Grandfather problem: Difference between revisions
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Conway offered a $50 cash prize to "the first person to settle the grandfather problem either way". But the problem of a '''grandfatherless''' pattern remained open until May {{year|2016}}, when "[[mtve]]" presented such a pattern.<ref name="mtve1" /> | Conway offered a $50 cash prize to "the first person to settle the grandfather problem either way". But the problem of a '''grandfatherless''' pattern remained open until May {{year|2016}}, when "[[mtve]]" presented such a pattern.<ref name="mtve1" /> {{POTY|name=This pattern|year=2016|rank=3|behind=the [[copperhead]] and the [[Caterloopillar]]s}} | ||
==Generation== | ==Generation== | ||
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|author = mtve | |author = mtve | ||
|date = May 5, 2016 | |date = May 5, 2016 | ||
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<ref name="mtve2">{{LinkForumThread | <ref name="mtve2">{{LinkForumThread | ||
Revision as of 20:19, 30 September 2021
| Grandfather problem | |||||||
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| Pattern type | Problem | ||||||
|---|---|---|---|---|---|---|---|
| Number of cells | 298 | ||||||
| Bounding box | 24 × 23 | ||||||
| Static symmetry | Unspecified | ||||||
| Discovered by | mtve | ||||||
| Year of discovery | 2016 | ||||||
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The grandfather problem is the following question, posed by John Conway in 1972 in Lifeline Volume 6,[1] along with the unique father problem:
- Is there a configuration which has a father but no grandfather?
Conway offered a $50 cash prize to "the first person to settle the grandfather problem either way". But the problem of a grandfatherless pattern remained open until May 2016, when "mtve" presented such a pattern.[2] This pattern ranked third place in the Pattern of the Year 2016 competition on the ConwayLife.com forums, behind the copperhead and the Caterloopillars.[3]
Generation
The pattern was found with the PicoSAT SAT solver, using an algorithm similar to the one employed by Nicolay Beluchenko to discover 
A196447:[4]
- Try setting the next cell on and off;
- Skip first level Gardens of Eden;
- Choose the minimum number of grandparents, where "minimum number" is not the exact number but a minimal distance between first and last.
The final configuration has a total of 17920 parents, but no grandparents.
Verification
"mtve"'s discovery was confirmed to solve the grandfather problem by Matthias Merzenich with JLS, using the following steps[5]:
- Run a search to find all 1-generation predecessors of mtve's pattern. Copy the cells that had the same setting in all solutions to the pattern.
- Mark all of unset cells with "X", increase the period by 1 and shift the pattern to the future by 1 generation. Set the outer cells to "X" in generation 0 and run another search, which eventually gives "Search finished: 0 solutions found".
Optimization
It is possible to reduce the size of this pattern by removing some cells, and also some other patterns with the same property exist[6].
Next levels
"A father and grandfather, but no great-grandfather" pattern[7], and a "father, grandfather and great-grandfather, but no great-great-grandfather" pattern[8], have also been constructed by the same method.
No further levels have been found yet, but they almost certainly do exist.
References
- ↑ Robert Wainwright (October 1972). Lifeline, vol 6, p. 1.
- ↑ mtve (May 5, 2016). Re: Thread for your unsure discoveries (discussion thread) at the ConwayLife.com forums
- ↑ Alexey Nigin (June 3, 2017). Pattern of the Year 2016 (Results) (discussion thread) at the ConwayLife.com forums
- ↑ mtve (May 6, 2016). Re: Thread for your unsure discoveries (discussion thread) at the ConwayLife.com forums
- ↑ Matthias Merzenich (May 6, 2016). Re: Thread for your unsure discoveries (discussion thread) at the ConwayLife.com forums
- ↑ mtve (June 2016). "Garden Of Eden 2G". Retrieved on July 8, 2016.
- ↑ mtve (June 2016). "Garden Of Eden 3G". Retrieved on July 8, 2016.
- ↑ mtve (December 12, 2016). "Garden Of Eden 4G". Retrieved on December 14, 2016.
External links
- Grandfatherless at the Life Lexicon