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The '''grandfather problem''' is the following question, posed by [[John Conway]] in 1972 in [[Lifeline Volume 6]],<ref name=" | The '''grandfather problem''' is the following question, posed by [[John Conway]] in 1972 in [[Lifeline Volume 6]],<ref name="lifelinevol6" /> along with the [[unique father problem]]: | ||
:''Is there a configuration which has a father but no grandfather?'' | :''Is there a configuration which has a father but no grandfather?'' | ||
Revision as of 10:32, 25 August 2017
| 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 | ||||
| |||||
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?
Although a 50$ cash prize was offered by Conway, the problem remained open until May 2016, when mtve presented such a pattern.[2]
Generation
The pattern was found with Mark Owen's picosat, using an algorithm similar to the one employed by Nicolay Beluchenko's 
A196447:[3]
- 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[4]:
- 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[5].
Next levels
"A father and grandfather, but no great-grandfather" pattern[6], and a "father, grandfather and great-grandfather, but no great-great-grandfather" pattern[7], have also been constructed by the same method.
No further levels have been found yet, but they almost certainly do exist.
Also see
References
- ↑ Robert Wainwright (October 1972). Lifeline, vol 6, p. 1.
- ↑ mtve (May 5, 2016). "Re: Thread for your unsure discoveries". ConwayLife.com forums. Retrieved on June 22, 2016.
- ↑ mtve (May 6, 2016). "Re: Thread for your unsure discoveries". ConwayLife.com forums. Retrieved on June 22, 2016.
- ↑ Matthias Merzenich (Sokwe) (May 6, 2016). "Re: Thread for your unsure discoveries". ConwayLife.com forums. Retrieved on June 22, 2016.
- ↑ 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.