The New Sudoku Players' Forum

by ab » Tue May 16, 2006 4:04 pm

I love your self referential puzzles Red ed and the minimal 29er is excellent. I'll give that an honourable mention, since it beats the current record, but it won't make the list because it has no symmetry

by **Ruud** » Tue May 16, 2006 5:26 pm

Red Ed wrote:OK, how about this: a minimal 29-stepper
Code: Select all
. 9 . . 8 . 2 . . . 1 . . . . 5 . . . 3 . . . . . 4 . . . . 6 . 3 4 . . 8 . . . . . . . . 5 . . . . . . . . . . . 1 . . . . 7 . . . . . . . 8 9 9 . . . 6 . . . .

Beautiful!

Let me propose this slight alteration that tells us a little more:

Code: Select all: 9 . .|. 3 .|. 5 . 7 . .|. . .|. 1 . . 8 .|. . .|. 4 . -----+-----+----- 8 . .|2 . 4|. . . . . .|. . .|3 . . . . .|. . .|7 . . -----+-----+----- . . 6|1 . .|. . . . 3 5|. . .|. . . . . .|. 2 .|5 . .

This puzzle is created by ED. Let us assume E=5, D=4.

Split the rows 5/4. The sum of the clues in the first 5 rows = 54 (ED). The sum of the last 4 rows = 29 (# steps)

Split the columns 5/4. The sum of the clues in the first 5 columns = 54 (ED). The sum of the last 4 columns = 29 (# steps)

Now the puzzle contains 'some symmetry' and should make it on the list.

Ruud.

by **Red Ed** » Tue May 16, 2006 5:27 pm

ab wrote:Also worth a mention are two 27 step non-symmetric puzzles posted by JPF and one 29 step non-symmetric puzzle posted by Red Ed, all taken from gfroyle's list of 17 clue puzzles:

My 29 is not taken (directly) from Gordon's list; it's derived from one of the puzzles there by inserting a new clue and changing two existing ones. I cheated, sure, but I did some work in the process.

Ah, just seen Ruud's post. Thank you -- of course I agree entirely

by **Ocean** » Tue May 16, 2006 8:28 pm

An 8-stepper with 19 clues. Minimal and with rotational symmetry.

Code: Select all: M19. 8 steps. # ...|...|.12 3..|..4|... ...|..5|..6 ---+---+--- ...|...|57. ..6|.3.|4.. .52|...|... ---+---+--- 7..|4..|... ...|6..|..1 83.|...|...

And a 23-stepper. 19 clues, minimal, rotational symmetry.

Code: Select all: M19. 23 steps. # ...|...|... ...|.12|..3 4..|...|56. ---+---+--- ...|..3|.12 ...|.7.|... 85.|9..|... ---+---+--- .23|...|..6 9..|48.|... ...|...|...

by **Red Ed** » Tue May 16, 2006 9:33 pm

Ocean wrote:And a 23-stepper. 19 clues, minimal, rotational symmetry.

If you change a few digits, you can turn that into a minimal 25-stepper:

Code: Select all: . . .|. . .|. . . . . .|. 8 2|. . 7 4 . .|. . .|5 6 . -----+-----+----- . . .|. . 3|. 1 2 . . .|. 7 .|. . . 8 5 .|9 . .|. . . -----+-----+----- . 2 3|. . .|. . 6 7 . .|4 9 .|. . . . . .|. . .|. . .

ab wrote:won't make the list because it has no symmetry

OK, how about this self-referential reflection-symmetric 25-stepper:

Code: Select all: . 1 4 . . . 5 2 . 2 . . 5 . 1 . . 7 . . . 4 . 2 . . . . . . 3 . 8 . . . . 3 7 . . . 1 8 . 5 . . . . . . . 6 4 . . . . . . . 2 1 . . 6 . 5 . . 8 . 5 6 . . . 3 7 .

by ab » Wed May 17, 2006 6:44 pm

Fantastic

I look forward to seeing a self referential 33 stepper

by **Red Ed** » Wed May 17, 2006 9:32 pm

Sudokus are just glorified Latin squares, right? So I thought it only appropriate to give you a symmetric self-referential puzzle with Roman XX = 20 steps.

Code: Select all: . . .|. . .|. . . 1 . .|4 . 2|. . 5 5 . .|7 . 3|. . 2 -----+-----+----- . 1 8|. . .|9 7 . . 6 5|. . .|1 2 . . 2 7|. . .|4 5 . -----+-----+----- 7 . .|9 . 6|. . 1 2 . .|3 . 1|. . 9 . . .|. . .|. . .

by ab » Wed May 17, 2006 10:06 pm

you must be aware that there's a 24 stepper in that there puzzle:

Code: Select all: . . .|. . .|. . . 1 . .|4 . 2|. . 5 5 . .|7 . 3|. . 2 -----+-----+----- . 1 8|. . .|9 7 . . 6 .|. . .|. 2 . . . 7|. . .|4 . . -----+-----+----- 7 . .|9 . 6|. . 1 2 . .|3 . 1|. . 9 . . .|. . .|. . .

by **Red Ed** » Wed May 17, 2006 10:11 pm

Nope, I didn't spot that ... but then I was looking specifically for self-referential puzzles.

Compensating for the loss of self-referentiality, your new puzzle is now minimal.

If you go a little further and relabel some of the cells then you can get a 26, albeit a non-minimal one, with your revised clue positions:

Code: Select all: . . .|. . .|. . . 1 . .|4 . 2|. . 5 5 . .|9 . 3|. . 2 -----+-----+----- . 1 8|. . .|4 7 . . 6 .|. . .|. 2 . . . 7|. . .|9 . . -----+-----+----- 2 . .|7 . 6|. . 1 6 . .|3 . 1|. . 9 . . .|. . .|. . .

Perhaps you can go further still with this pattern, I don't know.

by **Ocean** » Thu May 18, 2006 8:08 am

Red Ed wrote:
Ocean wrote:And a 23-stepper. 19 clues, minimal, rotational symmetry.
If you change a few digits, you can turn that into a minimal 25-stepper:

Good. Here is an even more spectacular pattern. First, a 28-stepper (20 clues, minimal):

Code: Select all: M20. 28 steps. # ...|...|.1. ..2|...|.34 5..|.26|... ---+---+--- ...|.67|... 1..|...|..3 ...|58.|... ---+---+--- ...|41.|..9 27.|...|6.. .5.|...|...

Then, at the opposite end, a 5-stepper:

Code: Select all: M20. 5 steps. # ...|...|.1. ..2|...|.34 5..|.67|... ---+---+--- ...|.31|... 7..|...|..5 ...|48.|... ---+---+--- ...|24.|..9 38.|...|6.. .1.|...|...

And also two more replacements:

Code: Select all: M20. 6 steps. 000000010002000034400056000000041000600000007000380000000230009780000500010000000 .......1...2....344...56.......41...6.......7...38.......23...978....5...1....... # M20. 7 steps. 000000010002000034300051000000036000700000002000810000000490007160000500020000000 .......1...2....343...51.......36...7.......2...81.......49...716....5...2.......

by **Red Ed** » Thu May 18, 2006 9:59 pm

This is a public service broadcasting announcement.

For "fun", I've compiled all the inferiors so far into a computer-readable list. It's shown below with:

field 1 = symmetry type
field 2 = number of steps
field 3 = 'M' if fully minimal; 'SM' if symmetric minimal; '-' if no symmetry
field 4 = number of clues *** new as of Sun 21st May ***
field 5 = the puzzle itself
field 6 = author
field 7 = puzzle number in ab's list at the start of this thread

The symmetry types are enumerated in Gordon Royle's paper here. In short:

Type I = Full dihedral symmetry
Type II = Full rotational symmetry
Type III = Horizontal and vertical reflection
Type IV = Diagonal and anti-diagonal reflection
Type V = 180-degree rotational symmetry
Type VI = Horizontal or vertical reflection
Type VII = Diagonal or anti-diagonal reflection

Here's the full list. The best of each type are highlighted in red.

I,20,SM,21,000000000040000060002907500007060200000538000008040900009206800060000050000000000,ab,60
I,20,SM,24,040000070200030004000901000003060500050809060002070900000206000400010008060000030,Ocean,37
I,20,SM,28,040050080700030004003704200004000100830000069006000800008506700600010008010020050,Ocean,39
I,20,M,21,000000000000623000005040800070000030089050740030000020006080900000472000000000000,ab,49
I,20,M,24,000060000000308000001509700065000140900000002072000360004705900000801000000020000,ab,16
I,20,M,24,000895000009000700010000080500020009900301006600040003040000030008000500000467000,Tarek,53
I,20,M,24,090050010200000006000106000008070200700601003003090400000504000300000002050060070,Ocean,47
I,21,SM,21,700000006040309020000000000020090050000471000090060030000000000030507090800000001,JPF,54
I,21,M,24,090000070100000006005409300007080600000506000002090400003607900200000003050000010,Ocean,61
I,22,SM,21,100000004050609080000000000030090060000274000090010020000000000060507090700000002,JPF,56
I,22,SM,24,000906000001030600040010080400000002076000950500000008050070040003090100000308000,Ocean,73
I,23,SM,24,000000000002103700089000340010080060000607000030040020046000930005706400000000000,Ocean,38
I,23,SM,24,000070000005000900030504020003040100400301009001050800080702050009000600000010000,Ocean,14
I,24,SM,24,000895000009000700010000080500020009900301006600080003040000030007000400000467000,Tarek,52
I,24,SM,24,050000020630090087000302000001000600090000050004000800000407000470050068020000090,Ocean,50
I,25,SM,24,007000200000405000400060008050020090001503700040090010800010009000706000002000600,Red Ed,99
I,26,M,20,000010000000234000001000500020000060630000024040000070005000800000967000000040000,Ocean,64
I,27,SM,24,050000020630090084000302000001000600090000050004000800000407000470050068020000090,Ocean/ab,51

II,20,SM,28,005021070100030500030004009309000000670000034000000206500800040003010005080260300,JPF,83
II,21,M,20,000000100000007900750086000034000000006000700000000860000240053001500000002000000,ab,43
II,21,M,24,100000002034500060000006050006010030000704000080030200070800000050007890800000004,Ocean,96
II,22,SM,29,870006003003400009000700040500804910000050000081603004060008000300001400100300096,Red Ed,79
II,22,M,24,000010000000002100031400500040607300800000004002504060004009270008300000000020000,Ocean,58
II,24,SM,28,540030701000102008100000000080060030400207005020040090000000002200806000804020013,gsf,89
II,25,SM,28,000450800020003070500208000089000701100000009703000580000705006050600040006014000,Red Ed,92

III,20,-,28,000000000100402005500703002018000970065000120027000450700906001200301009000000000,Red Ed,70
III,20,SM,28,000000000056109270709000104030608010000000000060904020208000701095201460000000000,gsf,5
III,20,M,26,090102050800000004507000902000281000000000000000695000102000305900000001060704020,JPF,86
III,21,SM,28,000000000053409270709000103030508010000000000060904020208000701095201460000000000,GSF/Red Ed,76
III,22,M,24,000902000070000050008301400700000001030406090600000004005109300080000060000504000,gsf,90
III,24,SM,24,120000034000403000005000600400030001000207000800060009009000500000701000630000087,Ocean,97
III,24,SM,28,046000320010807090900000005009702800000000000003906200400000003070309010031000970,Red Ed,78

IV,20,SM,23,960000034200000006000470000007800000008050300000002900000093000400000008650000093,ab,22
IV,20,SM,26,000907801000000000000501709402800607000000000305009108504602000000000000708403000,ab,40
IV,21,SM,28,034600100500000000608093002300700800009000600002008007800310509000000003003007240,JPF,87
IV,21,M,19,100050000000300020009000400030004000200030008000900060004000100060009000000020007,Nick70,55
IV,22,SM,24,070008060930040005000200000009100004020000030500004700000005000700080096010700020,Ocean/Red Ed,75
IV,23,M,22,000000001023004000050061000000700830005000600094002000000250040000800720300000000,Ocean,77
IV,24,SM,28,010405900209000000060012007500000603003000400802000009900370050000000704006804090,gsf,94
IV,24,M,24,000100020000000304000056070800030900009807400002090001060240000108000000070003000,Ocean,91
IV,25,SM,26,050302000600079000002000800200400098080000050310006007001000700000540006000907080,Red Ed,93

V,20,SM,24,000050009456100000000600010000005074300000002810900000070003000000008561500040000,gsf,7
V,20,SM,26,000040060300800700004050200005000080102504603060000400007090500003001006080020000,Tarek,23
V,20,SM,26,080009060005004200000730058193000000000000000000000694860012000004900700020400010,JPF,34
V,20,SM,27,160400005040020700009001040007000004050080010900000300020700100003060050400003067,JPF,35
V,20,M,22,000000100400008730205900000500000060080000020040000005000007203056400001003000000,Ocean,27
V,20,M,26,000007684000103090000040100706005003000000000500700802001050000070402000923800000,JPF,28
V,21,SM,26,000030608200008500009000001050020800060403020002080060100000700008100004704090000,JPF,29
V,21,SM,26,010000700003001000009030016000020940500109008062050000740060300000200400005000060,vidarino,12
V,21,SM,26,080200901004060050000007006060000508000805000308000070600700000010020600809001020,JPF,33
V,21,M,20,084000000090000000000006104507600000400000005000003609206100000000000050000000380,vidarino,9
V,21,M,25,900000542210000900004000008000841000000020000000376000400000800007000013628000007,Ocean,26
V,22,-,25,000000007018590000020030950005400000300070004000003100067040090000081260500000000,Tarek,42
V,22,SM,22,700020000000600504000700200000107900900000003006402000005006000804005000000070008,Ocean,19
V,22,SM,25,002000007604000010030006540000800000801020904000009000028500030060000709500000200,JPF,44
V,22,SM,26,000050241000900600000071000970000360200000009016000028000710000004003000597020000,Ocean,17
V,22,SM,26,700308050090000020000509000500060407000401000304070006000704000030000090050206008,Ocean,18
V,22,SM,27,001907503090300000000000270006700140000060000019005700083000000000003080405802300,vidarino,2
V,22,SM,28,050930006089002070400087000000000005004209100100000000000120004010400650800095020,JPF,45
V,22,M,26,076300000800005060900070100000058200020000080007930000008090005060200001000003820,vidarino,32
V,22,M,28,000029007000804065000100289001000003090000020500000700937001000410902000200340000,Ocean,30
V,23,SM,24,006080004070000090030901000250000000004307100000000029000809010040000080700030200,JPF,13
V,23,SM,25,103000090800000534600000080000014000000759000000630000010000006356000008080000207,Ocean,15
V,23,SM,26,000300200000807004000090605930000800076000540004000032205070000100405000003009000,Ocean,25
V,23,SM,26,100000020000800000309500140003001060050903080090400200062009305000005000030000002,JPF,66
V,23,SM,27,000000504000020010290500003040030600600481005008050040800003096030070000106000000,vidarino,10
V,23,M,19,000000000000012003400000560000003012000070000850900000023000006900480000000000000,Ocean,67
V,24,SM,24,007001000040500000860000003002100000031802690000007100300000045000008070000700200,JPF,48
V,25,SM,24,000000900000508004030070100000002706010403090208100000009080040800206000002000000,vidarino,8
V,25,SM,24,000002400002040085060003700900070050000000000070050004003600070540030100008100000,ruud,11
V,25,SM,26,001234000050100000260000000780000020009807300020000075000000053000003080000985400,Ocean,24
V,25,SM,28,090000500607000309000006087000300451000105000153008000710400000802000605005000070,JPF,46
V,25,M,19,000000000000082007400000560000003012000070000850900000023000006700490000000000000,Ocean/Red Ed,68
V,25,M,24,800072036500300000000008090001000000400605008000000300020800000000004001610290004,Ruud,4
V,26,SM,23,000000012007206000000900403105000900000070000002000806304008000000409100690000000,Ruud,41
V,26,SM,25,800030000020005000003800092400020108000040000709010005970006200000700040000080009,vidarino,21
V,26,M,23,305000600060000002000090170004300000800020005000009300056010000900000040003000908,Ruud,1
V,26,M,24,004003001700600000002800000300040850070000090028050003000002900000006007100500300,vidarino,20
V,26,M,24,004003001700600000002800000300040850070000090028050003000002900000006007100500300,vidarino,3
V,27,SM,25,200980000076000000000000420308040010004090300060020904035000000000000840000067003,vidarino,6
V,28,SM,24,500800002020060900040000037000100000003907800000008000830000010005040090200001005,vidarino,36
V,28,M,20,000000010002000034500026000000067000100000003000580000000410009270000600050000000,Ocean,74
V,28,M,21,005900008001000005002300000000400010007030200060001000000009400900000700800005300,Ruud,31

VI,21,SM,25,009050700400307008000000000140906057000000000050040010500000009900803001020060040,JPF,82
VI,22,SM,24,102304506000607000000000000000586000000000000058000190005000900020030060030201080,Ocean,98
VI,22,SM,27,025030680700801009000020000502000104300000007040000050080000010260000043000392000,JPF,85
VI,23,SM,25,609000301800403006030000050000050000001806900008000600190000023300000004000501000,JPF,88
VI,23,M,25,002400706000020004000005090019000800780500000054000900000001060000030008007600102,gsf,95
VI,24,M,24,000000000100402005500703002018000970060000020007000400700906001200301009000000000,Red Ed/ab,71
VI,24,M,24,001203400000000000560000072080000020000104000007000600040901080803405907000000000,Ocean,100
VI,25,-,28,014000520200501007000402000000308000037000180500000006400000002100605008056000370,Red Ed,69
VI,26,SM,24,000000000100402005500903002018000470060000020007000900200706001600301009000000000,Red Ed,72

VII,20,M,23,000001000000070305000500900003460000040302600200010007061050090000000200050004000,Ocean,57
VII,22,SM,25,000000050350700002807020000000060000019008400740000010000010300030590040000400260,ab,65
VII,22,SM,25,000001000600907300009000080000002048000000000327000090960500200205700000014800050,JPF,81
VII,23,M,21,000000000001020030040560700002000000018000000000000465003002000050009003000008091,Ocean,63
VII,25,SM,25,000001000600907300005000080000003048000000000327000090760500200903700000014800050,JPF/Red Ed,80
VII,25,M,21,010002030400000150000006000000000007000001800207080000030040000840000006000500029,Ocean,62
VII,26,SM,27,002800007000090240000005080020900600940010020060007009010000008706581000080040000,Red Ed,84
VII,28,M,23,010230004500600700000000830320000010700020008000000040089000000004305000600040000,Ocean,59

:!:

Now, a proposal. Why don't we raise the bar on this thread so that in future, up to puzzle #100 say, a puzzle is only accepted if (a) it is better than the current best of its type or (b) it is equal to the best so far and you've not already submitted such a puzzle.

So, for example, the following type VI puzzles would be allowed: (a) anything with 27+ steps; (a') any fully minimal 26-stepper; (b) a symmetrically-minimal 26-stepper from someone other than Red Ed.

The point of this proposal is to encourage better quality and diversity, and to agree a finishing point.

EDIT: those were the old rules. I think now you just need to beat your personal best for any puzzle type to qualify. Oh, and exhibit at least 20 steps.

by **Red Ed** » Thu May 18, 2006 10:31 pm

Red Ed wrote:Types II, III and IV look like easy pickings ...

Here's a start: a new best type IV (diagonal and anti-diagonal symmetry), borrowing heavily from Ocean's #59:

Code: Select all: . 7 .|. . 8|. 6 . 9 3 .|. 4 .|. . 5 . . .|2 . .|. . . -----+-----+----- . . 9|1 . .|. . 4 . 2 .|. . .|. 3 . 5 . .|. . 4|7 . . -----+-----+----- . . .|. . 5|. . . 7 . .|. 8 .|. 9 6 . 1 .|7 . .|. 2 .

Or, in the notation of my previous post:
IV,22,SM,070008060930040005000200000009100004020000030500004700000005000700080096010700020,Red Ed,???

And another: a new best type III based on gsf's #5:

Code: Select all: . . .|. . .|. . . . 5 3|4 . 9|2 7 . 7 . 9|. . .|1 . 3 -----+-----+----- . 3 .|5 . 8|. 1 . . . .|. . .|. . . . 6 .|9 . 4|. 2 . -----+-----+----- 2 . 8|. . .|7 . 1 . 9 5|2 . 1|4 6 . . . .|. . .|. . .

III,21,SM,000000000053409270709000103030508010000000000060904020208000701095201460000000000,Red Ed,???

by **JPF** » Thu May 18, 2006 11:10 pm

Red Ed wrote:This is a public service broadcasting announcement.
....
Comments? ...

What about :

-free-style (without any symmetry) just to see how far we can go ?
-low-steppers which are not easy to create (see Ocean's list).

JPF

by ab » Fri May 19, 2006 12:48 am

Red Ed wrote:Now, a proposal. Why don't we raise the bar on this thread so that in future, up to puzzle #100 say, a puzzle is only accepted if (a) it is better than the current best of its type or (b) it is equal to the best so far and you've not already submitted such a puzzle.

I'm happy with this suggestion

Also somewhat surprised to see I've contributed to two of the best puzzles in their class.

As JPF suggests, maybe we could add another type, type VIII=no symmetry. Any advances to your 29 stepper will be added to the honourary mentions list.

by **ronk** » Fri May 19, 2006 3:45 am

Red Ed wrote:This is a public service broadcasting announcement.

For "fun", I've compiled all the inferiors so far into a computer-readable list. It's shown below with:
field 1 = symmetry type
field 2 = number of steps
field 3 = 'M' if fully minimal; 'SM' if symmetric minimal
field 4 = the puzzle itself
field 5 = author
field 6 = puzzle number in ab's list at the start of this thread

Your "public service" project is appreciated. However, I suspect many solvers -- without alteration -- could batch process the puzzles, if only the field order were 4, 1, 2, 3, 5, and 6. IOW if field 4 were first, a solver could read 81 characters, process the puzzle, and then simply ignore characters until the beginning of a new line.

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