Difference between revisions of "Solutions to worst move puzzles"
(puzzle 2 solution) |
(answers for puzzles 3-5) |
||
| Line 40: | Line 40: | ||
The moves e1/f1 also block Blue's plan to play B, so they seem too strong. We're now a bit stumped, so we refer again [[Openings on 11 x 11#a9]]. We realize that not only is Red b10 strong (for Red) in combination with Red a9, but ''Blue'' b10 is also strong (for ''Blue'') against Red a9 — in other words, a9 is weak against Blue b10! The analogous statement in our puzzle is that Red f3 is weak against Blue b2. So we check if f3 is losing, and indeed, we come to the surprising fact that Red's unique losing move isn't on the top or bottom row. | The moves e1/f1 also block Blue's plan to play B, so they seem too strong. We're now a bit stumped, so we refer again [[Openings on 11 x 11#a9]]. We realize that not only is Red b10 strong (for Red) in combination with Red a9, but ''Blue'' b10 is also strong (for ''Blue'') against Red a9 — in other words, a9 is weak against Blue b10! The analogous statement in our puzzle is that Red f3 is weak against Blue b2. So we check if f3 is losing, and indeed, we come to the surprising fact that Red's unique losing move isn't on the top or bottom row. | ||
| + | |||
| + | === Puzzle 3 === | ||
| + | |||
| + | <hexboard size="4x4" | ||
| + | contents="R a1 b1 b3 B a2 a3 a4 R 1:c1 B 2:b4 R 3:d3 B 4:c2" | ||
| + | /> | ||
| + | |||
| + | === Puzzle 4 === | ||
| + | |||
| + | <hexboard size="4x4" | ||
| + | contents="R a3 B d2 R 1:d1 B 2:c2 R 3:b2 B 4:a4" | ||
| + | /> | ||
| + | |||
| + | === Puzzle 5 === | ||
| + | |||
| + | Red 1 is the unique losing move, and Blue 2 is the unique winning reply: | ||
| + | |||
| + | <hexboard size="7x7" | ||
| + | contents="R a6 e3 B b6 g4 R 1:d1 B 2:d2" | ||
| + | /> | ||
Revision as of 04:34, 2 July 2023
Contents
Puzzle 1
Red captures the cells shaded red, leaving room for only a ziggurat (shaded gray) below to connect. Blue has a 3rd row ladder escape on the left with (*). In order for Blue to win, Red should try not to intrude either the ladder escape or the ziggurat. Red 1 below achieves this, and it's in fact the unique losing move; Blue 2 is the unique winning reply.
Puzzle 2
Red's unique losing move is 1, and Blue's unique winning reply is 2:
Note that Blue captures the shaded region, hence killing Red 1. Here is a likely continuation:
How do we approach this puzzle? You could solve it with lots of trial and error, but here is one attempt at motivating the answer. Some of Blue's strongest threats at A, B, and C below:
In particular, A captures the entire corner region (shaded blue); B is a strong move in combination with d1, analogous to the combination of a9 and b10 in 11×11; and C works well with f4 in the same way c2+b5 is a strong combination on larger boards. This should make the entire bottom row unlikely candidates for Red's losing first move, because a6/b6 are connected to a5 making those too useful, and c6—f6 allow (*) to connect to bottom right even after Blue plays C.
The moves a1—c1 on the first row intrude on Blue's plan to play A, so they are also unlikely. Note that a1 is particularly tempting, because Blue b2 kills a1. However, Red still wins after Blue b2:
The moves e1/f1 also block Blue's plan to play B, so they seem too strong. We're now a bit stumped, so we refer again Openings on 11 x 11#a9. We realize that not only is Red b10 strong (for Red) in combination with Red a9, but Blue b10 is also strong (for Blue) against Red a9 — in other words, a9 is weak against Blue b10! The analogous statement in our puzzle is that Red f3 is weak against Blue b2. So we check if f3 is losing, and indeed, we come to the surprising fact that Red's unique losing move isn't on the top or bottom row.
Puzzle 3
Puzzle 4
Puzzle 5
Red 1 is the unique losing move, and Blue 2 is the unique winning reply:
