Difference between revisions of "Solutions to worst move puzzles"
m (→Approaches to solving the puzzles: added a link) |
(→Puzzle 4: fixed a typo) |
||
| (3 intermediate revisions by the same user not shown) | |||
| Line 3: | Line 3: | ||
There are several approaches to solving the worst move puzzles. The brute-force method is to try every possible move and check whether it is winning or losing, until a losing move is found. This method can be very labor intensive, especially since it is often hard to decide whether a particular move is winning or losing. | There are several approaches to solving the worst move puzzles. The brute-force method is to try every possible move and check whether it is winning or losing, until a losing move is found. This method can be very labor intensive, especially since it is often hard to decide whether a particular move is winning or losing. | ||
| − | A more principled approach is using the concept of the [[mustplay region]]. Let's say the puzzle is "Red to play the unique losing move". Since Red has a losing move, it is clear that [[passing]] would also be losing for Red. We may therefore start by asking: if it were Blue's turn in the puzzle, then how could Blue win? Once a Blue connection has been identified, we can then determine the [[carrier]] of that connection. The carrier of Blue's connection is the set of all cells that are required for the connection. If there is some cell that is not in the carrier of Blue's connection, then it is a losing move for Red. If | + | A more principled approach is using the concept of the [[mustplay region]]. Let's say the puzzle is "Red to play the unique losing move". Since Red has a losing move, it is clear that [[passing]] would also be losing for Red. We may therefore start by asking: if it were Blue's turn in the puzzle, then how could Blue win? Once a Blue connection has been identified, we can then determine the [[carrier]] of that connection. The carrier of Blue's connection is the set of all cells that are required for the connection. If there is some empty cell that is not in the carrier of Blue's connection, then it is a losing move for Red. If there is no such cell, then we must look for a different Blue connection. |
| − | Once a losing move has been found, proving that it is the ''only'' losing move is harder. However, this is not usually the objective of the puzzle | + | Once a losing move has been found, proving that it is the ''only'' losing move is harder. However, this is not usually the objective of the puzzle. |
== Solutions to individual puzzles == | == Solutions to individual puzzles == | ||
| Line 43: | Line 43: | ||
=== Puzzle 4 === | === Puzzle 4 === | ||
| − | This puzzle is a bit harder. With Blue to move, it is perhaps not immediately obvious how Blue can win. The key points for Blue are A, B, and C (and in fact, | + | This puzzle is a bit harder. With Blue to move, it is perhaps not immediately obvious how Blue can win. The key points for Blue are A, B, and C (and in fact, each one of these three moves is winning for Blue): |
<hexboard size="6x6" | <hexboard size="6x6" | ||
| Line 59: | Line 59: | ||
However, when we compute the carrier of this connection, we find that it consists of all of the empty cells on the board! So we have not yet found any losing move for Red. | However, when we compute the carrier of this connection, we find that it consists of all of the empty cells on the board! So we have not yet found any losing move for Red. | ||
| − | Now, consider what happens if Blue starts at B. After an optional bridge intrusion, Red must defend the upper left corner, and then | + | Now, consider what happens if Blue starts at B. After an optional bridge intrusion, Red must defend the upper left corner, and then Blue can get A, for example like this: |
<hexboard size="6x6" | <hexboard size="6x6" | ||
contents="R a5 d3 B d1 f4 B 1:e2 R 2:d2 B 3:e1 R 4:b2 B 5:b3 R 6:c2 B 7:c5 E *:a6,c4 S blue:area(e2,f1,f2)" | contents="R a5 d3 B d1 f4 B 1:e2 R 2:d2 B 3:e1 R 4:b2 B 5:b3 R 6:c2 B 7:c5 E *:a6,c4 S blue:area(e2,f1,f2)" | ||
| Line 83: | Line 83: | ||
/> | /> | ||
| + | '''Answer:''' d1 | ||
== See also == | == See also == | ||
Latest revision as of 03:31, 7 October 2023
Contents
Approaches to solving the puzzles
There are several approaches to solving the worst move puzzles. The brute-force method is to try every possible move and check whether it is winning or losing, until a losing move is found. This method can be very labor intensive, especially since it is often hard to decide whether a particular move is winning or losing.
A more principled approach is using the concept of the mustplay region. Let's say the puzzle is "Red to play the unique losing move". Since Red has a losing move, it is clear that passing would also be losing for Red. We may therefore start by asking: if it were Blue's turn in the puzzle, then how could Blue win? Once a Blue connection has been identified, we can then determine the carrier of that connection. The carrier of Blue's connection is the set of all cells that are required for the connection. If there is some empty cell that is not in the carrier of Blue's connection, then it is a losing move for Red. If there is no such cell, then we must look for a different Blue connection.
Once a losing move has been found, proving that it is the only losing move is harder. However, this is not usually the objective of the puzzle.
Solutions to individual puzzles
Puzzle 1
With Blue to move, Blue can win as follows, using edge template III2e:
The carrier of Blue's connection is highlighted. Since c1 is not in the carrier, c1 is a losing move for Red.
Answer: c1
Puzzle 2
With Blue to move, Blue can win as follows:
The carrier of Blue's connection is highlighted. Since d1 is not in the carrier, d1 is a losing move for Red.
Answer: d1
Puzzle 3
With Blue to move, Blue can win by playing at c4, getting a ziggurat on the right and a 3rd row ladder on the left, which b1 escapes:
The carrier of Blue's connection is highlighted. Since b5 is not in the carrier, b5 is a losing move for Red.
Answer: b5
Puzzle 4
This puzzle is a bit harder. With Blue to move, it is perhaps not immediately obvious how Blue can win. The key points for Blue are A, B, and C (and in fact, each one of these three moves is winning for Blue):
Note that A forms edge template IV2d with d1; B forms edge template II and a bridge to d1, and C forms edge template IV2h with f4.
Consider, for example, what happens if Blue starts at A. Then Blue captures the entire highlighted upper left corner, and Red must defend at B. After this, Blue plays C and threatens both a6 and c4.
However, when we compute the carrier of this connection, we find that it consists of all of the empty cells on the board! So we have not yet found any losing move for Red.
Now, consider what happens if Blue starts at B. After an optional bridge intrusion, Red must defend the upper left corner, and then Blue can get A, for example like this:
Note that after 7, Blue is again connected by edge template IV2h and a double threat at a6 and c4. Moreover, Blue 1 captures the highlighted triangle and kills f3. This means that f3 is not required for Blue's connection! Thus, the carrier of Blue's connection is the following:
Since f3 is not in the carrier, it is a losing move for Red.
In fact, after Red f3, Blue e2 is the unique winning reply.
Answer: f3
Puzzle 5
Red 1 is the unique losing move, and Blue 2 is the unique winning reply:
Answer: d1
