Difference between revisions of "Edge template V1b"
(Handled more cases. Intrusions w and x need more work.) |
(→Intrusion at x: Added lots of reductions.) |
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<div class="toccolours mw-collapsible mw-collapsed"> | <div class="toccolours mw-collapsible mw-collapsed"> | ||
| − | + | Red has several threats. Via [[double threat]]s: | |
<hexboard size="6x14" | <hexboard size="6x14" | ||
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edges="bottom" | edges="bottom" | ||
visible="area(f1,a6,n6,n4,l2,h1)" | visible="area(f1,a6,n6,n4,l2,h1)" | ||
| − | contents=" | + | contents="R e2 R g3 R d4 B c5 B d5 E *:e5 R f5 B e6 e3 R d3 S area(f2,d6,f6,g4,g2)-e6" |
/> | /> | ||
| − | and | + | Via [[double threat]] and [[edge template III2b]]: |
<hexboard size="6x14" | <hexboard size="6x14" | ||
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edges="bottom" | edges="bottom" | ||
visible="area(f1,a6,n6,n4,l2,h1)" | visible="area(f1,a6,n6,n4,l2,h1)" | ||
| − | contents=" | + | contents="R e2 S f2 g2 f3 R g3 R d4 S e4 f4 E *:g4 S h4 B c5 B d5 S e5 R f5 S g5 S h5 B e6 S f6 g6 h6 B e3 R d3 S g3 g4 f5" |
/> | /> | ||
| − | + | Via [[bridge]]s and [[Tom's move]]: | |
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<hexboard size="6x14" | <hexboard size="6x14" | ||
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edges="bottom" | edges="bottom" | ||
visible="area(f1,a6,n6,n4,l2,h1)" | visible="area(f1,a6,n6,n4,l2,h1)" | ||
| − | contents=" | + | contents="R e2 R g3 R d4 B c5 B d5 R f5 B e6 B e3 R d3 E *:f2 S area(f2,f6,l6,l4,j2)" |
/> | /> | ||
| − | ' | + | Via a [[wheel]] and [[Tom's move]]: |
<hexboard size="6x14" | <hexboard size="6x14" | ||
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edges="bottom" | edges="bottom" | ||
visible="area(f1,a6,n6,n4,l2,h1)" | visible="area(f1,a6,n6,n4,l2,h1)" | ||
| − | contents=" | + | contents="R e2 R g3 R d4 B c5 B d5 R f5 B e6 B e3 R d3 E *:e4 S area(f3,e4,e5,f6,l6,l4,j2,h2)" |
/> | /> | ||
| − | + | Via a [[double threat]] and [[Tom's move]]: | |
| − | + | ||
<hexboard size="6x14" | <hexboard size="6x14" | ||
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edges="bottom" | edges="bottom" | ||
visible="area(f1,a6,n6,n4,l2,h1)" | visible="area(f1,a6,n6,n4,l2,h1)" | ||
| − | contents=" | + | contents="R e2 R g3 R d4 B c5 B d5 R f5 B e6 B e3 R d3 E *:f4 S area(f2,f6,l6,l4,j2)+e4-g4" |
/> | /> | ||
| − | |||
| − | ' | + | Via a different [[double threat]] and [[Tom's move]]: |
<hexboard size="6x14" | <hexboard size="6x14" | ||
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edges="bottom" | edges="bottom" | ||
visible="area(f1,a6,n6,n4,l2,h1)" | visible="area(f1,a6,n6,n4,l2,h1)" | ||
| − | contents=" | + | contents="R e2 R g3 R d4 B c5 B d5 R f5 B e6 B e3 R d3 E *:e5 S area(f2,f6,l6,l4,j2)+e4+e5+d6-f6" |
/> | /> | ||
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| − | + | Blue [[mustplay region|must play]] in the overlap: | |
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| − | Blue must | + | |
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visible="area(f1,a6,n6,n4,l2,h1)" | visible="area(f1,a6,n6,n4,l2,h1)" | ||
| − | contents=" | + | contents="R e2 R g3 R d4 B c5 B d5 R f5 B e6 B e3 R d3 S f3 f4" |
/> | /> | ||
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</div> | </div> | ||
Revision as of 02:12, 25 July 2022
Edge template V1b is a 5th row edge template with 1 stone.
The validity and minimality of this template has been checked by computer. The template was mentioned on 2016-05-19 by the user shalev in this Little Golem thread, but likely predates that post.
Contents
Defense against intrusions
Reduction
Red has 3 main threats. Using the ziggurat:
Using edge template III1b:
And using edge_template_IV1d:
For a blocking attempt, Blue must play in the overlap:
Intrusion at a
If Blue intrudes at a, Red can start by forcing a 3rd or 2nd row ladder like this
or like this:
Red's continuation will be discussed below.
Intrusion at b
If Blue intrudes at b, Red can start by forcing a 3rd row ladder like this:
Red's continuation will be discussed below.
Intrusion at c
If Blue intrudes at c, Red can start by forcing a 2nd row ladder like this:
Red's continuation will be discussed below.
Continuation after 3rd row ladder
If Red achieved a 3rd row ladder after intrusions a or b as shown above, Red continues as follows.
Now Red is connected by Tom's move for 3rd and 5th row parallel ladders.
Continuation:
Now Red has two main threats. Via a ziggurat:
And via edge template IV2b:
Blue must play in the overlap:
Intrusion at p, q, r
Now Blue must play in one of the 3 shaded cells. If Blue plays in the left 2 of those 3, then Red connects via IV-2-b. Otherwise, Red connects via Tom's move.
Intrusion at s
Red is connected by edge template IV1d.
Intrusion at t
Now Red is connected by edge template V2m. If Blue plays 4 on the first row instead, Red connects by Tom's move:
Intrusion at u
Red is connected by Tom's move.
Intrusion at v
Red is connected by double threat.
Intrusion at w
To do.
Intrusion at x
Red can respond here:
Continuation:
Red has several threats. Via double threats:
Via double threat and edge template III2b:
Via bridges and Tom's move:
Via a wheel and Tom's move:
Via a double threat and Tom's move:
Via a different double threat and Tom's move:
Blue must play in the overlap:
Intrusion at y
Note that the hexes marked "*" are captured by Red 3, so Blue 4 is forced. Then Red is connected by edge template IV2e.
Intrusion at z
Note that the hexes marked "*" are captured by Red 3, so Blue 4 is forced. Then Red is connected by edge template IV2p.
Continuation after 2nd row ladder
If Red achieved a 2nd row ladder after intrusions a or c above, Red continues as follows.
Now Red connects in essentially the same way as Tom's move.
Continuation:
Red has these threats:
The overlap in which Blue must play is:
Four of these five possible moves can be analysed together. In the following diagram, assume Blue has played 1 in any one of the cells marked with +:
After Red 2, that group is safely connected to them bottom, now matter which of the pluses Blue chose before.
That leaves only one Blue move to deal with:
Note that Red 4 connects to the bottom with IV-2-b.
