The New Sudoku Players' Forum

by **Obi-Wahn** » Thu Jan 03, 2008 10:45 pm

coloin wrote:Fantastic "Golden Nugget"
11.5......Suexrat9 3400 +
Well done, How did you make it ?

Awaiting the swords and jelly count !!!!

Hm, it's a pity but I guess AW didn't see the Golden Nugget so far.
I tried to integrate his sword and jelly approach in my own solver (which already used the kind of tabling implications he described), although I'm not sure that the results are exactly the same.

Anyway, for the Easter Monster my solver counts 3 jellys, too, but only 11 swords.
For the Golden Nugget on the other hand only 1 jelly is counted, but a bunch of 20 swords still giving it the second place for this rating.

Nevertheless it's a very nice addition to the collection of hardest Sudokus.

Greets, Obi

by **tarek** » Sun Jan 06, 2008 3:08 am

Obi-Wahn wrote:Nevertheless it's a very nice addition to the collection of hardest Sudokus

that's great thanx Obi-Wahn........
The addition needed for many of the puzzles on the latest lists is the SE rating ...........

I'm awaiting the update on the taxonomy list .... maybe then some more info can be brought out (possibly more SXX ratings)

tarek

by **Obi-Wahn** » Sun Jan 06, 2008 2:03 pm

I've managed to cut down the time for a Jelly check to about one minute and for each Sword check to about half a second. So I could check a couple of hardest puzzles within reasonable time.

I checked coloin's M3 list of 2007-11-20 and the numbers 1, 6, 8, 9 and 10 didn't even require a sword check.
But col-201107-M3-3 scores 1 jelly & 5 swords and col-201107-M3-7 even 1 jelly & 11 swords (SE rates it 10.6 BTW).

I also checked JPF's list of last April and I found 20 puzzles requiring a Jelly check. Funnily of the top three SE 11.4 puzzles only the Easter Monster requires a jelly check. And further down the list there's coloin's St. Patrick 2 with 1 Jelly & 4 Swords and SE 10.6 next to tarek's ULTRA0213 which doesn't even require a sword check and rates SE 10.7.

As I said, my results don't exactly match those of AW. He built some basic solving techniques like Quads and Jellyfish in his solver, while I purely rely on pair implications. But the puzzles that require a Jelly check for my solver can't be solved with a combination of SSTS and Implication Tabling up to Sword check either. And I don't think that my Sword check is less effective than AW's because he rated dml 1/07 with 1 Jelly & 17 Swords while my solver only needs 1 Jelly & 12 Swords. (I'd really like to see how many Swords AW would award the Golden Nugget).

[edit] Houston, we have a problem ...
I just stumbled over coloin's old waiting list with the following SE 11.4 puzzle:

Code: Select all: coloin-04/13-1414 1.......2.9.4...5...6...7...5.3.4.......6........58.4...2...6...3...9.8.7.......1

After 7 Jellys & 11 Swords my solver resigned!
AW, I'd really like to have your results on this one. Currently I'm only checking for Jellys with True True assumptions, but at least for the Sword checks I never saw the other possibilities yield new implications when True True failed ...

[edit2] Another one from that list, that won't surrender after 5 Jellys & 8 Swords (SE 11.3):

Code: Select all: coloin-04/13-1426 1.......2.9.4...5...6...7...5.3.4......96.........8.4...2...6...3...9.8.7.......1

by **coloin** » Sun Jan 06, 2008 5:41 pm

Its good to have another approach to these hard puzzles.

Rather than post a long list of puzzles I am trying to decide which puzzles to post !!

here I mentioned these three puzzles to AW ...and he indeed went through similar emotions !!

This is what he reported here

The three puzzles took >7 hours with Explainer.....but were from the Easter Monster Template.

Possibly Tarek has similar puzzles in his list.

C

by **tarek** » Sun Jan 06, 2008 5:57 pm

the puzzles I posted last came from a HUGE pool of puzzles. I went for a cut-line for each rating method & posted puzzles that are above that.

SE would be a good extra filter, unfortunately it takes ages to rate puzzles.

another way probably would be as follows:
if you have a big pool of y puzzles: rank puzzles against each method from 1 to y, then (in this case q1,sxx,sx9):

Code: Select all: ( 5*(q1 rating RANK) + 5*(sxx rating RANK) + 2*(Sx9 rating RANK) ) / 12

This would give each puzzle in your list a score (biased to q1 & sxx, less to sx9), you could then submit the TOP x puzzles ranked by that score.

tarek

by **Obi-Wahn** » Sun Jan 06, 2008 6:52 pm

coloin wrote:here I mentioned these three puzzles to AW ...and he indeed went through similar emotions !!

This is what he reported here

Thanks, I just found his post myself. It's difficult to keep track of those different threads.
It's good to see that it doesn't seem to be a bug within my code. I could reproduce most of his other results, too.

My solver is currently sweating over coloin-04/13-1600.

And there's another one, that needs more than one Jelly run to be solved:

Code: Select all: coloin-04/13-1397 6.......2.9.4...5...1...7...5.34........6.......8.5.4.2.....6...3...9.8...7.....1

14 Swords - 2 Jellies! I wonder what its ER would be.

[edit] coloin-04/13-1535 also scores 14 Swords - 2 Jellies.

Ok, finally coloin-04/13-1600 forced my solver to surrender after 7 Jellies and 16 Swords.
And I added a check for Jellies with True False and False False assumptions, too. As I expected this didn't yield any new implications.

Unfortunately AW didn't mention if he added a check with 4 simultaneous constraints to his solver to make it work.

I also checked tarek's 363 puzzles and found 13 requiring Jellies (including the Golden Nugget).
Amongst them this one, requiring 23 Swords & 4 Jellies!

Code: Select all: tarek071223170000-170 ....71......9....1.6.4.2...5.....7...1...4..6..3....8..9.2....4..7...3..8......5.

And it's SE 11.1 btw.

by **gsf** » Mon Jan 07, 2008 3:53 am

tarek wrote:I'm awaiting the update on the taxonomy list .... maybe then some more info can be brought out (possibly more SXX ratings)

thanks for the urls
recent puzzles collated and merged in q1-taxonomy-2008-01-06.dat
as usual, no additional SE ratings

by **tarek** » Mon Jan 07, 2008 10:52 am

gsf wrote:
tarek wrote:I'm awaiting the update on the taxonomy list .... maybe then some more info can be brought out (possibly more SXX ratings)

thanks for the urls
recent puzzles collated and merged in q1-taxonomy-2008-01-06.dat
as usual, no additional SE ratings

thanks for your efforts, I'll try to digest the info on the list with time

tarek

by **coloin** » Mon Jan 07, 2008 12:18 pm

Here is a selection of hard puzzles for comparison.......

Code: Select all: sxt sx9 q1 puzzle 1862 2799 96387 .2.9..........7..4..7....92.9.3...7......53....8.1......5...6...4.2....71....8... # col0701-1 1710 2816 95097 .2.4..7.........2.....2..94.9.3...7.8...5.3.......1.....5..86...4.9....71........ # col0701-2 1515 2624 45274 .2.4..7.........2......3.94.9.3...7.8...5.3.......1.....5..86...4.9....71........ # col0701-3 1360 3422 45273 .2.4.37.........2.........4.9.2...7...8.5.........19..5....83...6.9....7..1...6.. # col0701-4 1347 2550 91856 .2.4..7.........2.6......94.9.3...7......53....8..1.....5..86...4.9....7..1...... # col0701-5 956 3346 55046 .2.4..7.........32.....7..4.9.3...7......59....8..1...5.........4.9....7..1..86.. # col0701-6 681 3698 46552 .2.4.37..........2.......34.4.2...7.8...5.........1...5.....9...3.9....7..1..86.. # col0701-7 679 3581 56249 .2.4..7..........2.......34.9.3...7...8..5.......91...5.....6...4.9....7..1..89.. # col-201107-M2-24

This is the tip of a very large iceberg !

C

by **tarek** » Mon Jan 07, 2008 12:59 pm

I've just rated the 141 puzzles on the latest taxonomy list that had a q1 rating of >95500 using Sx9 & sxt (10000 2 option)
I then ranked these puzzles according to each rating system
I then used the rankings in 2 formulas:
R1= (q1*5+sxt*5+XR*2)/12
R2= (q1*5+sxt*5+sx9*2)/12
the top 20 were similar.....out of these, only the Easter Monster has a known SE rating.

Code: Select all: ID q1 XR sxt sx9 R1 R2 ------------------------------------------------ tarek-1801 99071 2821 1541 2494 1 1 tarek071223170000-021 98827 2014 1269 2034 2 2 tarek071223170000-026 98803 2039 1247 2028 3 3 tarek071223170000-052 98821 2861 1084 2842 4 4 tarek071223170000-017 98602 2050 1304 2039 5 5 col-201107-M3-1 98773 4831 1062 2876 6 6 tarek071223170000-032 98759 1890 1169 1883 7 7 tarek071223170000-027 97508 2016 1226 2014 8 8 tarek071223170000-072 98776 1679 970 1700 13 9 tarek071223170000-029 96811 2002 1208 1968 11 10 col-201107-M2-12 96014 4553 1411 2826 10 11 col-201107-M3-5 97572 2723 1003 1899 9 12 tarek071223170000-013 96118 2012 1321 2024 12 13 tarek071223170000-048 96724 1795 1093 1797 16 14 Easter-Monster 99408 1895 766 1878 15 15 tarek071223170000-044 96112 2083 1085 2086 14 16 tarek071223170000-007 95770 2324 1500 2318 18 17 tarek071223170000-102 98775 1399 902 1407 20 18 tarek071223170000-008 95733 2278 1530 2304 19 19 tarek-1803 98870 2046 763 1711 17 20

here are the 141 puzzles in comma seperated form showing "Puzzle,ID,q1,XR,sxt,sx9" & sorted according to q1 then sxt

Puzzle,ID,q1,XR,sxt,sx9
100000002090400050006000700050903000000070000000850040700000600030009080002000001,Easter-Monster,99408,1895,766,1878
300000002080070010006900000050704000000000008000510070009000300010040080200000006,tarek-1801,99071,2821,1541,2494
900000005040300060002000100080740000000020000000806070100000900030007040005000002,tarek-ultra-0300,99038,1892,602,1431
500000007080009030004000200010036000000040000000108060002000400090300010700000005,tarek-1802,99029,1655,701,1425
000071000000900001060402000500000700010004006003000080090200004007000300800000050,tarek071223170000-170,98926,1526,737,1530
700000004020600010005000800030910000000050000000203090800000700060009020004000005,tarek-ultra-0301,98909,1929,626,1436
100000089000009102000000400007600000030040000900002005004070000500008010060300000,tarek-4/08,98898,1512,737,1535
300000005070008060002000900010006000000820000000107040009000200080600010500000003,tarek-1803,98870,2046,763,1711
400000006090070010002000500010307000000010000000908070000000400080030090605000002,tarek071223170000-021,98827,2014,1269,2034
001004000000060305000900000800000703000000028500070600300080006009200000040001000,tarek071223170000-052,98821,2861,1084,2842
200000006090010080007000300040508000000040001000900050003200000010050090600000007,tarek071223170000-026,98803,2039,1247,2028
700000300020006008004000050000091002000050000090208000003000040500000700060800009,tarek-1804,98782,1616,743,1355
007001000600090200030500000900000608000000030000080092200040009001300000050007000,tarek071223170000-072,98776,1679,970,1700
900000002080070030006000400070803000000010700000005080004000900050030010200000006,tarek071223170000-102,98775,1399,902,1407
003400700000009000600020000290064000000000000008300400005000001800030500000500074,col-201107-M3-1,98773,4831,1062,2876
100000002003400050060000700000890040000306000009040000020000100700000006005080030,jpf-04/14/08,98771,1504,742,1529
000000001080040050206000700050304000000090000000805040007000200090030080100000006,tarek071223170000-032,98759,1890,1169,1883
300009700060040000001800000500000093000003270000000008004010000200007050080600000,tarek071223170000-181,98722,1707,726,1717
100000080000009130000000506007040000300001050060200000500008900040070000002600000,col-201107-M3-3,98713,1845,680,1546
000000001070009020408000600000250030000007000050930000100000800030005070006000004,tarek071223170000-017,98602,2050,1304,2039
100000089000009130000000006007040000300001050060200000500008900040070000002600000,col-201107-M3-4,98572,1560,664,1403
400009100020030000007500000800000090000004610000000805003070000600001080050200000,tarek071223170000-190,98567,1534,706,1514
003080000700200000060009010000000003000005960090000054010004500800030000002700000,tarek071223170000-200,98483,1509,681,1521
700000004080060020001000300000800050000091000020650000400000100060500080003000007,tarek071223170000-234,97728,1019,651,1047
600000700010500020003000008020049000000080000000205040800000600040001050007000003,tarek-1805,97659,1596,777,1351
000500008700068000000210000002000040090000300600005001100070006040000020003000900,tarek071223170000-195,97644,1500,712,1516
003050000400009020080100000010030000005800000900004070000000037600000402000002906,col-201107-M3-5,97572,2723,1003,1899
100000080000009130000000504007040000060200000900001050002600000500008900040070000,col-201107-M3-6,97571,1416,754,1191
000600700000020004009003080300008010000700600000040002908000050510009000040000000,tarek071223170000-211,97557,1204,662,1196
000000089006000100000200605001500900800003000040070000300008000002100006070040000,col-201107-M3-7,97554,1493,651,1192
008000003020600010500000900040701000000030000000420070900000500010007020003000008,gsf-m3-2007-09-30,97554,1791,638,1305
500000003020600010008000900040701000000030000000420070900000500010007020003000008,tarek-ultra-0302,97548,1981,641,1443
003050000400009000080200001010800070005003000900040000000600007070000018000000320,coloin-2007-11-11-2,97542,1526,676,1503
000400080000009200600070001070060003000008090000200400530010000002000000061000007,col-201107-M2-11,97537,1405,753,1171
900000007006000020080010500040051000000608000000030100010005800002000090700000006,tarek071223170000-210,97537,1117,666,1137
007000005090040030001000200080403000000090000000806040002000700060030090500000001,tarek071223170000-027,97508,2016,1226,2014
700000001040050090002000600080009000500040000000803050006000700030090040100000002,tarek071223170000-194,97436,1082,695,1082
900000002080004070006000300050807000000420000000001080002000600040700050300000009,tarek-2801,97373,1585,730,1306
600000002090800070003000400000570000070108000000060050400000300050009080002000006,tarek-1806,97261,1441,622,1121
003000200070060050100000009000006000000097040050048000900000300040070060002000001,tarek-1807,97132,1526,518,1011
000000005040080030002000180090708000300060000000904070001000300080070040500000002,tarek071223170000-132,96984,1299,830,1290
100000900040700030008000005030407000000052000000300060500000100060004070009000008,tarek-1808,96813,1582,745,1301
200000100050090070004006000030007000908050000000300090001000200080070050600000004,tarek071223170000-029,96811,2002,1208,1968
900000003010060020008000500070006000000020704000001060000905000020040010300000008,tarek071223170000-048,96724,1795,1093,1797
100000002003400050060000700000050040000301000008940000020000100700000006005090030,jpf-04-10,96523,2262,689,1618
800000700050001002003000060000104000000030005090702000600000030007000800010020009,tarek071223170000-164,96364,1249,696,1253
100000000080503000002000900040700030000060000000384050900000100030007040006000002,tarek-1809,96359,2645,874,2403
000400700007109000680070000200000000001090800030000005008010600500700003000000020,col-201107-M3-8,96359,4651,618,2372
700000005060008090001000200000306400000804000040090030500000100080400060002000007,tarek071223170000-129,96326,1181,815,1190
000000004000370020600000800090030050000701000020950000400000100070500030008000006,tarek071223170000-187,96321,1785,713,1762
700000000060103000005000200000401030000080000090630010200000700030004060008000005,tarek071223170000-101,96316,1678,901,1657
230000000001006000506000090900001050000070800000400003000800007009005010000030400,tarek071223170000-215,96255,1042,653,1059
900000004000050030002400100070805000003000000000076080001000200030080070400000009,tarek071223170000-093,96134,1574,908,1580
400000002070001080009000600000780030000040000030105000200000900010300070006000004,tarek071223170000-221,96132,1060,658,1053
900004000030060070005000800020106000000070003000200010008000900070010060400000005,tarek071223170000-013,96118,2012,1321,2024
100000000040050030002000601050008000700040000000503070006000900080070040900000002,tarek071223170000-044,96112,2083,1085,2086
700000000040503000008000900000201030000060000010350020900000700030002010006000008,tarek071223170000-064,96110,1604,1012,1619
400000000020708000001000300060570080000090000000806050300000400080005060009000001,tarek071223170000-069,96110,1615,996,1610
100006009007080200800000050000900000000005060070010800034000000700020400002007000,col-201107-M3-9,96043,4570,647,2698
100000006020500040003000700040850000000010000000024080007000300050009020600000001,coloin,96039,1991,884,1609
003006080000100000090070000000530040000004608004000002010000000700900400005003060,col-201107-M2-12,96014,4553,1411,2826
003000000056700000780000006000030900008100007010002040000090300800500001000004020,col-201107-M2-13,95980,1432,729,1257
300000007000040080009700100050206000008000000000054020001000900080020060700000003,tarek071223170000-110,95977,1603,851,1579
500000007000090040006700200080109000004000000000083010002000600040010030700000005,tarek071223170000-126,95976,1538,840,1559
005000800010600070300000004000005000000067020060920000400000500020010060008000003,tarek071223170000-146,95937,1204,744,1197
500000007090040060008000100020406000000090000000203040100000500060030090700000008,tarek071223170000-062,95916,1838,1030,1842
700000004090060050001000300080602000000090000000805060300000700050020090400000001,tarek071223170000-055,95915,1797,1009,1806
500000008000070010006800300090200000401000000000097040003000600010020070800000005,tarek071223170000-144,95913,1445,821,1444
100000900030007040005000002000006070000010000040308000900000005070800030002000100,tarek071223170000-185,95895,1315,737,1308
900000006070003080002000400000001030000060000080507000600000200050800070004000009,tarek071223170000-106,95893,1331,865,1342
700000008030004060005000100000800030090106000000052000800000200040600090001000007,tarek-1810,95879,1834,557,1229
600007800000010000012400000700000056000006380000000009001020000300005070004900000,tarek071223170000-074,95828,2093,989,2103
300000600020500040007000008040001000000280000000405090800000300090002050006000007,tarek-2802,95826,1640,774,1365
700000005090030060001000200080304000006090000000800030002000100060040090500700000,tarek071223170000-081,95824,1489,965,1484
700000005060300080002000100090800000000073000000906040100000700030008060605000002,tarek-1172,95822,1621,602,1330
700000003090800050002000400060058000000197000000600010400000700050001090003000002,tarek-ultra-0303,95812,1806,853,1435
004000700080002090600000001000503020000068000030090000100000004090300080007000600,tarek071223170000-259,95812,1055,584,1039
800000000020010060005000908030100000700020000000306070000000400060070020409000005,tarek071223170000-058,95805,1994,1039,1996
003000700400009200080700005070600050000040000900003000010800500500000008700000061,col-201107-M3-10,95801,3180,781,1924
020000040001005800600000003000079000000008000005100900300000002040500060008090700,tarek071223170000-145,95799,1111,747,1101
002007000000010908000400000800000309000000056600030100900060001004500000070002000,tarek071223170000-182,95783,2175,740,2163
000600001090030080200000700030008000504090000000300050007000600080040090100000002,tarek071223170000-007,95770,2324,1500,2318
800000400020010060003000009000065000070900000000104020400000003010006070009000800,tarek-1811,95764,1608,696,1238
200000006050090020004002700080509000000030002000801050007000000090050030600000004,tarek071223170000-023,95748,1903,1198,1871
400000001000030020008100500060703000002000000000069070005000800020070030100000004,tarek071223170000-100,95741,1408,875,1406
000001007020050080004000900060302000008000000000065030009000100080030060700000004,tarek071223170000-038,95736,1838,1159,1840
000008007030090040005000100020609000004020000000003060001000800040060090700000005,tarek071223170000-008,95733,2278,1530,2304
007003000000020408000900000800000105000000064500010200400050002009600000030007000,tarek071223170000-207,95723,2127,685,2124
000003004070020090005000800060102000009000000000067010008000300090010060400000005,tarek071223170000-049,95719,1825,1139,1838
003000007010050090600000800000200010000043000090510000700000300050100020008000006,tarek071223170000-274,95710,738,527,741
001000004060080070900000300000600050000029000070850000400000900080500060003000001,tarek071223170000-218,95709,1050,668,1046
900000005040200030008000100070603000000080000000709060001000900030006040500000008,tarek071223170000-312,95693,853,404,863
100000003040600070008000500020704000000050000000290040005000100070002060300000008,tarek071223170000-229,95691,1044,629,1042
020006700400080000009000000000005003030000027601000500000040000800900005060007200,col-201107-M2-14,95685,3539,1117,2557
003000080050000100700002004200097000000860000000004007008000300600040002010000050,coloin-2007-11-11-6,95684,1103,664,1094
005007000200080060030900000600000140000000900000040086400020008009300000070005000,tarek071223170000-273,95680,911,503,908
003050700400009000080100000010800000005070600900004000000000860002000370000030025,col-201107-M2-15,95675,2161,918,1657
400000008060070020009000300010700000500060000000102050003000000020050060800000409,tarek071223170000-083,95672,1589,984,1588
003000400000501070000000008050009020000260000090105000400000300070900010008000006,tarek071223170000-256,95667,1436,583,1446
020056000400000100008000000001000800070030002900000040000067005000900000060305007,col-201107-M2-16,95664,1899,654,1448
500000000080904000007000200000300060000010400040680090200000500060003080001000007,tarek071223170000-147,95661,1540,807,1577
000000039000001005003050800008090006070002000100400000009080050020000600400700000,Golden-Nugget,95649,3792,2121,3635
700000001030090040005000200080609000000040800000300060002000700090060030100000005,tarek-1813,95641,2112,865,1472
900000005070400060003000200010780000000020000000106070200000900080007040005000003,tarek071223170000-143,95640,1315,783,1310
006000700090400020100000005020048000000900030000506000500000800030090040007000001,tarek-1814,95638,1766,657,1264
700000010000605900000000002090304000000080000060907400030009600200000008001000070,tarek071223170000-056,95630,1756,1017,1760
700000005000090030001500400060209000003000000000086020004000001030020060500000007,tarek071223170000-082,95630,1687,914,1673
600000002090800070001000400030907000000040000000350090400000600050009080002000001,tarek071223170000-159,95617,1316,780,1296
100000002030400050006000700090540000000309000000086040002000100050008030700000006,col-201107-M2-17,95613,2827,1280,2171
000007000000050109030800000900000602000000041200060500100090006008400000070003000,tarek071223170000-243,95611,1479,625,1476
006000800000105040000000009010007050000530000070201000800000600040700020009000003,tarek071223170000-206,95609,1440,667,1435
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tarek

by **Obi-Wahn** » Mon Jan 07, 2008 8:28 pm

Hi, everybody.

I have extended my solver with the next logical step, a simultaneous check of a combination of 4 constraints. The first question was how to name these things. To my knowledge the next step in fishes after Swordfish and Jellyfish would have been a Squirmbag. So I thought about Squirms, but it didn't have the right touch. (BTW does anybody know what kind of creature a squirmbag is? Couldn't find it in any dictionary and Google links only lead to Sudoku boards. ...)
Fortunately there was a poll and the majority voted for Starfish, so it was an easy decision to call the new implications award a Star.

And the first puzzle to be awarded with a Star is: coloin-04/13-1426

After the initial 5 Jelly and 8 Sword checks my solver went into a huddle for 1 hour and 45 minutes over the new Star check (at least it's quicker than SE) and came up with 136 new implications, which after another quick 3 Sword checks lead to the solution.

So the total result is: 1 Star - 5 Jellies - 11 Swords.

I have no doubt that the other 2 puzzles in question will surpass this score.

by **gsf** » Mon Jan 07, 2008 8:38 pm

Obi-Wahn wrote:I have extended my solver with the next logical step, a simultaneous check of a combination of 4 constraints.

can you provide a url or explain exactly (so that one could code it) what
a simultaneous check of a combination of 4 constraints
means

and also provide the 81-char grid or url for coloin-04/13-1426
its really easy (for me) to snarf the wrong grid by label only

thanks

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by **Obi-Wahn** » Mon Jan 07, 2008 9:47 pm

gsf wrote:
Obi-Wahn wrote:I have extended my solver with the next logical step, a simultaneous check of a combination of 4 constraints.

can you provide a url or explain exactly (so that one could code it) what
a simultaneous check of a combination of 4 constraints
means

and also provide the 81-char grid or url for coloin-04/13-1426
its really easy (for me) to snarf the wrong grid by label only

thanks

Sorry, I forgot the grid because I already posted it above:

Code: Select all: coloin-04/13-1426 1 . .|. . .|. . 2 . 9 .|4 . .|. 5 . . . 6|. . .|7 . . -----+-----+----- . 5 .|3 . 4|. . . . . .|9 6 .|. . . . . .|. . 8|. 4 . -----+-----+----- . . 2|. . .|6 . . . 3 .|. . 9|. 8 . 7 . .|. . .|. . 1

I assume that you are familiar with implication tabling. I keep track of the relations between any 2 candidates A and B in the grid, which can be: A => ~B , ~A => B , A => B , ~A => ~B or a any combination of them.
A constraint is any of the 324 sets of 9 candidates of which one must be true.
With simultaneous check of 4 constraints I mean, that I choose 2 assumptions A and B and look at any combination of 4 constraints in which any of the 2 assumptions eliminates at least one candidate. I then choose any of the remaining candidates in constraint 1 to be true which will eliminate some candidates in the other 3 constraints. Then I choose one of the remaining candidates of constraint 2 to be true which eliminates some candidates of the last 2 constraints. Finally I choose one of the remaining candidates in constraint 3 to be true which may eliminate some candidates in constraint 4 and look if constraint 4 still has any candidate left.
If yes, I can't prove anything and have to go on to another combination of constraints. If no, I have to try any other combination of candidates in the 4 constraints to prove that there is no solution under the assumptions A and B.
Therefor if A is true, B must be false and vice versa.

I'll try to let my solver generate some output about the assumptions and constraints when he finds a Star to give a practical example.

The thread in which AW explained his ideas is Looking for inspiration on implication and I think there's also a thread in the programmer's forum but I have to look it up first.

by **gsf** » Mon Jan 07, 2008 10:11 pm

Obi-Wahn wrote:I assume that you are familiar with implication tabling. I keep track of the relations between any 2 candidates A and B in the grid, which can be: A => ~B , ~A => B , A => B , ~A => ~B or a any combination of them.

thanks

what sudoku properties/techniques do you use to propagate the constraints?
i.e., I'm guessing to determine the A,B relationships you
(1) set A and see what happens to B
(2) unset A and see what happens to B
(3) set B and see what happens to A
(4) unset B and see what happens to A
my question then is: how do you determine see what happens

the q1 method starts with singles and singleton propositions
where proposition entails independently assuming each value in an n-value/location tuple
and applying the constraint (singles etc.) to determine the effect on other candidates
failing that (no eliminations/assignments) it tries singles with paired propositions
failing that it tries { singles + locked candidates } with paired propositions
all of the hardest solve with at most paired propositions using { singles + locked candidates }

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