ronk wrote:If one removes a single clue from a minimal 9x9 sudoku, the minimum number of solutions is 2 ... but what is the maximum? On what unavoidable set ... or entwined unavoidable sets ... is this maximum based?

I suggested the concept of a "Megaclue" and exampled a clue from one of the 17 puzzles in the SF

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`+---+---+---+`

|...|24.|7..|

|.8.|...|.9.|

|.1.|...|...|

+---+---+---+

|...|8..|..6|

|7..|...|...|

|4..|...|2..|

+---+---+---+

|3..|.7.|...|

|...|...|..2|

|...|..6|.18|

+---+---+---+ remove the 7 in r7c5

+---+---+---+

|...|24.|7..|

|.8.|...|.9.|

|.1.|...|...|

+---+---+---+

|...|8..|..6|

|7..|...|...|

|4..|...|2..|

+---+---+---+

|3..|...|...|

|...|...|..2|

|...|..6|.18|

+---+---+---+ 94763 sol.

This I thought was fairly spectacular untill I removed clues from one of this 17 from one of Groyles collection which was felt to be a little extraordinary [only one 3,7,8 and no 9]

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`+---+---+---+`

|...|...|13.|

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

|42.|...|...|

+---+---+---+

|6..|...|.2.|

|..5|.1.|...|

|...|...|4..|

+---+---+---+

|.7.|4.2|...|

|...|6..|2..|

|...|...|..1|

+---+---+---+

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`+---+---+---+`

|...|...|13.|

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

|42.|...|...|

+---+---+---+

|6..|...|.2.|

|..5|...|...|

|...|...|4..|

+---+---+---+

|.7.|4.2|...|

|...|6..|2..|

|...|...|..1|

+---+---+---+ removing the 1 ar r5c5 gives 1197093 sol. I didnt expect that !

So this really is a Megaclue !!!!!

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`If any one else wants to have a bash at the megaclue.........Download the program suexk`

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`and copy to "adirectory"`

copy a notepad textfile with a string of 81 characters like this one. This is 16 clues from one of Gfroyles 17s. The one with the megaclue.

......13.....8...542.......6......2...5............4...7.4.2......6..2..........1

store this in "adirectory" as file.txt

type c:\adirectory>suexk <file.txt> s9999999999 v99999999999

and the number of solutions is caluculated in around 10 seconds

C