The New Sudoku Players' Forum

[Leren]

We're a bit off topic in this thread, but I have some code that looks for easy 12 clue X puzzles. Of the 552,952 puzzles that were made available to ruud:

1. 10,117 appear to be solvable with singles. 2. Adding intersections increases that to 88,808 and 3. Adding some naked tuples increases that to 123,267.

Leren

[m_b_metcalf]

Some postings in another thread led me to look again at ruud's half-a-million 12-clue x-sudokus.

Another curiosity is that some of the puzzles have a symmetric representation. A sample:

Hidden Text: Show

Code: Select all

 . . . . . . . . 1
 . . 2 . . . . . .
 . . . . . 3 4 . .
 . . . . 5 . . . .
 . . . 2 . . . 3 .
 . . . . 6 . . . .
 . . . . . 4 7 . .
 . . 6 . . . . . .
 . . . . . . . . 8   ED=2.0/1.2/1.2

 . . . . . . . 1 .
 2 . 3 . . . . . .
 4 . . . . . . 5 .
 . . . . . . . 6 .
 . . . . . . . . .
 . 1 . . . . . . .
 . 5 . . . . . . 7
 . . . . . . 4 . 8
 . 9 . . . . . . .   ED=2.9/1.2/1.2  rot

 . . . . . . . . 1
 . . 2 . . 3 . . .
 . . . . . . 4 . .
 . . . . . . . 5 .
 . . . 2 6 . . . .
 . . . . . . . 7 .
 . . . . . . 8 . .
 . . 3 . . 5 . . .
 . . . . . . . . 4   ED=4.0/1.2/1.2

 . . . . . . . . .
 . . . . 1 . . . .
 . . 2 . . . . 3 .
 . . . 3 . . . . .
 . 4 . . . . 5 . .
 . . . . . 6 . . .
 . . . . 7 . . . 1
 . . 6 . . . . 4 .
 . . . . . . 8 . .   ED=5.7/1.5/1.5  tr

 . . . . . . . . 1
 . . 2 . 3 . . . .
 . . . . . . 4 . .
 . . . . 2 . . . .
 . 1 . . . . 5 . .
 . . . . 6 . . . .
 . . . . . . 7 . .
 . . 3 . 8 . . . .
 . . . . . . . . 5   ED=6.3/1.5/1.5

 . . . . . . . . .
 . . . . . 1 . . 2
 . . 3 . . . 4 . .
 . . . . . . 3 . .
 . . . 1 . 5 . . .
 . . . . . . 6 . .
 . . 6 . . . 7 . .
 . . . . . 8 . . 5
 . . . . . . . . .   ED=7.1/2.9/2.9

 . . . . . 1 2 3 .
 . . . . . . 4 . .
 . . 5 . . . . . .
 . . . . . . . . .
 . 5 . . 6 . . . .
 . . . . . . . . .
 . . 7 . . . . . .
 . . . . . . 3 . .
 . . . . . 2 1 8 .   ED=7.7/2.0/2.0

 . . . . . . 1 . .
 . . . . . . 2 . .
 . . 3 . . 4 . . .
 . . . . 5 . . . .
 . . . 1 . . . . 6
 . . . . 7 . . . .
 . . 8 . . 9 . . .
 . . . . . . 5 . .
 . . . . . . 7 . .   ED=8.3/3.4/2.9

 . . . . . . 1 . .
 . . . . . . 2 . .
 . . 3 . . 4 . . .
 . . . . 1 . . . .
 . . . . . 5 6 . .
 . . . . 2 . . . .
 . . 4 . . 7 . . .
 . . . . . . 5 . .
 . . . . . . 8 . .   ED=8.5/2.0/2.0

 . . 1 . 2 . . . .
 . . . . . . . 3 .
 . . . . . . 4 . .
 . . . . 1 . . . .
 . 5 . . . . 3 . .
 . . . . 6 . . . .
 . . . . . . 7 . .
 . . . . . . . 5 .
 . . 2 . 8 . . . .   ED=9.0/1.5/1.5

 . . . . . 1 . . 2
 . . 3 . . . . . .
 . . . . . . 4 . .
 . . . . 5 . . . .
 . . . 3 . . . 6 .
 . . . . 7 . . . .
 . . . . . . 8 . .
 . . 7 . . . . . .
 . . . . . 2 . . 1   ED=9.2/1.2/1.2

 . . 1 . . . 2 . .
 . 3 . . 4 . . 5 .
 . . . . . . . . .
 . . . . . . . . .
 . . . . . 6 1 . .
 . . . . . . . . .
 . . . . . . . . .
 . 4 . . 5 . . 7 .
 . . 8 . . . 6 . .   ED=9.3/9.2/2.9


[m_b_metcalf]

Some postings in another thread led me to look again at ruud's half-a-million 12-clue x-sudokus. Here are two rated selections, the first from the beginning of his file, the second from the end (the last column is a very rough indication of the length of the solution path):

And this one is harder than those posted above:

Code: Select all

 . . . . . . . . .
 . . . . . . . . .
 . . 1 . 2 . 3 . .
 . . . . . . . . .
 . . . 4 . 5 . 6 7
 . . 2 . . . . . .
 . . 8 . . . . . .
 . . . 7 . 4 . . .
 . 6 . . . . . . .   ED=10.1/1.5/1.5

....................1.2.3..............4.5.67..2........8.........7.4....6.......

Regards,

Mike

[m_b_metcalf]

I was intrigued by the serendipitous find of such a high rating in these puzzles, so I looked for more. A systematic search yielded even higher ratings:

Code: Select all

....................1..23......4......3...1......5...65..................7..8..4.   ED=10.0/4.3/2.9 
....................1.2...3.....4..5........16..7..2.............3............87.   ED=10.1/1.5/1.5 
.................1....2.3..14...........5....67.........2...8.......6......4.....   ED=10.3/10.3/2.9
....................1.2.3........4.....5.6..7....8....65.....8.....3.............   ED=10.4/1.5/1.5 
.................1.2.............34.1.5........6.........5......3........7..8...5   ED=10.6/1.2/1.2 

including some pearls. I found that surprising.


Mike

[m_b_metcalf]

A further feature of this half-million dataset is that almost all puzzles have an ED rating of 2.9 or less (mostly 1.2). I found eight exceptions:

Code: Select all

 
....................1.2.3............4...5.6.......7...6.....4.....1....2...8....   ED=4.3/4.3/4.3   
...............1.2..3.4.............1...............5..65.7...........8.....6.2..   ED=5.7/5.7/4.3   
...............1....2.3............41.3..5..........2...6..3.........7..........8   ED=7.9/7.9/4.3   
....................1.234.......5...67.8...........2...6.....7.....1.............   ED=8.4/8.4/4.3   
...............1....2.3..............43.5...2..6.......7.....1.8...........6.....   ED=8.9/4.3/4.3   
...............1....2.3............4..3.5...........6746.....7.......8...........   ED=8.9/8.9/4.0   
...............1....2.3............4..3.5...........6776.....4.......8...........   ED=9.0/9.0/4.0   
................1.23..................4.5..........3....6.45.........7...2....8..   ED=9.5/9.5/4.3   


Nothing higher than 4.3.

Mike