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Re: Minimum number of clues for 2x4 Sudokus
http://www.setbb.com/phpbb/viewtopic.php?mforum=sudoku&p=15466#15466
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Author: <a href='http://www.setbb.com/phpbb/profile.php?mforum=sudoku&mode=viewprofile&u=2555'>Afmob</a><br /><br />
Posted: Tue Feb 14, 2012 8:56 am<br /><br />
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I calculated all essentially different, uniquely solvable 2x4 Sudokus with 14 clues and my <a href="http://www.setbb.com/sudoku/viewtopic.php?p=14984&mforum=sudoku#14984" target="_blank" class="postlink">initial guess</a> of over 100,000 puzzles was way off.<br />
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There are only 8,280 essentially different puzzles which come from 6,600 essentially different solution grids. Note that the total number of solution grids is 1,673,187 (as calculated <a href="http://www.afjarvis.staff.shef.ac.uk/sudoku/" rel="nofollow" target="_blank" class="postlink">here</a>).http://www.setbb.com/phpbb/viewtopic.php?mforum=sudoku&p=15466#15466AfmobTue Feb 14, 2012 8:56 amhttp://www.setbb.com/phpbb/viewtopic.php?mforum=sudoku&p=15466#15466Minimum number of clues for 2x4 Sudokus
http://www.setbb.com/phpbb/viewtopic.php?mforum=sudoku&p=15152#15152
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Author: <a href='http://www.setbb.com/phpbb/profile.php?mforum=sudoku&mode=viewprofile&u=2555'>Afmob</a><br /><br />
Posted: Wed Nov 02, 2011 4:40 pm<br /><br />
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This is a continuation of the following <a href="http://www.setbb.com/sudoku/viewtopic.php?t=1897&start=0&mforum=sudoku" target="_blank" class="postlink">thread</a>.<br />
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I have proven that a 2x4 Sudoku needs at least 14 given clues to be uniquely solvable. I've done this by examining all essentially different patterns and their essentially different Sudokus regarding automorphisms.<br />
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There are 32,597,396 essentially different patterns (excluding ones with more than one free row or column per band) with one pattern having up to 2.5 million different puzzles.<br />
Since I haven't tested all patterns in one batch, I will calculate the total number of Sudokus being tested over the weekend.<br />
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Edit: The calculation was completed and the total number of Sudokus being tested is about 15.966 trillion (1.5966 * 10^13), so a pattern has an average of 490,000 essentially different Sudokus.http://www.setbb.com/phpbb/viewtopic.php?mforum=sudoku&p=15152#15152AfmobWed Nov 02, 2011 4:40 pmhttp://www.setbb.com/phpbb/viewtopic.php?mforum=sudoku&p=15152#15152