Difference between revisions of "Puzzles"

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(→‎Puzzle 4: Updated to new diagram format)
(→‎Puzzle 5: fixed wrong color (spotted by bobson))
 
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=== Puzzle 1 ===
 
=== Puzzle 1 ===
  
−
Red to play and win.
+
Red to play and win.  
  
 
<hex>R7 C7 Q1
 
<hex>R7 C7 Q1
Line 20: Line 20:
 
     Hc5 Ve5
 
     Hc5 Ve5
 
Va6</hex>
 
Va6</hex>
 +
 +
Try it on [https://hexworld.org/board/#7c1,d4:se5f3c4c5a6c3 HexWorld].
  
 
=== Puzzle 2 ===
 
=== Puzzle 2 ===
  
−
Red to play and win.
+
Red to play and win.  
  
 
<hex>R7 C7 Q1
 
<hex>R7 C7 Q1
Line 29: Line 31:
 
           Hf5
 
           Hf5
 
     Vb6</hex>
 
     Vb6</hex>
 +
 +
Try it on [https://hexworld.org/board/#7c1,c3:sb6f5 HexWorld].
  
 
=== Puzzle 3 ===
 
=== Puzzle 3 ===
Line 39: Line 43:
 
   contents="B c2 R f4"
 
   contents="B c2 R f4"
 
   />
 
   />
 +
 +
Try it on [https://hexworld.org/board/#6c1,f4c2 HexWorld].
  
 
=== Puzzle 4 ===
 
=== Puzzle 4 ===
Line 49: Line 55:
 
   />
 
   />
  
−
== Other authors ==
+
Try it on [https://hexworld.org/board/#7c1,d4:sf2e4f5f4 HexWorld].
 +
 
 +
== [[User:Demer|Eric Demer]] ==
 +
 
 +
Despite their small size, the following five 5x5 puzzles are quite difficult: ​ They come from computer brute-force search of sparse 5x5 positions via a tablebase, specifically aiming for the hardest puzzles from such positions. ​ For each of them, the player whose turn it is has exactly 1 winning move.
  
 
=== Puzzle 1 ===
 
=== Puzzle 1 ===
−
By [[John Tromp]]
 
  
 +
Red to move.
 +
 +
<hexboard size="5x5"
 +
  contents="R e4 a2 B c3 b2"
 +
  />
 +
 +
Try it on [https://hexworld.org/board/#5c1,e4c3a2b2 HexWorld].
 +
 +
=== Puzzle 2 ===
 +
 +
Blue to move.
 +
 +
<hexboard size="5x5"
 +
  contents="R d5 e1 B a2"
 +
  />
 +
 +
Try it on [https://hexworld.org/board/#5c1,d5a2e1 HexWorld].
 +
 +
=== Puzzle 3 ===
 +
 +
Blue to move.
 +
 +
<hexboard size="5x5"
 +
  contents="R a4 e3 B d1"
 +
  />
 +
 +
Try it on [https://hexworld.org/board/#5c1,a4d1e3 HexWorld].
 +
 +
=== Puzzle 4 ===
 +
 +
Red to move.
 +
 +
<hexboard size="5x5"
 +
  contents="R e5 a1 B e1 c1"
 +
  />
 +
 +
Try it on [https://hexworld.org/board/#5c1,e5e1a1c1 HexWorld].
 +
 +
=== Puzzle 5 ===
 +
 +
Red to move.
 +
 +
<hexboard size="5x5"
 +
  contents="R e2 a1 B b5 e1"
 +
  />
 +
 +
Try it on [https://hexworld.org/board/#5c1,e2b5a1e1 HexWorld].
 +
 +
 +
The next two puzzles are based on positions from games.
 +
 +
=== Puzzle 6 ===
 +
Red to play and win.
 +
 +
<hexboard size="6x6"
 +
  coords="show"
 +
  contents="R a3 b2 B d1 e1 f1"
 +
  />
 +
 +
Try it on [https://hexworld.org/board/#6c1,a6:sa3e1b2d1 HexWorld].
 +
 +
=== Puzzle 7 ===
 
Blue to play and win.
 
Blue to play and win.
  
 +
<hexboard size="7x7"
 +
  coords="show"
 +
  edges="all"
 +
  contents="R g3 g2 e5 e3 c5 b5 a2 B d7 e4 d5 c4 b4"
 +
  />
  
−
<hex> R10 C10 Q1
+
Try it on [https://hexworld.org/board/#7c1,a2:pg2c4b5b4e5d7c5d5e3e4g3 HexWorld].
−
                  Ri1
+
 
−
            Bg4 Rh4
+
=== Other ===
−
        Bf5 Rg5
+
Eric Demer also has a [[Worst_move_puzzles#Puzzle_3|worst-move puzzle]].
−
      Be6 Rf6
+
 
−
  Bd7
+
== Other authors ==
−
Rc8
+
 
−
    Rd9 </hex>
+
=== Puzzle 1 ===
 +
By [[John Tromp]]. Blue to play and win.
 +
 
 +
<hexboard size="10x10"
 +
  coords="show"
 +
  contents="R i1 h4 g5 f6 d9 c8 B g4 f5 e6 d7"
 +
  />
 +
Try it on [https://hexworld.org/board/#10c1,i1d7c8e6f6f5g5g4h4:pd9 HexWorld].
  
 
=== Puzzle 2 ===
 
=== Puzzle 2 ===
Line 74: Line 157:
 
Vb5
 
Vb5
 
</hex>
 
</hex>
 +
 +
Try it on [https://hexworld.org/board/#7c1,b2e3b5 HexWorld].
  
 
=== Puzzle 3 ===
 
=== Puzzle 3 ===
Line 83: Line 168:
 
B e2 f2 g2 h2 i2 b3 d3 d4 f4 b5 e5 d6 g8 c9 d9"
 
B e2 f2 g2 h2 i2 b3 d3 d4 f4 b5 e5 d6 g8 c9 d9"
 
   />
 
   />
 +
 +
Try it on [https://hexworld.org/board/#10c1,a3f4e7d9f5c9g4h2h4i2g3g2f3f2e3e2b4b3a4d3c5b5c4d4d5e5e6d6e4g8 HexWorld].
  
 
Source: this [[Little Golem]] forum [http://www.littlegolem.net/jsp/forum/topic2.jsp?forum=50&topic=14 thread].
 
Source: this [[Little Golem]] forum [http://www.littlegolem.net/jsp/forum/topic2.jsp?forum=50&topic=14 thread].
Line 95: Line 182:
 
B b2 g2 f3 f4 e5"
 
B b2 g2 f3 f4 e5"
 
   />
 
   />
 +
 +
Try it on [https://hexworld.org/board/#10c1,b4b2d7e5d8g2g3f3e4f4c6 HexWorld].
  
 
Source: this [[Little Golem]] forum [http://www.littlegolem.net/jsp/forum/topic2.jsp?forum=50&topic=212 thread].
 
Source: this [[Little Golem]] forum [http://www.littlegolem.net/jsp/forum/topic2.jsp?forum=50&topic=212 thread].
  
 
=== Puzzle 5 ===
 
=== Puzzle 5 ===
−
Designed by ''Arek Kulczycki''. Game where both players play very close to perfect. Move 7.b9 was the first mistake, however it was very hard to refute it.<br/>
+
By Ryan B. Hayward. Red to play and win.
−
Blue to move and win (there is just 1 winning sequence).
+
−
 
+
<hexboard size="6x6"
−
<hexboard size="11x11"
+
 
   coords="show"
 
   coords="show"
−
   contents="B 4:h2 R 1:a4 R 5:b5 R 3:c6 B 6:e7 B 2:g8 R 7:b9"
+
   contents="R a4 a6 B a5 b5"
 
   />
 
   />
 +
 +
Try it on [https://hexworld.org/board/#6c1,a4b5a6a5 HexWorld].
 +
 +
Note that this position is [[Equivalent patterns|equivalent]] to the position with the pieces at a5 and a6 removed.  This could arise in response to the [[Small_boards#Winner_depending_on_the_first_move|winning opening move a4]].
 +
 +
Source: Ryan B. Hayward, "A puzzling Hex primer" (https://webdocs.cs.ualberta.ca/~hayward/papers/puzzlingHexPrimer.pdf).
  
 
=== Puzzle 6 ===
 
=== Puzzle 6 ===
−
From Ryan B. Hayward, "A puzzling Hex primer". Red to play and win.
+
By [[User:Hexanna|Hexanna]]. Red to play and win.
  
−
<hexboard size="6x6"
+
<hexboard size="13x13"
−
  coords="show"
+
  coords="show"
−
  contents="R d1 B e1 R f1 B e2"
+
  contents="R a3 h3 g4 h5 g6 i6 c7 i7 j7 g8 k8 h9 k9 d10 i10 k11
−
  />
+
            B i2 g3 i3 d4 j4 j6 f7 g7 h7 h8 i8 i9 j9 l9 j10 k10"
 +
  />
  
 +
Try it on [https://hexworld.org/board/#13c1,a3j4d10d4g6g7h5f7i6i3g4g3h3i2c7h8j7j6i7i9k8j10k11l9i10j9h9i8g8h7k9k10 HexWorld].
 
== See also ==
 
== See also ==
  
 +
* [[Worst move puzzles]]
 
* [[Solutions to puzzles]]
 
* [[Solutions to puzzles]]
 
* [[Ladder puzzles]]
 
* [[Ladder puzzles]]

Latest revision as of 12:23, 5 January 2024

Solving puzzles is a very good way of becoming a stronger player. Solve as many as possible! And feel free to post your own puzzles here.

Piet Hein's puzzles

See article Piet Hein's puzzles

Claude Berge's puzzles

See article Claude Berge's puzzles

Bert Enderton

Puzzle 1

Red to play and win.

abcdefg1234567

Try it on HexWorld.

Puzzle 2

Red to play and win.

abcdefg1234567

Try it on HexWorld.

Puzzle 3

Red to play and win.

This is a very difficult puzzle whose complete solution is extremely complex.

abcdef123456

Try it on HexWorld.

Puzzle 4

Red to play and win.

abcdefg1234567

Try it on HexWorld.

Eric Demer

Despite their small size, the following five 5x5 puzzles are quite difficult: ​ They come from computer brute-force search of sparse 5x5 positions via a tablebase, specifically aiming for the hardest puzzles from such positions. ​ For each of them, the player whose turn it is has exactly 1 winning move.

Puzzle 1

Red to move.

abcde12345

Try it on HexWorld.

Puzzle 2

Blue to move.

abcde12345

Try it on HexWorld.

Puzzle 3

Blue to move.

abcde12345

Try it on HexWorld.

Puzzle 4

Red to move.

abcde12345

Try it on HexWorld.

Puzzle 5

Red to move.

abcde12345

Try it on HexWorld.


The next two puzzles are based on positions from games.

Puzzle 6

Red to play and win.

abcdef123456

Try it on HexWorld.

Puzzle 7

Blue to play and win.

abcdefg1234567

Try it on HexWorld.

Other

Eric Demer also has a worst-move puzzle.

Other authors

Puzzle 1

By John Tromp. Blue to play and win.

abcdefghij12345678910

Try it on HexWorld.

Puzzle 2

By lazyplayer. Blue to play and win.

abcdefg1234567

Try it on HexWorld.

Puzzle 3

By David J Bush. Taken from a game on Playsite in 2003. Red to play and win.

abcdefghij12345678910

Try it on HexWorld.

Source: this Little Golem forum thread.

Puzzle 4

Designed by Door1, helped by David J Bush. Inspired by a game on Kurnik in May 2005. Blue to play and win.

abcdefghij12345678910

Try it on HexWorld.

Source: this Little Golem forum thread.

Puzzle 5

By Ryan B. Hayward. Red to play and win.

abcdef123456

Try it on HexWorld.

Note that this position is equivalent to the position with the pieces at a5 and a6 removed. This could arise in response to the winning opening move a4.

Source: Ryan B. Hayward, "A puzzling Hex primer" (https://webdocs.cs.ualberta.ca/~hayward/papers/puzzlingHexPrimer.pdf).

Puzzle 6

By Hexanna. Red to play and win.

abcdefghijklm12345678910111213

Try it on HexWorld.

See also

Cameron Browne offers a lot of original puzzles in his book Hex Strategy Making the Right Connections

Matthew Seymour has created a website with 500 interactive Hex puzzles at http://www.mseymour.ca/hex_puzzle/hexpuzzle.html

Ryan Hayward and Bjarne Toft include several sets of puzzles in their book Hex: The Full Story, including 49 puzzles originally published in Politiken, 28 unpublished puzzles by Jens Lindhard, 99 puzzles by Henderson, and the 4 puzzles by Bert Enderton.

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