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While playing with this symmetric x-sudoku

Code: Select all

 . . 1 . . . . . 2
 . . . . 3 2 . . 4
 . . . . . 5 . . 1
 . . . . . . . . 3
 . 2 . . . . . 6 .
 7 . . . . . . . .
 8 . . 3 . . . . .
 1 . . 6 9 . . . .
 9 . . . . . 4 . .   ED=5.7/1.2/1.2, 18 clues

..1.....2....32..4.....5..1........3.2.....6.7........8..3.....1..69....9.....4..                   


I inadvertently copied it incorrectly such that top row was empty and the others pushed down by one, causing the bottom row to disappear. To my surprise, the resulting configuration also turned out to be a valid x-sudoku:

Code: Select all

 . . . . . . . . .
 . . 1 . . . . . 2
 . . . . 3 2 . . 4
 . . . . . 5 . . 1
 . . . . . . . . 3
 . 2 . . . . . 6 .
 7 . . . . . . . .
 8 . . 3 . . . . .
 1 . . 6 9 . . . .   ED=9.2/1.2/1.2, 16 clues

...........1.....2....32..4.....5..1........3.2.....6.7........8..3.....1..69....   

How likely is that?

Mike

Very strange, but amusing.
Shifting the puzzle to the right, left or up will give a puzzle with multiple solutions

I tried it on standard puzzles too, and found 4 similar ones in the first 28,000 from the Patterns Game. Here's the first:

Code: Select all

 . 1 2 . 3 . . . 4
 . 5 . . . 4 1 . .
 4 . . . 6 . . 7 .
 . . 8 4 2 . . 6 .
 . . . . . 7 4 . 1
 . . . . . 9 . . .
 . 7 . . . 3 . . 9
 . . 5 . . . . 2 3
 . . . . . . 7 . .   ED=5.7/4.7/2.6

.12.3...4.5...41..4...6..7...842..6......74.1.....9....7...3..9..5....23......7..   dobrichev

 . . . . . . . . .
 . 1 2 . 3 . . . 4
 . 5 . . . 4 1 . .
 4 . . . 6 . . 7 .
 . . 8 4 2 . . 6 .
 . . . . . 7 4 . 1
 . . . . . 9 . . .
 . 7 . . . 3 . . 9
 . . 5 . . . . 2 3   ED=2.0/1.2/1.2

..........12.3...4.5...41..4...6..7...842..6......74.1.....9....7...3..9..5....23

Very strange indeed ! Especially for the X-sudoku. The probability to maintain the diagonals seems incredible !
phil

The diagonals is not so incredible as I've noticed in creating X solutions that sometimes multiple other diagonals solve as well.