The New Sudoku Players' Forum

by **Ocean** » Tue Jun 20, 2006 11:45 am

I also liked the slash pattern.
Some slash-puzzles with various difficulty:

Code: Select all: #easy ("6-stepper"): 000000012000000345000006780000067900000538000005210000042300000973000000860000000 #medium ("20-stepper"): 000000012000000345000006780000068900000537000005210000042700000793000000860000000 #medium ("doubles and/or locked candidates"): 000000012000000345000001670000016800000439000004270000025300000678000000910000000 #advanced ("triples"): 000000012000000345000006780000017800000438000004290000042300000613000000790000000 #x-wing: 000000012000000345000006780000067200000132000001580000045300000293000000760000000 #xy-wing: 000000012000000345000001670000016800000439000004570000075300000928000000610000000 #xy-chain: 000000012000000345000006780000067900000498000004510000052300000967000000410000000 #

by **Carcul** » Tue Jun 20, 2006 12:13 pm

Those slash patterned puzzles are really very nice. Isn't it possible to increase the difficulty of your last one, Ocean?

Thanks, Carcul

by **Ocean** » Tue Jun 20, 2006 2:11 pm

Carcul wrote:Those slash patterned puzzles are really very nice. Isn't it possible to increase the difficulty of your last one, Ocean?

Thanks, Carcul

Sure. Since xy-chain is the only 'advanced' technique I have implemented, they come in two groups: a) xy-chains (any length), and b) unsolvable with only xy-chains. Finally the highest 'gsf-ratings'. (The lists might contain isomorphic puzzles, since they are not checked extensively for equivalence).

Code: Select all: # # Slash pattern: xy-chain (89) # 000000012000000345000001670000016700000437000004520000082300000763000000910000000 000000012000000345000001670000016800000438000005290000092300000817000000460000000 000000012000000345000001670000017800000436000004590000082300000473000000610000000 000000012000000345000002670000027800000346000003910000059400000814000000620000000 000000012000000345000002670000056800000438000004910000059300000761000000820000000 000000012000000345000003670000026800000457000004190000012900000758000000630000000 000000012000000345000003670000035800000497000004120000051900000629000000830000000 000000012000000345000003670000036500000417000004280000028100000951000000630000000 000000012000000345000003670000036800000487000004590000012900000763000000980000000 000000012000000345000003670000036800000487000004920000019200000763000000480000000 000000012000000345000003670000036800000497000004580000052900000679000000380000000 000000012000000345000003670000037800000496000004250000012900000758000000630000000 000000012000000345000003670000038200000496000004570000051900000679000000830000000 000000012000000345000005670000036800000498000004710000012900000869000000530000000 000000012000000345000005670000056800000438000004270000032900000719000000850000000 000000012000000345000005670000056800000824000004910000013200000489000000650000000 000000012000000345000005670000056800000894000004310000043900000689000000750000000 000000012000000345000005670000058900000439000004170000061300000923000000850000000 000000012000000345000005670000089200000437000004650000086300000713000000590000000 000000012000000345000006780000017500000438000004560000045200000613000000790000000 000000012000000345000006780000017800000438000004520000042300000183000000690000000 000000012000000345000006780000037200000168000001540000049300000852000000760000000 000000012000000345000006780000037200000468000004190000019300000253000000760000000 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000000012000000345000006780000067900000938000001520000042300000978000000160000000 000000012000000345000006780000068200000437000004910000059300000183000000670000000 000000012000000345000006780000068900000497000005130000012300000943000000760000000 000000012000000345000006780000068900000517000005240000012400000943000000760000000 000000012000000345000006780000068900000924000004510000053100000792000000860000000 000000012000000345000006780000069800000487000005130000012300000843000000760000000 000000012000000345000006780000097100000238000002540000045300000821000000760000000 000000012000000345000006780000097100000431000004580000059300000183000000760000000 000000012000000345000003670000036800000298000004750000052900000819000000630000000 000000012000000345000006780000017900000348000003560000052400000914000000780000000 000000012000000345000006780000029100000437000004580000052300000673000000980000000 000000012000000345000006780000067800000438000004210000042100000813000000670000000 000000012000000345000006780000067900000431000004280000052300000469000000710000000 000000012000000345000006780000067900000431000004280000082300000173000000640000000 000000012000000345000006780000067900000431000004280000082300000649000000170000000 000000012000000345000006780000067900000431000004580000085300000173000000640000000 000000012000000345000006780000067900000431000004580000085300000649000000170000000 000000012000000345000006780000069200000738000001540000045300000723000000860000000

Code: Select all: # # Slash pattern: not solved with xy-chains alone (113) # 000000012000000345000001670000016700000437000004520000082600000763000000910000000 000000012000000345000001670000016700000437000005280000054300000783000000160000000 000000012000000345000001670000086200000439000004170000058300000793000000610000000 000000012000000345000002670000018900000436000004570000045300000629000000830000000 000000012000000345000002670000026800000437000004910000059300000762000000830000000 000000012000000345000002670000026800000438000004710000051300000763000000890000000 000000012000000345000002670000026800000438000004710000051300000763000000920000000 000000012000000345000002670000026800000457000004380000019500000365000000720000000 000000012000000345000002670000027800000416000004530000079300000148000000620000000 000000012000000345000002670000027800000416000004980000059300000813000000620000000 000000012000000345000002670000028900000439000004710000051300000783000000920000000 000000012000000345000002670000056800000418000004730000057300000813000000620000000 000000012000000345000003670000036800000481000004970000079200000163000000580000000 000000012000000345000003670000036800000487000004290000012900000763000000480000000 000000012000000345000003670000037200000516000005890000098100000641000000730000000 000000012000000345000004670000046100000731000008590000092300000173000000650000000 000000012000000345000005670000056800000132000001490000049300000283000000650000000 000000012000000345000005670000056800000138000004270000012300000893000000670000000 000000012000000345000005670000056800000438000004970000019300000823000000670000000 000000012000000345000005670000068900000937000004510000012300000587000000960000000 000000012000000345000005670000068900000937000004510000012300000963000000580000000 000000012000000345000005670000086900000937000004510000012300000567000000980000000 000000012000000345000005670000086900000937000004510000012300000983000000560000000 000000012000000345000005670000086900000937000004520000012300000467000000980000000 000000012000000345000006780000017900000348000003560000025400000914000000780000000 000000012000000345000006780000029500000431000004780000072300000863000000950000000 000000012000000345000006780000037200000468000005210000049300000213000000760000000 000000012000000345000006780000037200000468000005910000049300000213000000760000000 000000012000000345000006780000037500000468000004910000012500000985000000760000000 000000012000000345000006780000037500000468000004910000019300000852000000760000000 000000012000000345000006780000037900000298000008450000052300000913000000760000000 000000012000000345000006780000037900000468000004910000012500000895000000760000000 000000012000000345000006780000037900000469000004280000052300000193000000760000000 000000012000000345000006780000037900000469000004280000052300000913000000780000000 000000012000000345000006780000047800000938000001560000042300000793000000860000000 000000012000000345000006780000062500000431000004890000097300000813000000260000000 000000012000000345000006780000062500000437000004190000098300000713000000260000000 000000012000000345000006780000062500000437000004910000098300000213000000760000000 000000012000000345000006780000062500000438000004190000097300000813000000260000000 000000012000000345000006780000062900000439000004810000058300000791000000260000000 000000012000000345000006780000063200000498000004510000095300000831000000760000000 000000012000000345000006780000063800000549000003210000052400000974000000860000000 000000012000000345000006780000067100000138000004920000025300000918000000760000000 000000012000000345000006780000067100000231000002580000048300000193000000760000000 000000012000000345000006780000067100000238000002940000049300000613000000780000000 000000012000000345000006780000067100000431000004280000052300000163000000790000000 000000012000000345000006780000067100000431000004580000059300000248000000760000000 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000000012000000345000006780000067200000438000004910000049300000582000000760000000 000000012000000345000006780000067200000438000004910000049300000782000000160000000 000000012000000345000006780000067200000438000004910000059300000613000000870000000 000000012000000345000006780000067200000438000004910000082300000149000000760000000 000000012000000345000006780000067200000814000004350000059100000831000000760000000 000000012000000345000006780000067400000139000001580000059300000243000000760000000 000000012000000345000006780000067400000139000001580000085300000924000000760000000 000000012000000345000006780000067400000538000001940000045300000892000000760000000 000000012000000345000006780000067400000938000009210000012300000964000000870000000 000000012000000345000006780000067500000238000004950000052300000873000000960000000 000000012000000345000006780000067500000418000004530000092300000873000000650000000 000000012000000345000006780000067500000439000004180000042300000813000000760000000 000000012000000345000006780000067500000498000004520000021900000579000000360000000 000000012000000345000006780000067800000231000009540000092300000841000000760000000 000000012000000345000006780000067800000238000002540000041300000293000000670000000 000000012000000345000006780000067800000238000002540000041300000293000000780000000 000000012000000345000006780000067800000438000004250000059300000812000000760000000 000000012000000345000006780000067800000439000005810000042300000971000000860000000 000000012000000345000006780000067800000538000005290000052300000183000000760000000 000000012000000345000006780000067900000132000001580000045200000293000000860000000 000000012000000345000006780000067900000139000001450000052300000183000000670000000 000000012000000345000006780000067900000139000001450000052300000183000000790000000 000000012000000345000006780000067900000198000001230000032400000194000000860000000 000000012000000345000006780000067900000418000001230000052300000318000000760000000 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000000012000000345000006780000067900000451000004830000025300000813000000760000000 000000012000000345000006780000067900000458000007210000012500000869000000450000000 000000012000000345000006780000067900000498000004310000072500000836000000590000000 000000012000000345000006780000067900000498000004510000052300000368000000710000000 000000012000000345000006780000067900000498000004510000052300000719000000360000000 000000012000000345000006780000067900000498000008310000013200000276000000590000000 000000012000000345000006780000067900000538000004920000051300000872000000960000000 000000012000000345000006780000067900000849000001530000052300000983000000760000000 000000012000000345000006780000068900000437000004510000052300000413000000670000000 000000012000000345000006780000069100000437000004250000042500000183000000960000000 000000012000000345000006780000069100000438000004750000025300000371000000960000000 000000012000000345000006780000069200000138000001540000048300000725000000960000000 000000012000000345000006780000069200000432000004810000051300000728000000960000000 000000012000000345000006780000069200000432000004810000051300000928000000760000000 000000012000000345000006780000069200000531000004270000052300000813000000960000000 000000012000000345000006780000069500000437000004210000018300000572000000960000000 000000012000000345000006780000069800000431000004570000025300000378000000960000000 000000012000000345000006780000069800000438000004270000042100000813000000690000000 #

Code: Select all: #highest gsf-ratings: 95050,.......12......345.....267.....268.....438.....471.....513.....763......92....... 89219,.......12......345.....267.....268.....438.....471.....513.....763......89....... 86921,.......12......345.....678.....632.....498.....451.....953.....831......76....... 75148,.......12......345.....678.....679.....439.....481.....513.....928......76....... 67464,.......12......345.....678.....679.....439.....428.....583.....913......76....... 60541,.......12......345.....267.....289.....439.....471.....513.....783......92....... 51023,.......12......345.....678.....679.....418.....123.....523.....318......76....... #

The 75148-rated solves with 3 (possibly less?) short xy-chains @42 (longest cycle-length 5).
While for instance this ('only' 4648-rated) needed 7 eliminations by xy-chains (cycle length 9 for the longest needed chain). The counts are not objective, since eliminations were picked by chance from the shortest available xy-chains, and therefore alternative (shorter) solution paths may exist. The xy-chains were needed @41(cycle-length 5), @43(cycle-length 7) and @45(cycle-length 9):
000000012000000345000006780000067900000483000004510000045100000813000000760000000
#

by **gsf** » Tue Jun 20, 2006 4:38 pm

Ocean wrote:Finally the highest 'gsf-ratings'. (The lists might contain isomorphic puzzles, since they are not checked extensively for equivalence).
The counts are not objective, since eliminations were picked by chance from the shortest available xy-chains, and therefore alternative (shorter) solution paths may exist. The xy-chains were needed @41(cycle-length 5), @43(cycle-length 7) and @45(cycle-length 9):
000000012000000345000006780000067900000483000004510000045100000813000000760000000
#

with the -O option the ratings will be based on shortest xy cycle needed to advance the solution at each step (the -O ratings will typically be lower)
for the last one it showed a y-cycle of length 7 and an xy-cycle of length 11
this depends on the cycle edges and also the constraints that take precedence over xy-cycles
which may be different between our solvers

by **Ocean** » Tue Jun 20, 2006 10:56 pm

gsf wrote:with the -O option the ratings will be based on shortest xy cycle needed to advance the solution at each step (the -O ratings will typically be lower)

Thanks.
With the -O option all ratings dropped below 50000. It's probably better to use this option, to avoid false highs. Started a new search and found a few thousands more puzzles with the slash pattern. Among these >100 were 'unsolvable with xy-chain'. Since those already posted will take weeks to solve, it's no point to post more similar puzzles.
Highest gsf-rating (-O option) for the new puzzles is 71546, for this:

Code: Select all: # .......12......345.....678.....678.....459.....621.....125.....968......45....... #

by **Guest** » Tue Jun 20, 2006 11:04 pm

Ocean -- how are you finding these 'slash' puzzles?

by **Carcul** » Wed Jun 21, 2006 7:30 am

Good job Ocean, very good puzzles. Thanks.

Carcul

by **Ocean** » Wed Jun 21, 2006 8:21 pm

timunotspf wrote:Ocean -- how are you finding these 'slash' puzzles?

I used my own experimental programs, and it seems they worked in this case. These programs are not suitable for publication, they are too messy, they are not well documented, and not user-friendly. Besides, I think there are lots of other good programs out there (but I like the fun of using my own stuff). When it comes to details, this forum is probably not the right place for discussing algorithms for finding ('generating') puzzles.

Carcul: Glad you liked the puzzles.

by **udosuk** » Thu Jun 22, 2006 1:32 am

Ocean, any luck of your programs to generate this pattern? :?:

Code: Select all: x x x | x x x | x x x x x x | . . . | x x x x x x | . . . | x x x -------+-------+------- x . . | . . . | . . x x . . | . x . | . . x x . . | . . . | . . x -------+-------+------- x x x | . . . | x x x x x x | . . . | x x x x x x | x x x | x x x

Thanks...

by **claudiarabia** » Fri Jun 30, 2006 10:31 pm

If I would add r9c7 it would become to easy.

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

Claudia

by **Carcul** » Fri Jun 30, 2006 11:32 pm

Claudiarabia wrote:If I would add r9c7 it would become to easy.

It is still quite easy: r1c6=2 or r6c3=2, and so r1c4<>2 which solve the puzzle.
This pattern is also very pleasant: is it possible to make your puzzle harder, Claudiarabia?

Thanks, Carcul

by **Ocean** » Fri Jun 30, 2006 11:45 pm

udosuk wrote:Ocean, any luck of your programs to generate this pattern?

Code: Select all
x x x | x x x | x x x x x x | . . . | x x x x x x | . . . | x x x -------+-------+------- x . . | . . . | . . x x . . | . x . | . . x x . . | . . . | . . x -------+-------+------- x x x | . . . | x x x x x x | . . . | x x x x x x | x x x | x x x

Thanks...

Not sure how to attack this. A few attempts resulted in puzzles with two solutions (as known from previous postings). My programs are not suitable for a complete search in this pattern. Was also not able to do a thorough analysis. So as far as I know there might still be valid puzzles hiding somewhere. Might come back to it later if I come up with better strategies.

by **gsf** » Sat Jul 01, 2006 12:41 am

Ocean wrote:Not sure how to attack this. A few attempts resulted in puzzles with two solutions (as known from previous postings). My programs are not suitable for a complete search in this pattern. Was also not able to do a thorough analysis. So as far as I know there might still be valid puzzles hiding somewhere. Might come back to it later if I come up with better strategies.

I also let a program go for a day or so and got down to 2 solutions
with an algorithm slower than ocean's

by **r.e.s.** » Sat Jul 01, 2006 3:24 am

Ocean wrote:
Code: Select all
Slash pattern: not solved with xy-chains alone [...]

Not sure what's meant by "xy-chains alone", but a few puzzles in this part of your list are solved by Sudoku Susser with only xy-chains ("Simple Forcing Chains") and simple moves including naked pairs & line-box interactions ...

000000012000000345000006780000067400000538000001940000045300000892000000760000000
15 x Simple Forcing Chains
1 x Intersection Removal
6 x Pinned Squares

000000012000000345000006780000063800000549000003210000052400000974000000860000000
2 x Simple Forcing Chains
1 x Intersection Removal
1 x Simple Naked Sets
12 x Pinned Squares

For this one a naked quad is used ...
000000012000000345000006780000067100000238000002940000049300000613000000780000000
2 x Simple Forcing Chains
1 x Comprehensive Naked Sets
4 x Intersection Removal
1 x Simple Naked Sets
8 x Pinned Squares

by **ravel** » Sat Jul 01, 2006 12:05 pm

susser 2.5 needs "Simple Forcing Loops" and/or "Comprehensive Forcing Chains" for the 3 puzzles, which (in general) cannot be expressed as xy-chains.

xy-chains are bivalue/bilocation chains that always start in a bivalue cell with candidates xy, showing that a y in the cell would lead to an x in another one, so that either of the 2 cells must hold an x. Then x can be eliminated from cells that see both.
Simple Forcing loops (closed bivalue chains) make the eliminations from the fact that 2 cells of the loop that share a unit must hold a common number (all cells in the loop only allow 2 possible solutions).
Comprehensive Forcing Chains (bivalue/bilocation chains) start with one number in a cell with possibly more than 2 candidates and lead to a contradiction then. They are equivalent to multiple (bivalue/bilocation chains) forcing chains.

Only Simple Forcing Chains (bivalue chains with contradiction) always can be expressed as xy-chains.

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