Difference between revisions of "Sixth row template problem"
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== Possible paths to answer == | == Possible paths to answer == | ||
| + | ===By "hand"...=== | ||
| + | ====...answering "Yes" ==== | ||
| + | This would involve placing a stone on the 6th row of a sufficiently wide board, and showing how to always connect to the bottom. (Note this does not necessarily identify the minimal template needed.) | ||
| + | |||
| + | Here is a start. Just from edge [[Edge template IV1a]], Blue's first move must be one of the following: | ||
| + | <hex> | ||
| + | R6 C19 Q0 | ||
| + | 1:BBBBBBBBBRBBBBBBBBB | ||
| + | Si2 Sj2 | ||
| + | Si3 | ||
| + | Sg4 Sh4 Si4 Sj4 | ||
| + | Sf5 Sg5 Sh5 Si5 Sj5 | ||
| + | Se6 Sf6 Sg6 Sh6 Si6 Sj6 | ||
| + | </hex> | ||
| + | Many of these moves will be easy to dismiss. Others will benefit from the [[Parallel ladder]] trick. Of course, symmetry will cut our work in half! | ||
| + | |||
| + | ====...answering "No" ==== | ||
| + | This would involve showing how to connect (in the diagram above) the Blue stones to the right (plus Blue stones on the far right edge) to Blue stones on the left (plus Blue stones on the far left edge), no matter how wide the board is. | ||
| + | |||
=== Computer Aided demonstration ... === | === Computer Aided demonstration ... === | ||
==== ... answering "Yes" ==== | ==== ... answering "Yes" ==== | ||
Revision as of 03:59, 10 January 2009
As of January 2009 the following problem is still open. Javerberg-Wccanard Problem is simply put as follow.
Is there any one stone sixth row template ?
It is still unknown whether one stone edge templates can be found for every heights. Such templates have been found for sizes up to 5 but none above. Answering with "No" to the former question answers the latter.
Contents
Description
Is there a width n such that the game on the board of width n designed as follow with turn to Blue is won by Red ?
Generalisation
The general problem of knowing if there is n such that there is no one stone edge template on the n^th row<math>n^th</math> is also referred to as Javerberg-Wccanard Problem.
Possible paths to answer
By "hand"...
...answering "Yes"
This would involve placing a stone on the 6th row of a sufficiently wide board, and showing how to always connect to the bottom. (Note this does not necessarily identify the minimal template needed.)
Here is a start. Just from edge Edge template IV1a, Blue's first move must be one of the following:
Many of these moves will be easy to dismiss. Others will benefit from the Parallel ladder trick. Of course, symmetry will cut our work in half!
...answering "No"
This would involve showing how to connect (in the diagram above) the Blue stones to the right (plus Blue stones on the far right edge) to Blue stones on the left (plus Blue stones on the far left edge), no matter how wide the board is.
Computer Aided demonstration ...
... answering "Yes"
Such a proof would use the computer to find the template and it's carrier. Afterwards it should be easy to manually check that every Blue intrusion does not prevent Red from connecting to bottom.
... answering "No"
TODO
See Also
External link
- The thread were the names were associated.
