Difference between revisions of "Open problems"
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* Are there cells other than a1 and b1 which are theoretically losing first moves? | * Are there cells other than a1 and b1 which are theoretically losing first moves? | ||
| − | * Is it true that for every cell (defined in terms of direction and distance from an [[acute corner]]) there is an ''n'' such that for any [[Board]] of size at least ''n'' that cell is a losing [[opening move]]? | + | * Is it true that for every cell (defined in terms of direction and distance from an [[Board#Corners|acute corner]]) there is an ''n'' such that for any [[Board]] of size at least ''n'' that cell is a losing [[opening|opening move]]? |
* Conversely, is it true that, for example, c3 is a winning first move on every Hex board of size at least 5? | * Conversely, is it true that, for example, c3 is a winning first move on every Hex board of size at least 5? | ||
| − | * | + | * Seventh row template problem: Does there exist an [[edge template]] which guarantees a secure [[connection]] for a [[piece]] on the seventh row? |
| − | * Is the [[center hex]] on every Hex board of [[ | + | * Is the [[center opening|center hex]] on every Hex board of [[Board_size|odd size]] a winning opening move? |
| − | * | + | * On boards of all [[board size|sizes]], is every opening move on the [[Board#Diagonals|short diagonal]] winning? |
| + | |||
| + | * Is the following true? Assume one player is in a winning position (will win with [[optimal play]]) and opponent plays in a hex X. Let the set A consist of all empty hexes that are members of any path between opponents edges that uses the stone at X. If A is non-empty, A contains a winning move. Otherwise any move are winning, even [[passing]] the turn. (This problem was posed by [[Jory]] in the [http://www.littlegolem.net/jsp/forum/topic2.jsp?forum=50&topic=167 Little Golem forum].) | ||
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| + | == Formerly open problems == | ||
| + | |||
| + | * [[Sixth row template problem]]: Does there exist an [[edge template]] which guarantees a secure [[connection]] for a [[piece]] on the sixth row? The answer is yes, and [[edge template VI1a]] is such a template. | ||
[[category: Open problems]] | [[category: Open problems]] | ||
Revision as of 02:14, 4 October 2021
- Are there cells other than a1 and b1 which are theoretically losing first moves?
- Is it true that for every cell (defined in terms of direction and distance from an acute corner) there is an n such that for any Board of size at least n that cell is a losing opening move?
- Conversely, is it true that, for example, c3 is a winning first move on every Hex board of size at least 5?
- Seventh row template problem: Does there exist an edge template which guarantees a secure connection for a piece on the seventh row?
- Is the center hex on every Hex board of odd size a winning opening move?
- On boards of all sizes, is every opening move on the short diagonal winning?
- Is the following true? Assume one player is in a winning position (will win with optimal play) and opponent plays in a hex X. Let the set A consist of all empty hexes that are members of any path between opponents edges that uses the stone at X. If A is non-empty, A contains a winning move. Otherwise any move are winning, even passing the turn. (This problem was posed by Jory in the Little Golem forum.)
Formerly open problems
- Sixth row template problem: Does there exist an edge template which guarantees a secure connection for a piece on the sixth row? The answer is yes, and edge template VI1a is such a template.
