Difference between revisions of "Ladder creation template"

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(Added a page on ladder generation templates.)
 
(→‎Ladder creation templates on the 6th row: Added a new template)
 
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A '''ladder generation template''' is a kind of edge template that guarantees that the owner of the template can either connect to the edge or, failing that, get a specified ladder or ladders.
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A '''ladder creation template''' is a kind of edge template that guarantees that the owner of the template can either connect to the edge or, failing that, get a specified ladder or ladders.
  
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There is not yet a [[naming of templates|naming convention]] for ladder generation templates, so all examples on this page are currently unnamed. Like edge templates, we classify ladder generation templates by the row on which the connecting stone is located, rather than by the kind of ladder it generates. In fact, some templates generate more than one ladder, for example a 4th row ladder going left or a 3rd row ladder going right. In an attempt to avoid confusion, we say "ladder generation template on the 3rd row", rather than "3rd row ladder generation template", to indicate that the template is a 3rd row template (but may, for example, generate a 2nd row ladder).
+
There is not yet a [[naming of templates|naming convention]] for ladder creation templates, so all examples on this page are currently unnamed. Like edge templates, we classify ladder creation templates by the row on which the connecting stone is located, rather than by the kind of ladder it generates. In fact, some templates generate more than one ladder, for example a 4th row ladder going left or a 3rd row ladder going right. In an attempt to avoid confusion, we say "ladder creation template on the 3rd row", rather than "3rd row ladder creation template", to indicate that the template is a 3rd row template (but may, for example, generate a 2nd row ladder).
  
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On [http://www.drking.org.uk/hexagons/hex/templates.html David King's Hex template page], ladder generation templates are called "cascading templates". However, they should not be confused with what [http://www.mseymour.ca/hex_book/hexstrat.html Matthew Seymour's book] calls "cascading ladders", which is a different concept.
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On [http://www.drking.org.uk/hexagons/hex/templates.html David King's Hex template page], ladder creation templates are called "cascading templates". However, they should not be confused with what [http://www.mseymour.ca/hex_book/hexstrat.html Matthew Seymour's book] calls "cascading ladders", which is a different concept.
  
 
== Examples ==
 
== Examples ==
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When checking the templates, keep in mind that the templates do not in general guarantee that Red will get the indicated ladder. They only guarantee that Red will get at least the indicated ladder (or a better one) if Red doesn't connect to the edge outright.
 
When checking the templates, keep in mind that the templates do not in general guarantee that Red will get the indicated ladder. They only guarantee that Red will get at least the indicated ladder (or a better one) if Red doesn't connect to the edge outright.
  
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=== Ladder generation templates on the 2nd row ===
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=== Ladder creation templates on the 2nd row ===
  
 
<hexboard size="2x2"
 
<hexboard size="2x2"
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   />
 
   />
  
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=== Ladder generation templates on the 3rd row ===
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=== Ladder creation templates on the 3rd row ===
  
 
<hexboard size="3x3"
 
<hexboard size="3x3"
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   />
 
   />
  
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=== Ladder generation templates on the 4th row ===
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<hexboard size="3x5"
 +
  coords="none"
 +
  edges="bottom"
 +
  visible="-a1 a2 b1 e1"
 +
  contents="R c1 S grey:d3 S red:(e2 e3) E →:(e2 e3)"
 +
  />
 +
 
 +
=== Ladder creation templates on the 4th row ===
  
 
<hexboard size="4x4"
 
<hexboard size="4x4"
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   />
 
   />
  
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=== Ladder generation templates on the 5th row ===
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<hexboard size="4x4"
 +
  coords="none"
 +
  edges="bottom"
 +
  visible="-a1"
 +
  contents="R b1 S red:(d1 d2 d3 d4) E →:(d1 d2 d3 d4)"
 +
  />
 +
 
 +
=== Ladder creation templates on the 5th row ===
  
 
<hexboard size="5x6"
 
<hexboard size="5x6"
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   contents="R ↑:e1 e3 S red:(e4--e5) red:(c3--a5) E →:(e4--e5) ←:(c3--a5)"
 
   contents="R ↑:e1 e3 S red:(e4--e5) red:(c3--a5) E →:(e4--e5) ←:(c3--a5)"
 
   />
 
   />
 +
 +
<hexboard size="5x6"
 +
  coords="none"
 +
  edges="bottom"
 +
  visible="-area(a1,a4,d1)"
 +
  contents="R e1 f1 S red:(f4--f5) red:(c3--a5) E →:(f4--f5) ←:(c3--a5)"
 +
  />
 +
Red can choose between getting a 2nd row ladder to the right and a 3rd row ladder to the left, or vice versa.
 +
 +
<hexboard size="5x5"
 +
  coords="none"
 +
  edges="bottom"
 +
  visible="area(c1,b2,a5,d5,e2,e1)-d1"
 +
  contents="R arrow(12):(c1,e1) S red:(d4--d5) E arrow(3):(d4--d5)"
 +
  />
 +
 +
=== Ladder creation templates on the 6th row ===
 +
 +
<hexboard size="6x7"
 +
  coords="none"
 +
  edges="bottom"
 +
  visible="-area(a1,a5,e1)"
 +
  contents="R f1 e2 S red:(g5--g6) blue:(b5--a6) E →:(g5--g6) ←:(b5--a6) +:d4"
 +
  />
 +
Red must choose between the ladder going left and the ladder going right (Red cannot force both simultaneously). The cell marked "+" is the only place where Blue can move to prevent Red from connecting to the edge outright.
 +
 +
<hexboard size="6x7"
 +
  coords="none"
 +
  edges="bottom"
 +
  visible="-area(a1,a5,e1)"
 +
  contents="R f1 g1 S red:(g4--g6) blue:(c4--a6) E →:(g4--g6) ←:(c4--a6)"
 +
  />
 +
Red must choose between the ladder going left and the ladder going right (Red cannot force both simultaneously).
 +
 +
<hexboard size="6x8"
 +
  coords="none"
 +
  edges="bottom"
 +
  visible="-area(a1,a5,e1)"
 +
  contents="R f1 g1 S red:(h5--h6) E →:(h5--h6)"
 +
  />
 +
 +
<hexboard size="6x6"
 +
  coords="none"
 +
  edges="bottom"
 +
  visible="-area(a1,a5,e1)"
 +
  contents="R ↑:f1 f3 S red:(f4--f6) blue:(d3--a6) E →:(f4--f6) ←:(d3--a6)"
 +
  />
 +
Red must choose between the ladder going left and the ladder going right (Red cannot force both simultaneously).
 +
 +
<hexboard size="6x9"
 +
  coords="none"
 +
  edges="bottom"
 +
  visible="area(b6,h6,h3,g3,g1)"
 +
  contents="R ↑:g1 g3 S red:(h5--h6) E →:(h5--h6)"
 +
  />
 +
 +
<hexboard size="6x9"
 +
  coords="none"
 +
  edges="bottom"
 +
  visible="area(a6,i6,i4,g2,g1,e3,d3)"
 +
  contents="R ↑:g1 g3 S red:(i5--i6) red:(b5--a6) E →:(i5--i6) ←:(b5--a6) +:(g2 e4 g4)"
 +
  />
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Red can get both ladders simultaneously. The cells marked "+" are the only ones where Blue can move to prevent Red from connecting to the edge outright.
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 +
[[category:edge templates]]
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[[category:definition]]

Latest revision as of 14:19, 5 September 2022

A ladder creation template is a kind of edge template that guarantees that the owner of the template can either connect to the edge or, failing that, get a specified ladder or ladders.

There is not yet a naming convention for ladder creation templates, so all examples on this page are currently unnamed. Like edge templates, we classify ladder creation templates by the row on which the connecting stone is located, rather than by the kind of ladder it generates. In fact, some templates generate more than one ladder, for example a 4th row ladder going left or a 3rd row ladder going right. In an attempt to avoid confusion, we say "ladder creation template on the 3rd row", rather than "3rd row ladder creation template", to indicate that the template is a 3rd row template (but may, for example, generate a 2nd row ladder).

On David King's Hex template page, ladder creation templates are called "cascading templates". However, they should not be confused with what Matthew Seymour's book calls "cascading ladders", which is a different concept.

Examples

We use horizontal arrows "→" and sometimes "←" to indicate where the ladder(s) will start. If the right and left ladders use the same color, it means that Red can get both ladders. If they use different colors, it means that Red has a choice between starting a ladder on the right or on the left, but cannot do both. The cells marked "→" and "←" must be empty for the templates to be valid.

As usual, Red stones marked "↑" are assumed to be connected upwards, i.e., these are the stones that Red wants to connect to the bottom edge or ladder. Any cells that are shaded in grey are not part of the template and can be occupied by Blue.

Many of the below templates are taken from David King's Hex template page.

When checking the templates, keep in mind that the templates do not in general guarantee that Red will get the indicated ladder. They only guarantee that Red will get at least the indicated ladder (or a better one) if Red doesn't connect to the edge outright.

Ladder creation templates on the 2nd row

Ladder creation templates on the 3rd row

Ladder creation templates on the 4th row

Ladder creation templates on the 5th row

Red can choose between getting a 2nd row ladder to the right and a 3rd row ladder to the left, or vice versa.

Ladder creation templates on the 6th row

Red must choose between the ladder going left and the ladder going right (Red cannot force both simultaneously). The cell marked "+" is the only place where Blue can move to prevent Red from connecting to the edge outright.

Red must choose between the ladder going left and the ladder going right (Red cannot force both simultaneously).

Red must choose between the ladder going left and the ladder going right (Red cannot force both simultaneously).

Red can get both ladders simultaneously. The cells marked "+" are the only ones where Blue can move to prevent Red from connecting to the edge outright.

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