Problem 1966. Kaggle: Reverse Game of Life - Single Move to One Cell Case

Created by Richard Zapor

Solve Later

{"relationships":[{"relationshipType":"http://schemas.mathworks.com/matlab/code/2013/relationships/document","targetMode":"","relationshipId":"rId1","target":"/matlab/document.xml"},{"relationshipType":"http://schemas.mathworks.com/matlab/code/2013/relationships/output","targetMode":"","relationshipId":"rId2","target":"/matlab/output.xml"}],"parts":[{"partUri":"/matlab/document.xml","relationship":[],"contentType":"application/vnd.mathworks.matlab.code.document+xml","content":"<?xml version=\"1.0\" encoding=\"UTF-8\"?>\n<w:document xmlns:w=\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\"><w:body><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:hyperlink w:docLocation=\"http://www.kaggle.com/c/conway-s-reverse-game-of-life\"><w:r><w:t>Kaggle's Conway's Reverse Game of Life</w:t></w:r></w:hyperlink><w:r><w:t> contest inspires this Single Reverse step in Life challenge. The kaggle contest runs from Oct-14-2013 thru Mar-02-2014. References:</w:t></w:r><w:r><w:t> </w:t></w:r><w:hyperlink w:docLocation=\"http://mathworld.wolfram.com/GameofLife.html\"><w:r><w:t>Game of Life at Wolfram</w:t></w:r></w:hyperlink><w:r><w:t>.</w:t></w:r><w:r><w:t> </w:t></w:r><w:hyperlink w:docLocation=\"http://en.wikipedia.org/wiki/Conway%27s_Game_of_Life\"><w:r><w:t>Wiki Life</w:t></w:r></w:hyperlink><w:r><w:t>.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"code\"/></w:pPr><w:r><w:t><![CDATA[1. Any live cell with fewer than two live neighbors dies, as if caused by under-population.\n2. Any live cell with two or three live neighbors lives on to the next generation.\n3. Any live cell with more than three live neighbors dies, as if by overcrowding.\n4. Any dead cell with exactly three live neighbors becomes a live cell, as if by reproduction.\n5. No wrap around. Beyond edge is zero. Eight Neighbors.]]></w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>Find all the 4x4 Life matrices that upon one evolution produce a single living cell. This is a single evolution reversal set. The 4x4 gets appended by a ring of zeros for processing. The single living cell may be anywhere in the final 6x6 matrix, but none are expected to occur in the outer ring for a valid solution.</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:rPr><w:b/></w:rPr><w:t>Input:</w:t></w:r><w:r><w:t> None</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:rPr><w:b/></w:rPr><w:t>Output:</w:t></w:r><w:r><w:t> Cell array of unique 4x4 matrices that evolve to a single cell</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:rPr><w:b/></w:rPr><w:t>Scoring:</w:t></w:r><w:r><w:t> 600 - (Number of valid unique 4x4 matrices)</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:rPr><w:b/></w:rPr><w:t>Examples:</w:t></w:r><w:r><w:t> A few valid matrices that produce a single cell</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"code\"/></w:pPr><w:r><w:t><![CDATA[0000 0010 1101\n0001 1000 1110\n0000 0000 0100\n0101 0110 1001]]></w:t></w:r></w:p></w:body></w:document>"},{"partUri":"/matlab/output.xml","contentType":"text/xml","content":"<?xml version=\"1.0\" encoding=\"UTF-8\" standalone=\"no\" ?><embeddedOutputs><metaData><evaluationState>manual</evaluationState><layoutState>code</layoutState><outputStatus>ready</outputStatus></metaData><outputArray type=\"array\"/><regionArray type=\"array\"/></embeddedOutputs>"}]}

<a href = "http://www.kaggle.com/c/conway-s-reverse-game-of-life">Kaggle's Conway's Reverse Game of Life</a> contest inspires this Single Reverse step in Life challenge. The kaggle contest runs from Oct-14-2013 thru Mar-02-2014. References: <a href = "http://mathworld.wolfram.com/GameofLife.html">Game of Life at Wolfram</a>. <a href = "http://en.wikipedia.org/wiki/Conway%27s_Game_of_Life">Wiki Life</a>.<pre class="language-matlab">1. Any live cell with fewer than two live neighbors dies, as if caused by under-population.
2. Any live cell with two or three live neighbors lives on to the next generation.
3. Any live cell with more than three live neighbors dies, as if by overcrowding.
4. Any dead cell with exactly three live neighbors becomes a live cell, as if by reproduction.
5. No wrap around. Beyond edge is zero. Eight Neighbors.
</pre>Find all the 4x4 Life matrices that upon one evolution produce a single living cell. This is a single evolution reversal set. The 4x4 gets appended by a ring of zeros for processing. The single living cell may be anywhere in the final 6x6 matrix, but none are expected to occur in the outer ring for a valid solution.Input: NoneOutput: Cell array of unique 4x4 matrices that evolve to a single cellScoring: 600 - (Number of valid unique 4x4 matrices)Examples: A few valid matrices that produce a single cell<pre class="language-matlab">0000 0010 1101
0001 1000 1110
0000 0000 0100
0101 0110 1001
</pre>

<http://www.kaggle.com/c/conway-s-reverse-game-of-life Kaggle's Conway's Reverse Game of Life> contest inspires this Single Reverse step in Life challenge. The kaggle contest runs from Oct-14-2013 thru Mar-02-2014. References: <http://mathworld.wolfram.com/GameofLife.html Game of Life at Wolfram>. <http://en.wikipedia.org/wiki/Conway%27s_Game_of_Life Wiki Life>.

1. Any live cell with fewer than two live neighbors dies, as if caused by under-population.
  2. Any live cell with two or three live neighbors lives on to the next generation.
  3. Any live cell with more than three live neighbors dies, as if by overcrowding.
  4. Any dead cell with exactly three live neighbors becomes a live cell, as if by reproduction.
5. No wrap around. Beyond edge is zero. Eight Neighbors.

Find all the 4x4 Life matrices that upon one evolution produce a single living cell. This is a single evolution reversal set. The 4x4 gets appended by a ring of zeros for processing. The single living cell may be anywhere in the final 6x6 matrix, but none are expected to occur in the outer ring for a valid solution.

*Input:* None

*Output:* Cell array of unique 4x4 matrices that evolve to a single cell

*Scoring:* 600 - (Number of valid unique 4x4 matrices)

*Examples:*  A few valid matrices that produce a single cell

0000  0010  1101
  0001  1000  1110
  0000  0000  0100
  0101  0110  1001

Solve

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Last Solution submitted on Apr 18, 2023

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3 Comments

Osman on 26 May 2019

Is it possible to correct the test suite? I have 8 cases where they are not accepted by test suite even though they evolve to having one cell.

Apart from that, is the minimum achievable score 0?. i.e. are there 600 combinations ending with one cell? Since even if I solve the problem mentioned in my first paragraph, I end up with 552 cases ending with one cell. Can someone please enlighten me on this?

Rafael S.T. Vieira on 4 Jul 2020

Testing for alive cells at the borders makes no difference to the solution apparently.

Richard Zapor on 2 Oct 2020

I only find 544 cases. Back in the day scoring could be a function of performance. Thus a score of zero was not expected. Scoring is now code size thus I will need to tweak the passing criteria to some minimum unique solutions.

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Problem 1966. Kaggle: Reverse Game of Life - Single Move to One Cell Case

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Problem 1966. Kaggle: Reverse Game of Life - Single Move to One Cell Case

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