Difference between revisions of "Open problems"
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* 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? | ||
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* Is the [[center opening|center hex]] on every Hex board of [[Board_size|odd size]] a winning opening move? | * Is the [[center opening|center hex]] on every Hex board of [[Board_size|odd size]] a winning opening move? | ||
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contents="R i1 g3 e5 c7 a9"/> | contents="R i1 g3 e5 c7 a9"/> | ||
| + | === Seventh row template problem === | ||
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| + | Does there exist an [[edge template]] which guarantees a secure [[connection]] for a [[piece]] on the seventh row? | ||
| + | '''Answer:''' Yes. See [[Seventh row edge templates]]. | ||
[[category: Open problems]] | [[category: Open problems]] | ||
[[category: Forums]] | [[category: Forums]] | ||
Revision as of 02:14, 9 November 2023
- 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?
- 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.)
Contents
[hide]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.
Triangle template problem
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.
In fact, using a variant of Tom's move, it is easy to see that even the following triangle, which has more red stones, is not an edge template:
To see why, imagine that the right edge is a blue edge and that all cells outside the carrier are occupied by Blue. Note that Blue gets a 2nd-and-4th row parallel ladder. Blue wins by playing the tall variant of Tom's move:
There is in fact a template of height 8 continuing the above sequence, but it requires slightly more space:
The corresponding template of height 9 requires this much space:
Seventh row template problem
Does there exist an edge template which guarantees a secure connection for a piece on the seventh row?
Answer: Yes. See Seventh row edge templates.
