|
|
| Line 106: |
Line 106: |
| | /> | | /> |
| | | | |
| − | Now Red is connected by [[Tom's_move#Tom.27s_move_for_3rd-and-5th_row_parallel_ladders|Tom's move for 3rd and 5th row parallel ladders]]. | + | Now Red is connected by [[Tom's move for 3rd and 5th row parallel ladders]]. |
| − | | + | |
| − | Continuation:
| + | |
| − | | + | |
| − | <div class="toccolours mw-collapsible mw-collapsed">
| + | |
| − | | + | |
| − | Now Red has two main threats. Via a [[ziggurat]]:
| + | |
| − | | + | |
| − | <hexboard size="6x14"
| + | |
| − | coords="hide"
| + | |
| − | edges="bottom"
| + | |
| − | visible="area(f1,a6,n6,n4,l2,h1)"
| + | |
| − | contents="R e2 d4 d3 B c3 d5 e3 c5 R 1:g3 E *:f4 S f2 g2 f3 e4 area(d6,f4,g4,g6)"
| + | |
| − | />
| + | |
| − | And via [[edge template IV2b]]:
| + | |
| − | <hexboard size="6x14"
| + | |
| − | coords="hide"
| + | |
| − | edges="bottom"
| + | |
| − | visible="area(f1,a6,n6,n4,l2,h1)"
| + | |
| − | contents="R e2 d4 d3 B c3 d5 e3 c5 R 1:g3 E *:f4 S f2 g2 f3 e4 area(e6,i6,i4,h3,f4)"
| + | |
| − | />
| + | |
| − | | + | |
| − | Blue must play in the overlap:
| + | |
| − | <hexboard size="6x14"
| + | |
| − | coords="hide"
| + | |
| − | edges="bottom"
| + | |
| − | visible="area(f1,a6,n6,n4,l2,h1)"
| + | |
| − | contents="R e2 d4 d3 B c3 d5 e3 c5 R 1:g3 S f2 g2 f3 e4 area(e6,f4,g4,g6)
| + | |
| − | E p:f2 q:g2 r:f3 s:e4 t:f4 u:g4 v:f5 w:g5 x:e6 y:f6 z:g6"
| + | |
| − | />
| + | |
| − | | + | |
| − | | + | |
| − | ==== Intrusion at p, q, r ====
| + | |
| − | | + | |
| − | <hexboard size="6x14"
| + | |
| − | coords="hide"
| + | |
| − | edges="bottom"
| + | |
| − | visible="area(f1,a6,n6,n4,l2,h1)"
| + | |
| − | contents="R e2 d4 d3 B c3 d5 e3 c5 R 1:g3 B 2:(f3 f2 g2) R 3:e4 S d6 e5 e6"
| + | |
| − | />
| + | |
| − | | + | |
| − | 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 [[Edge_template_IV2b|IV-2-b]]. Otherwise, Red connects via [[Tom's move]].
| + | |
| − | | + | |
| − | <hexboard size="6x14"
| + | |
| − | coords="hide"
| + | |
| − | edges="bottom"
| + | |
| − | visible="area(f1,a6,n6,n4,l2,h1)"
| + | |
| − | contents="R e2 d4 d3 B c3 d5 e3 c5 R 1:g3 B 2:(f3 f2 g2) R 3:e4 5:e5 7:f5 9:i4 B 2:(f3 f2 g2) 4:e6 6:d6 8:f6"
| + | |
| − | />
| + | |
| − | | + | |
| − | ==== Intrusion at s ====
| + | |
| − | | + | |
| − | <hexboard size="6x14"
| + | |
| − | coords="hide"
| + | |
| − | edges="bottom"
| + | |
| − | visible="area(f1,a6,n6,n4,l2,h1)"
| + | |
| − | contents="R e2 d4 d3 B c3 d5 e3 c5 R 1:g3 B 2:e4 R 3:f2"
| + | |
| − | />
| + | |
| − | | + | |
| − | Red is connected by [[edge template IV1d]].
| + | |
| − | | + | |
| − | ==== Intrusion at t ====
| + | |
| − | | + | |
| − | <hexboard size="6x14"
| + | |
| − | coords="hide"
| + | |
| − | edges="bottom"
| + | |
| − | visible="area(f1,a6,n6,n4,l2,h1)"
| + | |
| − | contents="R e2 d4 d3 B c3 d5 e3 c5 R 1:g3 B 2:f4 R 3:e4 B 4:e5 R 5:h2"
| + | |
| − | />
| + | |
| − | | + | |
| − | Now Red is connected by [[Fifth_row_edge_templates#V-2-m|edge template V2m]]. If Blue plays 4 on the first row instead, Red connects by [[Tom's move]]:
| + | |
| − | <hexboard size="6x14"
| + | |
| − | coords="hide"
| + | |
| − | edges="bottom"
| + | |
| − | visible="area(f1,a6,n6,n4,l2,h1)"
| + | |
| − | contents="R e2 d4 d3 B c3 d5 e3 c5 R 1:g3 B 2:f4 R 3:e4 B 4:e6 R 5:e5 B 6:d6 R 7:f5 B 8:f6 R 9:i4"
| + | |
| − | />
| + | |
| − | | + | |
| − | ==== Intrusion at u ====
| + | |
| − | | + | |
| − | <hexboard size="6x14"
| + | |
| − | coords="hide"
| + | |
| − | edges="bottom"
| + | |
| − | visible="area(f1,a6,n6,n4,l2,h1)"
| + | |
| − | contents="R e2 d4 d3 B c3 d5 e3 c5 R 1:g3 B 2:g4 R 3:f4 B 4:e6 R 5:f5 B 6:f6 R 7:i4"
| + | |
| − | />
| + | |
| − | Red is connected by [[Tom's move]].
| + | |
| − | | + | |
| − | ==== Intrusion at w ====
| + | |
| − | | + | |
| − | Red responds with
| + | |
| − | | + | |
| − | <hexboard size="6x14"
| + | |
| − | coords="hide"
| + | |
| − | edges="bottom"
| + | |
| − | visible="area(f1,a6,n6,n4,l2,h1)"
| + | |
| − | contents="R e2 d4 d3 B c3 d5 e3 c5 R 1:g3 B 2:g5 R 3:i4 S red:area(i4,g6,j6,j4)"
| + | |
| − | />
| + | |
| − | | + | |
| − | Continuation:
| + | |
| − | <div class="toccolours mw-collapsible mw-collapsed">
| + | |
| − | | + | |
| − | We will assume that Red simply defends the pink [[ziggurat]], and therefore we will not need to consider any Blue intrusions there.
| + | |
| − | | + | |
| − | Red's main threats are
| + | |
| − | | + | |
| − | <hexboard size="6x14"
| + | |
| − | coords="hide"
| + | |
| − | edges="bottom"
| + | |
| − | visible="area(f1,a6,n6,n4,l2,h1)"
| + | |
| − | contents="R e2 d4 d3 B c3 d5 e3 c5 R 1:g3 3:i4 5:e4 B 2:g5 S d6 e6 e5 e4 f4 f3 h3 h4 i3 S red:area(i4,g6,j6,j4)"
| + | |
| − | />
| + | |
| − | | + | |
| − | and
| + | |
| − | | + | |
| − | <hexboard size="6x14"
| + | |
| − | coords="hide"
| + | |
| − | edges="bottom"
| + | |
| − | visible="area(f1,a6,n6,n4,l2,h1)"
| + | |
| − | contents="R e2 d4 d3 B c3 d5 e3 c5 R 1:g3 3:i4 5:f2 B 2:g5 S f2 g2 e6 f6 f5 f4 g4 f3 h3 h4 i3 S red:area(i4,g6,j6,j4)"
| + | |
| − | />
| + | |
| − | | + | |
| − | Blue [[mustplay region|must play]] in the overlap:
| + | |
| − | | + | |
| − | <hexboard size="6x14"
| + | |
| − | coords="hide"
| + | |
| − | edges="bottom"
| + | |
| − | visible="area(f1,a6,n6,n4,l2,h1)"
| + | |
| − | contents="R e2 d4 d3 B c3 d5 e3 c5 R 1:g3 3:i4 B 2:g5 S e6 f4 f3 h3 h4 i3 E c:e6 b:f4 a:f3 d:h3 f:h4 e:i3 S red:area(i4,g6,j6,j4)"
| + | |
| − | />
| + | |
| − | | + | |
| − | If Blue plays at a, then Red plays 5, after which Red connects via
| + | |
| − | | + | |
| − | <hexboard size="6x14"
| + | |
| − | coords="hide"
| + | |
| − | edges="bottom"
| + | |
| − | visible="area(f1,a6,n6,n4,l2,h1)"
| + | |
| − | contents="R e2 d4 d3 B c3 d5 e3 c5 R 1:g3 3:i4 5:e4 7:f4 B 2:g5 4:f3 6:e5 6:d6 E *:f5 *:h3 S red:area(i4,g6,j6,j4)"
| + | |
| − | />
| + | |
| − | | + | |
| − | or
| + | |
| − | | + | |
| − | <hexboard size="6x14"
| + | |
| − | coords="hide"
| + | |
| − | edges="bottom"
| + | |
| − | visible="area(f1,a6,n6,n4,l2,h1)"
| + | |
| − | contents="R e2 d4 d3 B c3 d5 e3 c5 R 1:g3 3:i4 5:e4 7:e5 9:f5 11:h3 B 2:g5 4:f3 6:e6 8:d6 10:f6 S red:area(i4,g6,j6,j4)"
| + | |
| − | />
| + | |
| − | | + | |
| − | If Blue plays at b, then Red plays 5, after which Red connects via
| + | |
| − | | + | |
| − | <hexboard size="6x14"
| + | |
| − | coords="hide"
| + | |
| − | edges="bottom"
| + | |
| − | visible="area(f1,a6,n6,n4,l2,h1)"
| + | |
| − | contents="R e2 d4 d3 B c3 d5 e3 c5 R 1:g3 B 2:g5 R 3:i4 B 4:f4 R 5:e4 B 6:(e5 d6) R 7:h2 B 8:h3 R 9:g4 S red:area(i4,g6,j6,j4) E *:(g1 f3 f5 h4)"
| + | |
| − | />
| + | |
| − | | + | |
| − | or
| + | |
| − | | + | |
| − | <hexboard size="6x14"
| + | |
| − | coords="hide"
| + | |
| − | edges="bottom"
| + | |
| − | visible="area(f1,a6,n6,n4,l2,h1)"
| + | |
| − | contents="R e2 d4 d3 B c3 d5 e3 c5 R 1:g3 3:i4 5:e4 7:e5 9:f5 11:h3 B 2:g5 4:f4 6:e6 8:d6 10:f6 S red:area(i4,g6,j6,j4)"
| + | |
| − | />
| + | |
| − | | + | |
| − | If Blue plays at c, then Red responds with
| + | |
| − | | + | |
| − | <hexboard size="6x14"
| + | |
| − | coords="hide"
| + | |
| − | edges="bottom"
| + | |
| − | visible="area(f1,a6,n6,n4,l2,h1)"
| + | |
| − | contents="R e2 d4 d3 B c3 d5 e3 c5 R 1:g3 3:i4 5:h3 B 2:g5 4:e6 S red:area(i4,g6,j6,j4)"
| + | |
| − | />
| + | |
| − | | + | |
| − | This forces Blue to defend towards the top, after which
| + | |
| − | | + | |
| − | <hexboard size="6x14"
| + | |
| − | coords="hide"
| + | |
| − | edges="bottom"
| + | |
| − | visible="area(f1,a6,n6,n4,l2,h1)"
| + | |
| − | contents="R e2 d4 d3 B c3 d5 e3 c5 R 1:g3 3:i4 5:h3 7:e4 B 2:g5 4:e6 6:(f2 f3 g2) S red:area(i4,g6,j6,j4)"
| + | |
| − | />
| + | |
| − | | + | |
| − | connects directly or via red 1.
| + | |
| − | | + | |
| − | <hexboard size="6x14"
| + | |
| − | coords="hide"
| + | |
| − | edges="bottom"
| + | |
| − | visible="area(f1,a6,n6,n4,l2,h1)"
| + | |
| − | contents="R e2 d4 d3 B c3 d5 e3 c5 R 1:g3 3:i4 5:h3 7:e4 9:e5 11:f5 B 2:g5 4:e6 6:(f2 f3 g2) 8:f4 10:d6 S red:area(i4,g6,j6,j4)"
| + | |
| − | />
| + | |
| − | | + | |
| − | If Blue plays at d or e, then Red plays like this:
| + | |
| − | | + | |
| − | <hexboard size="6x14"
| + | |
| − | coords="hide"
| + | |
| − | edges="bottom"
| + | |
| − | visible="area(f1,a6,n6,n4,l2,h1)"
| + | |
| − | contents="R e2 d4 d3 B c3 d5 e3 c5 R 1:g3 B 2:g5 R 3:i4 B 4:(h3 i3) R 5:e5 B 6:e4 R 7:f2 B 8:f4 R 9:g4 E *:(f5 h4) S red:area(i4,g6,j6,j4)"
| + | |
| − | />
| + | |
| − | | + | |
| − | If Blue plays at f, then Red plays like this:
| + | |
| − | | + | |
| − | <hexboard size="6x14"
| + | |
| − | coords="hide"
| + | |
| − | edges="bottom"
| + | |
| − | visible="area(f1,a6,n6,n4,l2,h1)"
| + | |
| − | contents="R e2 d4 d3 B c3 d5 e3 c5 R 1:g3 B 2:g5 R 3:i4 B 4:h4 R 5:f5 E *:(f2 e4) +:f4 S red:area(i4,g6,j6,j4)"
| + | |
| − | />
| + | |
| − | | + | |
| − | Now Red threatens to play in one of the cells marked "*", and the only overlap (apart from the two [[captured cell]]s below 5) is at "+", so Blue must play there. Then Red responds like this:
| + | |
| − | | + | |
| − | <hexboard size="6x14"
| + | |
| − | coords="hide"
| + | |
| − | edges="bottom"
| + | |
| − | visible="area(f1,a6,n6,n4,l2,h1)"
| + | |
| − | contents="R e2 d4 d3 B c3 d5 e3 c5 R 1:g3 B 2:g5 R 3:i4 B 4:h4 R 5:f5 B 6:f4 R 7:h2 E *:(g1 e4) +:(g4 i3) S red:area(i4,g6,j6,j4)"
| + | |
| − | />
| + | |
| − | | + | |
| − | Now Red is connected left by double threats "*" and right by double threats "+".
| + | |
| − | | + | |
| − | </div>
| + | |
| − | | + | |
| − | ==== Intrusion at x ====
| + | |
| − | | + | |
| − | Red can respond here:
| + | |
| − | | + | |
| − | <hexboard size="6x14"
| + | |
| − | coords="hide"
| + | |
| − | edges="bottom"
| + | |
| − | visible="area(f1,a6,n6,n4,l2,h1)"
| + | |
| − | contents="R e2 d4 d3 1:g3 3:e5 B c3 d5 e3 c5 2:e6"
| + | |
| − | />
| + | |
| − | | + | |
| − | Continuation:
| + | |
| − | <div class="toccolours mw-collapsible mw-collapsed">
| + | |
| − | | + | |
| − | Red's main threat is as follows,
| + | |
| − | | + | |
| − | <hexboard size="6x14"
| + | |
| − | coords="hide"
| + | |
| − | edges="bottom"
| + | |
| − | visible="area(f1,a6,n6,n4,l2,h1)"
| + | |
| − | contents="R e2 d4 d3 1:g3 3:e5 5:f5 B c3 d5 e3 c5 2:e6 E *:e4 *:f2 S d6 e4 f3 f2 g2 g4 f4 f5 f6"
| + | |
| − | />
| + | |
| − | | + | |
| − | connecting back via one of the cells marked "*".
| + | |
| − | | + | |
| − | If Blue plays either of the two of those cells adjacent to the edge, then Red plays the
| + | |
| − | | + | |
| − | <hexboard size="6x14"
| + | |
| − | coords="hide"
| + | |
| − | edges="bottom"
| + | |
| − | visible="area(f1,a6,n6,n4,l2,h1)"
| + | |
| − | contents="R e2 d4 d3 1:g3 3:e5 5:f5 B c3 d5 e3 c5 2:e6 E *:(d6 f6 i4) S blue:(d6 f6)"
| + | |
| − | />
| + | |
| − | | + | |
| − | same move anyway, connecting down via the other of those two cells or [[Tom's move]].
| + | |
| − | | + | |
| − | If Blue plays one of the five upper-right of those cells
| + | |
| − | <hexboard size="6x14"
| + | |
| − | coords="hide"
| + | |
| − | edges="bottom"
| + | |
| − | visible="area(f1,a6,n6,n4,l2,h1)"
| + | |
| − | contents="R e2 d4 d3 1:g3 3:e5 B c3 d5 e3 c5 2:e6 S blue:(f3 f2 g2 g4 f4)"
| + | |
| − | />
| + | |
| − | then Red still connects via [[Tom's move]],
| + | |
| − | | + | |
| − | <hexboard size="6x14"
| + | |
| − | coords="hide"
| + | |
| − | edges="bottom"
| + | |
| − | visible="area(f1,a6,n6,n4,l2,h1)"
| + | |
| − | contents="R e2 d4 d3 1:g3 3:e5 5:e4 7:f5 9:i4 B c3 d5 e3 c5 2:e6 6:d6 8:f6 E *:(f3 f4 g4) S blue:(f3 f2 g2 g4 f4)"
| + | |
| − | />
| + | |
| − | | + | |
| − | since at least two of the three cells marked "*" are still available to Red 1 to connect to Red's left group.
| + | |
| − | | + | |
| − | This leaves only two remaining tries for Blue:
| + | |
| − | | + | |
| − | <hexboard size="6x14"
| + | |
| − | coords="hide"
| + | |
| − | edges="bottom"
| + | |
| − | visible="area(f1,a6,n6,n4,l2,h1)"
| + | |
| − | contents="R e2 d4 d3 1:g3 3:e5 B c3 d5 e3 c5 2:e6 S e4 f5"
| + | |
| − | />
| + | |
| − | | + | |
| − | If Blue plays the right of those two,
| + | |
| − | | + | |
| − | <hexboard size="6x14"
| + | |
| − | coords="hide"
| + | |
| − | edges="bottom"
| + | |
| − | visible="area(f1,a6,n6,n4,l2,h1)"
| + | |
| − | contents="R e2 d4 d3 1:g3 3:e5 5:e4 B c3 d5 e3 c5 2:e6 4:f5 E *:d6 *:h4"
| + | |
| − | />
| + | |
| − | | + | |
| − | then Red connects via [[double threat]].
| + | |
| − | | + | |
| − | Thus Blue instead plays the left of those two. Red responds as follows.
| + | |
| − | | + | |
| − | <hexboard size="6x14"
| + | |
| − | coords="hide"
| + | |
| − | edges="bottom"
| + | |
| − | visible="area(f1,a6,n6,n4,l2,h1)"
| + | |
| − | contents="R e2 d4 d3 1:g3 3:e5 5:f2 7:f3 B c3 d5 e3 c5 2:e6 4:e4 6:g2 S d6 e6"
| + | |
| − | />
| + | |
| − | | + | |
| − | Now, it does not matter which of the two shaded cells Blue 2 is at, since
| + | |
| − | | + | |
| − | * if Blue plays the other too then the order in which they were played doesn't matter, and
| + | |
| − | * if instead Red plays the other, then whichever one Blue played will be [[Dead cell|dead]].
| + | |
| − | | + | |
| − | So this is equivalent to Red having a [[Theorems_about_templates#Corner_clipping|clipped]] version of [[Edge template IV1d]].
| + | |
| − | | + | |
| − | In particular, Red is connected down.
| + | |
| − | | + | |
| − | </div>
| + | |
| − | | + | |
| − | ==== Intrusion at v or y or z ====
| + | |
| − | | + | |
| − | If Blue plays one of the three highlighted cells, then Red responds as shown below.
| + | |
| − | | + | |
| − | <hexboard size="6x14"
| + | |
| − | coords="hide"
| + | |
| − | edges="bottom"
| + | |
| − | visible="area(f1,a6,n6,n4,l2,h1)"
| + | |
| − | contents="R e2 d4 d3 B c3 d5 e3 c5 R 1:g3 3:e5 E *:d6 *:e6 S blue:(f5 f6 g6)"
| + | |
| − | />
| + | |
| − | | + | |
| − | This [[captured cell|captures]] the two cells marked "*", forcing Blue 4, and then Red 5
| + | |
| − | | + | |
| − | <hexboard size="6x14"
| + | |
| − | coords="hide"
| + | |
| − | edges="bottom"
| + | |
| − | visible="area(f1,a6,n6,n4,l2,h1)"
| + | |
| − | contents="R e2 d4 d3 B c3 d5 e3 c5 R 1:g3 3:e5 5:f2 B 4:e4 E *:d6 *:e6 S blue:(f5 f6 g6)"
| + | |
| − | />
| + | |
| − | | + | |
| − | connects by [[double threat]] or [[edge template IV2e]] or [[Fourth_row_edge_templates#IV-2-q|edge template IV2p]].
| + | |
| − | | + | |
| − | </div>
| + | |
| | | | |
| | === Continuation after 2nd row ladder === | | === Continuation after 2nd row ladder === |
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.
If Blue intrudes at a, Red can start by forcing a 3rd or 2nd row ladder like this
If Red achieved a 3rd row ladder after intrusions a or b as shown above, Red continues as follows.
If Red achieved a 2nd row ladder after intrusions a or c above, Red continues as follows.
