Mosch - I think the various ways one can portray essentially similar grids is confusing.....there are 29 17s in this grid...it is a representation of the SF grid...see page 19 of the minimum clues thread.

As to the likelihood of a 16.......well I hate to agree that it is unlikely but it is looking that way.....it depends really on how Gordon's program searched the space.

The number of 17s in a 16 [if there was one] would indeed be 65 non-minimal plus there would also be a few minimal ones.......so thats a few more reasons to have found the grid - if it was there.

We would indeed like to know what proportion of randomly produced 17grids are in Gordon's list. A problem exists however that although Gordon can find 17s - it is very difficult to get a 17 from a grid even from one which we know has at least one in it.

Wolfgang has a program which analyses a grid and the rookeries......possibly similar to the suexsf program from dukuso.

Take the following four grids

- Code: Select all
`grid SF SFB Random 17 [number 1122] Random`

suexsf value 24.10 24.02 24.17 24.42

number of 17s 29 3 1 0

number of 18s* 2076 [71] 240 [80] 89 [89] 1 [estimate]

number of 19s* 75211 10089 4182 80 [estimate]

where * is the number of puzzles generated using a "backbone" of the grid - there may well be many more 18s & 19s.

The suexsf value - indicates suitable grids that might have a 17 - but is fairly non specific.

The suexsf program from dukuso is a program which calculates the occurance rate of clues in a large number of minimal sudoku puzzles - all generated from one particular valid grid. It can be used to pinpoint the backbone of 14 clues in the SF.....I will provide more details if anyone is interested.

Here is the backbone of the SF [Strangely Familiar grid - 29 sudoku puzzle grids]

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

|...|.4.|7..|

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

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

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

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

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

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

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

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

|...|...|...|

|...|..6|.18| 14 clues - 29 different ways to add 3 more clues.

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

and here is the output at clue 14

- Code: Select all

58 0 265 290 1694 0 1689 0 154

285 1694 0 7 86 190 0 246 186

240 1694 774 222 0 0 175 319 51

0 91 105 1694 110 54 107 63 1674

1694 0 97 219 201 197 0 134 36

1694 138 20 85 112 162 1671 206 236

1691 45 427 216 1694 0 201 206 265

0 114 222 215 207 197 77 242 385

0 0 182 103 212 1670 46 1693 1694

these are the counts of clues in 17,18,19,20,21,22 minimal sudoku puzzles generated at random from the SF grid. The "best" clues are fixed at each step.

But it has not been perfected [or automised or fast] to reliably get 17s from a grid containing a 17.

I would be interested to see how others determine 17s from a grid and maybe we can answer Gordons's question.

C