Puzzle design by remove-add and remove-remove-add steps

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Puzzle design by remove-add and remove-remove-add steps

Postby Thierry Moreau » Mon Jan 02, 2012 6:36 pm

Hi!

A new variant of my sudoku interactive tool is now on-line. It allows the manual search for sudoku puzzles starting from an ideal one (i.e. devoid of extra clues) and ending in a new puzzle derived by removing clues and adding different clues. Here is the summary of an sample session. I reduced the number of clues from 22 to 20 and I guess I kept the problem difficulty in the same range.

Start with an ideal sudoku problem (from HardestSudokusThread-00218):
...4...8...7..92......3...526...1.....19.....7.....1..5......4...6..29..9..8....3 pr 1
removing 9 in <9,1> opens 45 alternatives (fertile ground for remove-remove-add), but a remove-add step was preferred instead.

Remove 2 in <4,1>
...4...8...7..92......3...5.6...1.....19.....7.....1..5......4...6..29..9..8....3 pr 9
add 7 in <5,6>
...4...8...7..92......3...5.6...1.....19.7...7.....1..5......4...6..29..9..8....3 pr 10
giving a valid puzzle with an opportunity for 51 alternatives by removing 7 in <6,1>; start a remove-remove-add step from there.

Remove 7 in <6,1>
...4...8...7..92......3...5.6...1.....19.7.........1..5......4...6..29..9..8....3 pr 11
remove 6 in <8,3>
...4...8...7..92......3...5.6...1.....19.7.........1..5......4......29..9..8....3 pr 12
add 2 in <4,3>
...4...8...7..92......3...5.62..1.....19.7.........1..5......4......29..9..8....3 pr 13
giving a valid puzzle with an opportunity for 16 alternatives by removing 9 in <5,4>; start a remove-remove-add step from there.

Remove 9 in <5,4>
...4...8...7..92......3...5.62..1.....1..7.........1..5......4......29..9..8....3 pr 14
remove 9 in <8,7>
...4...8...7..92......3...5.62..1.....1..7.........1..5......4......2...9..8....3 pr 16
add 9 in <5,7>
...4...8...7..92......3...5.62..1.....1..79........1..5......4......2...9..8....3 pr 17
giving a valid puzzle with little hope for further remove-remove-add opportunities.

This manual process is assisted by the puzzle solution and investigation tool at http://sudoku.connotech.com

Further developments could include:
1) automated search for every possible remove-add and remove-remove-add steps given an ideal sudoku,
2) improvements in the site explanations and user guidance, and
3) a document describing the core algorithm, the efficiency of which makes such investigations practical.

Regards,

- Thierry
Thierry Moreau
 
Posts: 6
Joined: 20 December 2011

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