For this kind of puzzles, so far I've (manually) worked out 6 tours/circuits/"near circuits". I've decided to show all the completed grids out. So what puzzlers need to do is just to solve the sequence of digits and the links between the cells. And the interested programmers could verify the results using computers and starting from a blank grid, backtracking all the possibilities (very challenging programming exercise I'd say, especially the knight's tour/near circuit). Okay, here are the grids:
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Sudoku Dragon (minimum numbered Wazir's tour)
Complete the grid with orthogonal links between adjacent cells such that it's a valid sudoku grid with a hamilton path and the 81 entries along the path form the minimum 81-digit number.
1 2 7 6 5 8 9 3 4
8 3 6 7 9 4 1 2 5
5 9 4 2 1 3 8 7 6
9 8 2 1 4 5 7 6 3
7 5 1 3 2 6 4 9 8
6 4 3 9 8 7 2 5 1
3 6 9 8 7 1 5 4 2
4 7 8 5 6 2 3 1 9
2 1 5 4 3 9 6 8 7
Starts from: R3C5=1
Finishes at: R1C7=9
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Sudoku Dragon 1.5 (minimum numbered Wazir's near circuit)
Complete the grid with orthogonal links between adjacent cells such that it's a valid sudoku grid with a hamilton near circuit (i.e. the starting and finishing cells must be diagonally adjacent) and the 81 entries along the circuit form the minimum 81-digit number.
1 4 8 9 6 7 2 3 5
3 2 9 4 5 8 1 7 6
5 6 7 2 1 3 4 8 9
8 9 2 1 4 5 7 6 3
6 7 1 3 2 9 8 5 4
4 5 3 7 8 6 9 2 1
9 8 5 6 7 4 3 1 2
2 3 6 8 9 1 5 4 7
7 1 4 5 3 2 6 9 8
Starts from: R3C5=1
Finishes at: R2C6=8
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Sudoku Dragon 2 (minimum numbered King's tour)
Complete the grid with orthogonal and diagonal links between adjacent cells such that it's a valid sudoku grid with a hamilton path and the 81 entries along the path form the minimum 81-digit number.
1 2 8 4 3 7 9 6 5
4 9 3 5 6 2 1 7 8
5 7 6 9 8 1 3 2 4
2 8 9 6 1 5 7 4 3
6 3 4 2 7 9 8 5 1
7 5 1 3 4 8 6 9 2
8 1 5 7 9 4 2 3 6
9 6 2 8 5 3 4 1 7
3 4 7 1 2 6 5 8 9
Starts from: R2C7=1
Finishes at: R9C9=9
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Sudoku Dragon 3 (minimum numbered King's circuit)
Complete the grid with orthogonal and diagonal links between adjacent cells such that it's a valid sudoku grid with a hamilton circuit (i.e. the starting and finishing cells must be adjacent) and the 81 entries along the circuit form the minimum 81-digit number.
1 2 6 4 3 9 5 8 7
4 8 3 5 7 2 1 9 6
5 9 7 6 8 1 3 2 4
2 5 8 9 1 6 7 4 3
9 3 4 2 5 7 8 6 1
6 7 1 3 4 8 9 5 2
8 1 5 7 6 4 2 3 9
7 6 2 8 9 3 4 1 5
3 4 9 1 2 5 6 7 8
Starts from: R2C7=1
Finishes at: R2C8=9
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Sudoku Dragon 4 (minimum numbered Knight's tour)
Complete the grid with knight-movement links between cells such that it's a valid sudoku grid with a hamilton path and the 81 entries along the path form the minimum 81-digit number.
1 6 4 3 9 8 7 5 2
7 5 3 2 6 4 9 1 8
9 2 8 5 7 1 4 6 3
4 3 7 1 2 9 5 8 6
8 1 5 6 3 7 2 4 9
6 9 2 8 4 5 3 7 1
3 8 1 7 5 2 6 9 4
5 4 6 9 1 3 8 2 7
2 7 9 4 8 6 1 3 5
Starts from: R2C8=1
Finishes at: R5C1=8
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Sudoku Dragon 4.5 (minimum numbered Knight's near circuit)
Complete the grid with knight-movement links between cells such that it's a valid sudoku grid with a hamilton near circuit (i.e. the starting and finishing cells must be diagonally adjacent) and the 81 entries along the circuit form the minimum 81-digit number.
1 7 5 9 4 3 8 6 2
4 6 3 2 7 8 5 1 9
8 2 9 5 6 1 3 4 7
9 3 4 1 2 7 6 8 5
7 1 8 4 5 6 2 9 3
6 5 2 8 3 9 4 7 1
3 9 1 6 8 2 7 5 4
5 8 7 3 1 4 9 2 6
2 4 6 7 9 5 1 3 8
Starts from: R2C8=1
Finishes at: R1C7=8
