The New Sudoku Players' Forum

[StrmCkr]

removed

[StrmCkr]

removed

[coloin]

I hope it works out !

If it helps my furthur thoughts are.....

Its all to do with the unavoidable sets - in an attempt to complete a band

Code: Select all

+---+---+---+
|123|476|895|
|456|893|271|
|..9|152|346|
+---+---+---+
|...|...|...|
|...|...|...|
|...|...|...|
+---+---+---+
|.7.|...|...|
|...|...|...|
|...|...|...|
+---+---+---+

Code: Select all

+---+---+---+
|...|...|...|
|...|...|...|
|78.|...|...|
+---+---+---+
|...|...|...|
|...|...|...|
|...|...|...|
+---+---+---+
|87.|...|...|
|...|...|...|
|...|...|...|
+---+---+---+

The 7 clue in box 7 is necessary to be a clue in this unavoidable set

Code: Select all

+---+---+---+
|*..|...|...|
|...|..1|...|
|...|...|..1|
+---+---+---+
|...|...|...|
|.1.|...|...|
|...|...|...|
+---+---+---+
|...|...|...|
|...|...|...|
|..1|...|...|
+---+---+---+ thie clue * is inserted because of the 4 given clues

Code: Select all

+---+---+---+
|12.|...|...|
|4*.|...|...|
|...|...|..5|
+---+---+---+
|...|...|...|
|...|...|...|
|...|...|...|
+---+---+---+
|...|...|...|
|...|...|...|
|..5|...|...|
+---+---+---+ the clue * is inserted bcause of the 5 given clues

The given clues cover every unavoidable set that our inserted clue is in.

It is quite amazing that 17 clues can define a grid [all unavoidables have a clue in them]

With respect to completing a band.......
With 18 clues we only had 9 extra to define - this is easily possible with clues within the band.
With 17 clues we had 9 plus 1 more within a band to define - and we couldnt do it. We had to resort to inserting clues ouside the band, and use cross constraints to complete our band/grid.

Code: Select all

+---+---+---+    +---+---+---+
|7.3|8..|...|    |753|842|6..|
|...|6..|4..|    |891|657|432|
|2..|...|...|    |264|319|7..|
+---+---+---+    +---+---+---+
|...|...|.73|    |186|294|573|
|.4.|1..|...|    |547|1..|2..|
|...|...|...|    |932|765|8..|
+---+---+---+    +---+---+---+
|61.|...|9..|    |615|4..|927|
|...|.2.|1..|    |379|526|1..|
|..8|.7.|...|    |428|971|3..|
+---+---+---+    +---+---+---+  17 clues solves the first vertical band

With 16 clues the gulf is "exponentially" wider. We know that we are going to have to insert clues outside the band.

There will be clues in the band
There will be clues outside the band

We have two scenarios - comparing the clue distribution in our 16 attempt with our valid 17.

1.Number of clues within the band the same - but one less clue available to insert outside the band to cover the unavoidable sets.
2.One less clue in the band - one extra clue in the band which has to be covered by one less clue within the band and a similar number of clues outside the band.

If it is difficult as I think it is to cover the band with 17 clues - doing it with 16 is going to be impossible.

If we can never fill a band with 16 clues.......we can never complete a grid !
When we can get rid of the "if" it will be proof !

C

[StrmCkr]

removed

[RW]

im postulating that a minimual of 2 numbes must be list 3 times each (as all puzzles that are valid have this trait)

What's wrong with 222222221?

010000009000300800000000600000012400703000000500000000800600000000040020000700050
030600080019000000000020000700000450000031000200000000400800000060500000000000900
052400000000070100000000000000802000300000600090500000106030000000000089700000000
092300000000080100000000000107040000000000065800000000060502000400000700000900000
800000001000950000000000000000070420301600000000000000040000570600308000000000200

RW