There are pattens that can't provide a single-solution vanilla sudoku.

I am hoping that this may inspire some programmer (other than myself) to test if it would be feasible to try it out.

In a PM grid ....

- Code: Select all
`. . . | a b c | . . .`

. . d | . . . | e . .

. f . | . . . | . g .

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

h . . | . . . | . . i

j . . | . . . | . . k

l . . | . . . | . . m

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

. n . | . . . | . o .

. . p | . . . | q . .

. . . | r s t | . . .

cells containing given clues are labelled (in this example alphabetically) .... notice that labelling is sorted incrementally.

While candidate cells are labelled numerically

- Code: Select all
`01 02 03 | . . . | 07 08 09`

10 11 . | 13 14 15 | . 17 18

19 . 21 | 22 23 24 | 25 . 27

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

. 29 30 | 31 32 33 | 34 35 .

. 38 39 | 40 41 42 | 43 44 .

. 47 48 | 49 50 51 | 52 53 .

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

55 . 57 | 58 59 60 | 61 . 63

64 65 . | 67 68 69 | . 71 72

73 74 75 | . . . | 79 80 81

also note that cells' labels are sorted incrementally

If you can get an automorphic puzzle (through symmetry operations) where candidate cells labels are not incrementally sorted then this provides a proof that this pattern will ALWAYS produce multiple solutions.

Now,

Correct me if I'm wrong. If all possible isomorphically different 16 clue patterns undergo this process we would then prove that a valid 16 puzzle cannot exist. If it can exist then we can tell through which pattern & limit our search for that elusive 16.

tarek