d5 f5 e6 e7
 +
B e2 f2 g2 h2 i2 b3 d3 d4 f4 b5 e5 d6 g8 c9 d9
 +
R 1:e9 3:f8 5:g7 7:i5 9:j6
 +
B 2:e8 4:f7 6:g6 8:h6"
 +
  />
 +
 +
=== Puzzle 4 ===
 +
 +
<hexboard size="10x10"
 +
  coords="show"
 +
  contents="
 +
R g3 b4 e4 c6 d7 d8
 +
B b2 g2 f3 f4 e5
 +
B 1:c4
 +
E *:line(g4,h4,j2,j3)
 +
"
 +
  />
 +
 +
Blue 1. c4 threatens to connect to the left edge by b5 or c3  and to the group of 4 Blue pieces by d5, d4 or e3. If Red replies in the region a2-c2-c4-a6, other than at c3 to threaten c4's connection to the left edge, then Blue 3. c3 connects to the left edge, and to the group of 4 pieces via e2 or d5.  The only reply outside the region a2-c2-c4-a6 that prevents the group of 4 Blue pieces connecting immediately to the left edge by d5, d4 or e3 is Red 2. d4. However, Red 2. d4 and 2. c3 can be answered by 3. e2.
 +
 +
Blue also threatens to connect the group of 4 pieces to the right edge by 3. g5, connecting via [[Edge template IV1d]] and by the [[ladder escape fork]] 3. i1 4. j1 5. i3 6. i2 7. g4.  Red can only meet both these threats by playing in overlap of these templates, in the marked cells.  However these replies can be met by:
 +
 +
2. i3 3. i2 4. h2 5. g4 6. h3 7. h5
 +
 +
2. j3 3. i2 4. h2 5. g4 6. h3 7. h4 8. i3 9. i5
 +
 +
2. g4 3. i1 4. j1 5. i2 6. j2 7. i3 8. j3 9. i5 10. i4 11. h5 12. h4 13. f6
 +
 +
2. h4 then either 3. g4 threatening 5. i2 and 5. g6 - or simply 3. i2 4. h2 5. g4 6. h3 7. g6 - forming a [[crescent]] and connecting with the assistance of the second row [[ladder escape]] at i2
 +
 +
2. j2 3. h2 4. i2 ([[Dominated_cell#Capture-domination|capture-dominates]] the alternatives i1 & j1) 5. h5 - a double [[Ziggurat]] connection
 +
 +
[Note that although we used [[Edge template IV1d]] from g5 in the above explanation to minimise the overlap and the resulting case analysis, we don't need the whole template or the method of connection used for that.  If however we use the smaller and simpler [[Edge template IV1a]] from g5, then the overlap with the ladder escape fork template is larger and we need to consider the additional replies h3, i2 and j1 (although j1 is [[Dominated_cell#Capture-domination|capture-dominated]] by i2, so any winning variations against i2 also work against j1).  Although 3. g5, connecting via Edge template IV1d, works against all these replies, there are simpler and quicker responses, e.g.: 2. h3 3. i4; 2. i2 3. h3 4. i3 5. h5 or 4.j3 5. i5; 2. j1 3. i3.  So the analysis above only demonstrates that Blue is connected, rather than showing the smallest connection template or the quickest or simplest method of connection.]
 +
 +
=== Puzzle 5 ===
 +
part 1:
 
<hexboard size="11x11"
 
<hexboard size="11x11"
   coords="hide"
+
   coords="show"
 
   contents="B h2 R a4 R b5 R c6 B 3:d7 B e7 R 4:b8 B g8 R b9 R 2:c9 R 8:e9 R 10:f9 B 1:b10 R 6:c10 B 9:e10 B 7:b11 B 5:c11"
 
   contents="B h2 R a4 R b5 R c6 B 3:d7 B e7 R 4:b8 B g8 R b9 R 2:c9 R 8:e9 R 10:f9 B 1:b10 R 6:c10 B 9:e10 B 7:b11 B 5:c11"
 
   />
 
   />
 +
part 2:
 
<hexboard size="11x11"
 
<hexboard size="11x11"
   coords="hide"
+
   coords="show"
 
   contents="B h2 R a4 R b5 R c6 R 10:j6 B d7 B e7 B 9:i7 R 6:j7 R b8 B g8 B 7:i8 R 8:j8 R b9 R c9 R e9 R f9 R 2:g9 B 5:h9 R 4:i9 B b10 R c10 B e10 B 1:f10 B 3:g10 B b11 B c11"
 
   contents="B h2 R a4 R b5 R c6 R 10:j6 B d7 B e7 B 9:i7 R 6:j7 R b8 B g8 B 7:i8 R 8:j8 R b9 R c9 R e9 R f9 R 2:g9 B 5:h9 R 4:i9 B b10 R c10 B e10 B 1:f10 B 3:g10 B b11 B c11"
 
   />
 
   />
 +
part 3:
 
<hexboard size="11x11"
 
<hexboard size="11x11"
   coords="hide"
+
   coords="show"
 
   contents="B h2 R 2:j2 R a4 R b5 B 1:g5 R c6 R j6 B d7 B e7 B 3:f7 B i7 R j7 R b8 B g8 B i8 R j8 R b9 R c9 R e9 R f9 R g9 B h9 R i9 B b10 R c10 B e10 B f10 B g10 B b11 B c11"
 
   contents="B h2 R 2:j2 R a4 R b5 B 1:g5 R c6 R j6 B d7 B e7 B 3:f7 B i7 R j7 R b8 B g8 B i8 R j8 R b9 R c9 R e9 R f9 R g9 B h9 R i9 B b10 R c10 B e10 B f10 B g10 B b11 B c11"
 
   />
 
   />

Revision as of 11:35, 19 February 2021

Piet Hein

See Solutions to Piet Hein's puzzles

Claude Berge

See Solutions to Claude Berge's puzzles

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).

abcdefg12345671

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:

abcdefg12345672475361

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.

abcdefg12345671

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).

abcdef1234561

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

Puzzle 4

abcdefg12345671

Red 1. c4 is the only way to prevent Blue from connecting immediately by b5, c3 or c4. Red threatens to connect c4 to the top and bottom edges with assistance from the ladder escapes at f2 and f5.

Blue 2. c5 is met by Red 3. a6, which connects to the bottom edge with assistance from the ladder escape at f5 and threatens to connect to c4 or climb to a4 and then connect to the top edge with assistance from the ladder escape at f2.

Blue may attempt a ladder escape fork by playing in the edge template between c4 and the top edge, but 2. c3 is met by 3. b4 and 2. c2 is met by 3. b3, which maintain the connection to the top edge and block Blue's ladder escape.

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 *.

abcdefg1234567

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.

abcdefg1234567321

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

abcdefg1234567231
,

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

abcdefghij12345678910768945231

Puzzle 4

abcdefghij123456789101

Blue 1. c4 threatens to connect to the left edge by b5 or c3 and to the group of 4 Blue pieces by d5, d4 or e3. If Red replies in the region a2-c2-c4-a6, other than at c3 to threaten c4's connection to the left edge, then Blue 3. c3 connects to the left edge, and to the group of 4 pieces via e2 or d5. The only reply outside the region a2-c2-c4-a6 that prevents the group of 4 Blue pieces connecting immediately to the left edge by d5, d4 or e3 is Red 2. d4. However, Red 2. d4 and 2. c3 can be answered by 3. e2.

Blue also threatens to connect the group of 4 pieces to the right edge by 3. g5, connecting via Edge template IV1d and by the ladder escape fork 3. i1 4. j1 5. i3 6. i2 7. g4. Red can only meet both these threats by playing in overlap of these templates, in the marked cells. However these replies can be met by:

2. i3 3. i2 4. h2 5. g4 6. h3 7. h5

2. j3 3. i2 4. h2 5. g4 6. h3 7. h4 8. i3 9. i5

2. g4 3. i1 4. j1 5. i2 6. j2 7. i3 8. j3 9. i5 10. i4 11. h5 12. h4 13. f6

2. h4 then either 3. g4 threatening 5. i2 and 5. g6 - or simply 3. i2 4. h2 5. g4 6. h3 7. g6 - forming a crescent and connecting with the assistance of the second row ladder escape at i2

2. j2 3. h2 4. i2 (capture-dominates the alternatives i1 & j1) 5. h5 - a double Ziggurat connection

[Note that although we used Edge template IV1d from g5 in the above explanation to minimise the overlap and the resulting case analysis, we don't need the whole template or the method of connection used for that. If however we use the smaller and simpler Edge template IV1a from g5, then the overlap with the ladder escape fork template is larger and we need to consider the additional replies h3, i2 and j1 (although j1 is capture-dominated by i2, so any winning variations against i2 also work against j1). Although 3. g5, connecting via Edge template IV1d, works against all these replies, there are simpler and quicker responses, e.g.: 2. h3 3. i4; 2. i2 3. h3 4. i3 5. h5 or 4.j3 5. i5; 2. j1 3. i3. So the analysis above only demonstrates that Blue is connected, rather than showing the smallest connection template or the quickest or simplest method of connection.]

Puzzle 5

part 1:

abcdefghijk123456789101134281016975

part 2:

abcdefghijk123456789101110967825413

part 3:

abcdefghijk1234567891011213

See Also

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