the two runs over known 17's, each using slightly different techniques, agreed

the second one completed in 10h11m on a 3.2Ghz pentium

papy's 3 and Red Ed's 1 were corroborated

and 5 new 17's popped out

- Code: Select all
`000400000056000100000230000200000930600005000000070000370000005000004600000000000`

000406700050700000089000004000090050004000000000000200000000006500200000010000090

003450700000000000890000010005060000700000008000001020000000600010008000000000005

100000700000009030608200000000500600000000190030002000000000000500610000000000020

103000000000000060000007005008000000306000090000042100000600004070000008000300000

the second (and faster) technique used a

neighborhood tour:

For each input puzzle remove each clue, one at a time, and determine (and tour)

the valid puzzles that result when each empty cell is assigned all possible

values. This induces a partition on the input puzzles. The output is the list

of puzzles, one puzzle per line, containing two space separated fields: the

puzzle in %c form and the partition class ordinal.

each puzzle is canonicalized early to prune tours that have already been done

so there are now 36637 17 clue sudoku

here are the class size (#puzzles) and #classes with that size for the partitions induced by the tour

- Code: Select all
`1 15774`

2 3815

3 1021

4 590

5 253

6 162

7 97

8 59

9 46

10 30

11 26

12 18

13 16

14 8

15 3

16 9

17 5

18 5

19 4

20 4

21 1

22 3

23 1

24 5

25 5

27 2

28 1

30 1

31 2

32 2

33 1

37 1

38 1

41 2

42 1

50 1

55 1

87 1

173 1

560 1

616 1

e.g. "616 1" means that there was 1 class containing 616 puzzles -- take any member

from the class and tour it and it will produce 616 17's

here is the first (in row-normal canonical order) member of the 616 class:

- Code: Select all
`000000000000009100700200005090004000000000027010000006000000300041000900000670000`

here are the number of 17's per grid and the number of grids containing that number

- Code: Select all
`1 32247`

2 1504

3 228

4 80

5 18

6 20

7 7

8 3

9 1

11 1

12 1

14 1

20 1

29 1

[edit]

finally, Red Ed's and three of the new 5 were from new solution grids

- Code: Select all
`123456789456789123789231564215648937637925841948173256371862495592314678864597312`

123456789456789123798132564274593816861274935935618247312965478587341692649827351

123456789457189263869237415218963547346715892795842136531628974674591328982374651

123456789457189263896327514245863197761942358938571426382795641514638972679214835