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. . .  . . .  . . .
. . .  . . .  . . .
. . .  . . .  . . .
++
. . .  . . .  . . .
. . .  . . .  . . .
. . .  . . .  . . .
++
. . .  . . .  . . .
. . .  . . .  . . .
. . .  . . .  . . .
Place the digits in this Sudoku such that the resulting 81 digit number formed by stringing the rows one after the other in order from top to bottom is minimum.
This one isn't too hard that a normal player could probably solve in a few minutes. But it intrigued me to create some harder puzzles which are quite enjoyable to solve...
We can change the rule that the 9 rows must form the smallest increasing sequence, which is equivalent to the following 8clue puzzle with tso's rule:
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1 . .  . . .  . . .
2 . .  . . .  . . .
3 . .  . . .  . . .
++
4 . .  . . .  . . .
5 . .  . . .  . . .
6 . .  . . .  . . .
++
7 . .  . . .  . . .
8 . .  . . .  . . .
. . .  . . .  . . .
Place the digits in this Sudoku such that the resulting 81 digit number formed by stringing the rows one after the other in order from top to bottom is minimum.
Or we can require that the 162digit number formed by the 1st row followed by the 1st column followed by the 2nd row then the 2nd column... must be minimum. The solving starts out like this:
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1 2 3  4 5 6  7 8 9
4 . .  . . .  . . .
5 . .  . . .  . . .
++
2 . .  . . .  . . .
3 . .  . . .  . . .
6 . .  . . .  . . .
++
7 . .  . . .  . . .
8 . .  . . .  . . .
9 . .  . . .  . . .
Or, we can define certain paths that run through all 81 numbers, and require that the 81digit number formed by that path must be minimum. For example, the following zigzag path is of the same difficulty of tso's original puzzle:
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0  0  0  0  0  0  0  0  0

0  0  0  0  0  0  0  0  0

0  0  0  0  0  0  0  0  0

0  0  0  0  0  0  0  0  0

0  0  0  0  0  0  0  0  0

0  0  0  0  0  0  0  0  0

0  0  0  0  0  0  0  0  0

0  0  0  0  0  0  0  0  0

0  0  0  0  0  0  0  0  0
But if we use a "spiral" path instead, the puzzles are much more fun to solve:
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0  0  0  0  0  0  0  0  0

0  0  0  0  0  0  0  0 0
  
0 0  0  0  0  0  0 0 0
    
0 0 0  0  0  0 0 0 0
      
0 0 0 0  0 0 0 0 0
       
0 0 0 0  0  0 0 0 0
     
0 0 0  0  0  0  0 0 0
   
0 0  0  0  0  0  0  0 0
 
0  0  0  0  0  0  0  0  0
And there are 2 different approaches: inbound spiral (from topleft corner to centre) and outbound spiral (from center to topleft corner).
Of course, by introducing the idea of "minimum" and "comparison of numbers" the puzzle is no longer a pure logical one, but a bit mathematical as well...