- Code: Select all
`+---+---+---+`

|.23|456|789|

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

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

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

|8..|...|...|

|9..|...|...|

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

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

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

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

|6..|...|...|

+---+---+---+ 16 clues

But 16 clues can define a large proportion of the grid to make one complete box, one complete row and one complete column -

- Code: Select all
`+---+---+---+ +---+---+---+`

|..3|456|7.9| |123|456|789|

|4.6|...|.5.| |496|...|.5.|

|78.|...|...| |785|...|...|

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

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

|8..|...|...| |8..|...|...|

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

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

|9..|...|...| |9..|...|...|

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

|...|...|...| |6..|...|...|

+---+---+---+ 16 clues +---+---+---+

Even better - more box envolvement

- Code: Select all
`+---+---+---+ +---+---+---+`

|...|3.1|...| |5.9|3.1|...|

|2.4|...|...| |2.4|.95|13.|

|...|...|...| |1.3|...|59.|

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

|8..|52.|...| |891|523|...|

|...|...|9.1| |35.|...|9.1|

|...|...|3..| |74.|91.|3.5|

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

|..7|.4.|.5.| |627|149|853|

|91.|...|...| |915|.3.|...|

|.3.|...|...| |438|.5.|.19|

+---+---+---+ 16 clues +---+---+---+ 190 grid solutions

If we were unable to make fill a grid to this extent with 16 clues then this this might have been a proof for....

The number of grid solutions with 16 clues is always = 0 or > 1........[i.e. never 1]

It might be impossible getting this complete box/row/colum pattern with only 15 clues......therefore proof for ?15

C