Difference between revisions of "Ladder puzzle 1/Solution"

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(Alternative: e5 then f5: Refined solution.)
(Added another alternative solution: switchback)
 
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Now Red plays f4 completing the win.  f4 is connected to the lower-right group in two non-overlapping ways, through f5 and g4.  f4 is also connected to the central group in two non-overlapping ways, through f3 and e5.  Therefore, all of Red's pieces form a single group which is connected to both the top and bottom.
 
Now Red plays f4 completing the win.  f4 is connected to the lower-right group in two non-overlapping ways, through f5 and g4.  f4 is also connected to the central group in two non-overlapping ways, through f3 and e5.  Therefore, all of Red's pieces form a single group which is connected to both the top and bottom.
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== Alternative Solution: switchback ==
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Red can also use h4 to do a [[switchback]]. To set this up, Red starts playing the 2nd row ladder and breaks the ladder at f7:
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<hex>R8 C8 Q1 Vc6 Vd5 Vd4 Ve3 Vh4 Hd6 Hb8 Hc1 He4 Hg3 V1c7 H2c8 V3d7 H4d8 V5f7 H6e7</hex>
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Now the killer move is f5, which connects to Red's main group by double threat, and is also connected to h4. Blue is forced to play at f6, but Red reconnects with h5 via [[Fourth_row_edge_templates#IV-2-d|edge template IV-2-d]].
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<hex>R8 C8 Q1 Vc6 Vd5 Vd4 Ve3 Vh4 Hd6 Hb8 Hc1 He4 Hg3 Vc7 Hc8 Vd7 Hd8 Vf7 He7 V7f5 H8f6 V9h5</hex>
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This method works no matter the size of the board or how far away the 5th row stone is. If h5 is further to the right, the 2nd row ladder will just turn into a 4th row ladder going the opposite way, eventually connecting with d5.
  
 
[[category:ladder puzzle]]
 
[[category:ladder puzzle]]

Latest revision as of 01:58, 21 May 2020

Correct: e5 then c7

Red's main threat is the ladder starting at c7. If Red plays out this ladder, Blue can block it. So Red needs a helping stone somewhere on the right and on the second line from the bottom. Red 1.e5 threatens the follow-up moves at *, which Blue must defend.


abcdefgh123456781

The potential connection at d7 passes through e6, c7, c8, and d8. The potential connection at f6 passes through e6, f5, and Template IIIa. These two potential connections only overlap at the two hexes marked +, so Blue must play there. However, if Blue plays 2.d8, Red wins with the following sequence of forcing moves:


abcdefgh123456781736542

Therefore, Blue must play 2.e6. Red can now play the ladder at c7, break the ladder at g7, and win:


abcdefgh1234567813121211357109468

Alternative: e5 then f5

Alternatively, after 1.e5 2.e6, Red could have continued the 4th row ladder with 3.f5, to which Blue may reply 4.f6. This allows Red to play a double threat 5.g7. This stone is the ladder helper, and it also threatens to connect along the top. Either way, Red wins.


abcdefgh1234567813245

However, this play is more complicated to analyze, because Blue may also respond in a number of other places instead of f6. If Blue plays 4.e8, then 5.g7 still works, albeit for slightly different reasons:


abcdefgh12345678132679584

Note that in the final position, the red stone at e7 is connected up via * and down via +, so it is a winning position.

If Blue plays 4.f7 or anything to the right of it, Red gets their ladder escape at 5.e7:


abcdefgh123456781326754

Again, e7 is connected upwards via *.

Alternative Solution: f6


abcdefgh1234567812

The stone at f6 is a ladder breaker for the ladder starting at c7, and it also threatens to connect via e5. This looks very strong, but Blue can still defend at e7, which is a ladder breaker and threatens a connection at the lower side.


abcdefgh123456786345

Now Red plays f4 completing the win. f4 is connected to the lower-right group in two non-overlapping ways, through f5 and g4. f4 is also connected to the central group in two non-overlapping ways, through f3 and e5. Therefore, all of Red's pieces form a single group which is connected to both the top and bottom.

Alternative Solution: switchback

Red can also use h4 to do a switchback. To set this up, Red starts playing the 2nd row ladder and breaks the ladder at f7:


abcdefgh12345678136524

Now the killer move is f5, which connects to Red's main group by double threat, and is also connected to h4. Blue is forced to play at f6, but Red reconnects with h5 via edge template IV-2-d.


abcdefgh12345678798

This method works no matter the size of the board or how far away the 5th row stone is. If h5 is further to the right, the 2nd row ladder will just turn into a 4th row ladder going the opposite way, eventually connecting with d5.