The minimum clues for the below sudoku must be more than 18 since it is constructed by 9 independent mini-puzzles, each of which needs at least 2 clues. However, 18 clues might not be enough. What is the minimum clues then?

The sudoku:

*-----------*

|123|456|789|

|456|789|123|

|789|123|456|

|---+---+---|

|231|564|897|

|564|897|231|

|897|231|564|

|---+---+---|

|312|645|978|

|645|978|312|

|978|312|645|

*-----------*

One of the mini-puzzles is:

*-----------*

|...|456|789|

|456|789|123|

|789|123|456|

|---+---+---|

|...|564|897|

|564|897|231|

|897|231|564|

|---+---+---|

|...|645|978|

|645|978|312|

|978|312|645|

*-----------*

which needs at least two hints to solve. There are 9 such independent mini-puzzles, needing at least 2*9 hints.

Another kind of mini-puzzles is in another orientation:

*-----------*

|.23|.56|.89|

|.56|.89|.23|

|.89|.23|.56|

|---+---+---|

|231|564|897|

|564|897|231|

|897|231|564|

|---+---+---|

|312|645|978|

|645|978|312|

|978|312|645|

*-----------*

One possibility will be to create hints shared by these mini-puzzles:

*-----------*

|1..|...|7..|

|.5.|.8.|...|

|...|..3|..6|

|---+---+---|

|...|5..|8..|

|.6.|...|.3.|

|..7|..1|...|

|---+---+---|

|3..|6..|...|

|...|.7.|.1.|

|..8|...|..5|

*-----------*

However, the above configure leads to many solutions. How to reduce this sudoku to its minimum hints B.W.