Difference between revisions of "Open problems"
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== Formerly open problems == | == 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?<br> '''Answer:''' Yes, | + | * [[Sixth row template problem]]: Does there exist an [[edge template]] which guarantees a secure [[connection]] for a [[piece]] on the sixth row?<br> '''Answer:''' Yes, [[edge template VI1a]] is such a template. |
* Are the templates below valid in their generalization to larger sizes? (This problem was posed by [[Jory]] in the [http://www.littlegolem.net/jsp/forum/topic2.jsp?forum=50&topic=167 Little Golem forum].) <br> <hexboard size="1x1" | * Are the templates below valid in their generalization to larger sizes? (This problem was posed by [[Jory]] in the [http://www.littlegolem.net/jsp/forum/topic2.jsp?forum=50&topic=167 Little Golem forum].) <br> <hexboard size="1x1" | ||
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coords="none" | coords="none" | ||
visible="area(c1,a3,c3)" | visible="area(c1,a3,c3)" | ||
| − | contents="R c1"/><hexboard size="4x4" | + | contents="R c1 c3"/><hexboard size="4x4" |
float="inline" | float="inline" | ||
edges="bottom" | edges="bottom" | ||
Revision as of 22:03, 5 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 the 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 is 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?
Answer: Yes, edge template VI1a is such a template.
- Are the templates below valid in their generalization to larger sizes? (This problem was posed by Jory in the Little Golem forum.)
Answer: No. The first one in the sequence that is not connected is the one of height 8. Instead, it requires this much space:
The corresponding template of height 9 requires this much space:
