Difference between revisions of "Edge template IV2l"
(Since the analysis of connecting two stones is now simpler than that of connecting one, deleted the latter.) |
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''This page is about edge template IV2l (four two ell). There is also an [[edge template IV2i]] (four two eye).'' | ''This page is about edge template IV2l (four two ell). There is also an [[edge template IV2i]] (four two eye).'' | ||
| − | + | Template IV2-l is a 4th row [[edge template]] with 2 stones. | |
<hexboard size="4x6" | <hexboard size="4x6" | ||
coords="hide" | coords="hide" | ||
| + | edges="bottom" | ||
| + | visible="area(d1,a4,f4,f1)" | ||
contents="E *:a1 E *:b1 E *:c1 R d1 R f1 E *:a2 E *:b2 E *:a3" | contents="E *:a1 E *:b1 E *:c1 R d1 R f1 E *:a2 E *:b2 E *:a3" | ||
/> | /> | ||
(From: [http://www.drking.org.uk/hexagons/hex/templates.html www.drking.org.uk]) | (From: [http://www.drking.org.uk/hexagons/hex/templates.html www.drking.org.uk]) | ||
| + | |||
| + | == Defending the template == | ||
Red can connect both of the two stones to the bottom, i.e., Red does not have to choose which of the two stones to connect. To show this, we consider every possible intrusion into the template. Since the template is symmetric, we only need to consider intrusions by Blue into the right-hand side of the template (or on the center line). | Red can connect both of the two stones to the bottom, i.e., Red does not have to choose which of the two stones to connect. To show this, we consider every possible intrusion into the template. Since the template is symmetric, we only need to consider intrusions by Blue into the right-hand side of the template (or on the center line). | ||
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<hexboard size="4x6" | <hexboard size="4x6" | ||
| − | coords=" | + | coords="bottom right" |
| + | edges="bottom" | ||
| + | visible="area(d1,a4,f4,f1)" | ||
contents="E *:a1 E *:b1 E *:c1 R d1 R f1 E *:a2 E *:b2 E *:a3 E +:e1 +:e2 +:e3 +:e4 +:f2 +:f3 +:f4 R 2:d3" | contents="E *:a1 E *:b1 E *:c1 R d1 R f1 E *:a2 E *:b2 E *:a3 E +:e1 +:e2 +:e3 +:e4 +:f2 +:f3 +:f4 R 2:d3" | ||
/> | /> | ||
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<hexboard size="4x6" | <hexboard size="4x6" | ||
| − | coords=" | + | coords="bottom right" |
| + | edges="bottom" | ||
| + | visible="area(d1,a4,f4,f1)" | ||
contents="E *:a1 E *:b1 E *:c1 R d1 R f1 E *:a2 E *:b2 E *:a3 E +:d3 +:d4 R 2:c3" | contents="E *:a1 E *:b1 E *:c1 R d1 R f1 E *:a2 E *:b2 E *:a3 E +:d3 +:d4 R 2:c3" | ||
/> | /> | ||
[[category:edge templates]] | [[category:edge templates]] | ||
Latest revision as of 16:49, 10 December 2020
This page is about edge template IV2l (four two ell). There is also an edge template IV2i (four two eye).
Template IV2-l is a 4th row edge template with 2 stones.
(From: www.drking.org.uk)
Defending the template
Red can connect both of the two stones to the bottom, i.e., Red does not have to choose which of the two stones to connect. To show this, we consider every possible intrusion into the template. Since the template is symmetric, we only need to consider intrusions by Blue into the right-hand side of the template (or on the center line).
If Blue plays in any of the cells marked "+", Red can respond at d3.
Then d1 is connected by edge template IV2d and f1 connects via e1 or e2 or edge template III2e. Since Blue has so far played only one of the cells marked "+", at least two of those three are still available. Also, since d3 captures c4 and d4, the overlap between edge template IV2d and edge template III2e does not matter.
If Blue plays d3 or d4, Red can respond at c3. d1 connects via two bridges, and f1 connects via e1 or e3. Since Blue has so far played only one of the cells marked "+", two of d3, d4, e4 are still available, which is sufficient to connect e3 to the edge.
