Difference between revisions of "Ladder puzzle 1/Solution"
m (→Alternative Solution: f6) |
(→Correct: e5: Improved the solution. The problem with the old solution is that Blue has other options besides 4.f6) |
||
| Line 1: | Line 1: | ||
== Correct: e5 == | == Correct: e5 == | ||
| − | + | 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. | |
| − | + | <hex>R8 C8 Q1 Vc6 Vd5 Vd4 Ve3 Vh4 Hd6 Hb8 Hc1 He4 Hg3 N:on Ve5 *d7 *f6 +e6 +d8</hex> | |
| − | + | 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: | |
| − | Red | + | <hex>R8 C8 Q1 Vc6 Vd5 Vd4 Ve3 Vh4 Hd6 Hb8 Hc1 He4 Hg3 N:on Ve5 Hd8 Vd7 Hc8 Vf7 He7 Vf6</hex> |
| + | |||
| + | Therefore, Blue must play 2.e6. Red can now play the ladder at c7, break the ladder at g7, and win: | ||
| + | |||
| + | <hex>R8 C8 Q1 Vc6 Vd5 Vd4 Ve3 Vh4 Hd6 Hb8 Hc1 He4 Hg3 N:on Ve5 He6 Vc7 Hc8 Vd7 Hd8 Ve7 He8 Vg7 Hf7 Vg6 Hf6 Vg4</hex> | ||
| + | |||
| + | == Alternative == | ||
| + | |||
| + | 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. | ||
<hex>R8 C8 Q1 Vc6 Vd5 Vd4 Ve3 Vh4 Hd6 Hb8 Hc1 He4 Hg3 N:on Ve5 He6 Vf5 Hf6 Vg7</hex> | <hex>R8 C8 Q1 Vc6 Vd5 Vd4 Ve3 Vh4 Hd6 Hb8 Hc1 He4 Hg3 N:on Ve5 He6 Vf5 Hf6 Vg7</hex> | ||
| − | + | However, this play is more complicated, because Blue may also respond in a number of other places instead of f6. If Blue plays 4.e8, the winning sequence looks like this: | |
| + | |||
| + | <hex>R8 C8 Q1 Vc6 Vd5 Vd4 Ve3 Vh4 Hd6 Hb8 Hc1 He4 Hg3 N:on Ve5 He6 Vf5 He8 Vc7 Hc8 Vg7 Hg6 Ve7 *d7 *f6 +d8 +f7</hex> | ||
| + | |||
| + | 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: | ||
| + | |||
| + | <hex>R8 C8 Q1 Vc6 Vd5 Vd4 Ve3 Vh4 Hd6 Hb8 Hc1 He4 Hg3 N:on Ve5 He6 Vf5 Hf7 Ve7 Hf6 Vc7</hex> | ||
| + | |||
| + | Again, e7 is connected upwards via *. | ||
== Alternative Solution: f6 == | == Alternative Solution: f6 == | ||
Revision as of 20:39, 1 March 2020
Correct: e5
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.
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:
Therefore, Blue must play 2.e6. Red can now play the ladder at c7, break the ladder at g7, and win:
Alternative
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.
However, this play is more complicated, because Blue may also respond in a number of other places instead of f6. If Blue plays 4.e8, the winning sequence looks like this:
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:
Again, e7 is connected upwards via *.
Alternative Solution: f6
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.
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.
