The New Sudoku Players' Forum

[dobrichev]

Hi,

The updated collection is available for downloading here.

It contains list with 81 UA62, 22 524 UA61, and 1 024 029 UA60 generating pseudo-puzzles.
The collection is closed up to {-2} and less than 3000 solutions for {-2} seed.
Bi-directional search is done, i.e. each 2 solutions A and B are compared A to B then B to A in order to capture possible weakly-minimal UA.
The pseudo-puzzles with more than two solutions generate only one weakly-minimal UA, the rest UA are non-minimals.

Pseudo-puzzles statistics:

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Large Unavoidable Sets statistics

  Count Exemplar                                                                         Givens Solutions
     70 ................12..3..4........53...1..6....2..7.......5..34...6.2....87...1..9.    19     2
      4 ..............1..2..3.4..5............4.5.63..1...78......8.19...6.3.....2......7    19     3
      6 ........1..2..3....4..5..6......72...1.......6...4...5....6..5...7...3...8.1....9    19     4
      1 ..............1..2..3.4..5.......4....6.3.7...2.8....1..4.7..3..5...2..91........    19     6
----------------------
     81 Number of UA62 generating pseudo-puzzles

  17371 .................1..1..2.3...2....43.5..6..7.7..8..5....4..3..2.6..7....8..5.....    20     2
   3953 .................1..2..3.4.......5....4.6..7..8.1....3..5..4.2..3.9....81...7.6..    20     3
    748 .................1..2..3.4.....5......6..43...1.7....8..3..62...8.1...9.7...9..5.    20     4
    301 ................12..3..4........56....4.7...3.8.1...5...6..3..4.1..5..8.2.....7..    20     5
     62 .................1.23.45..........6...1..3..78...274......1.8....7.....3.4..6.2..    20     6
     62 ...............123..4..5..6..1..47...2..8....3..9.......5..7..4.8..3....9..2.....    20     7
      6 ................12..3..4.....1..3.4..5..2...67..8.......4..13...2..5...79..6.....    20     8
     11 ................12..3..45......1...6...2...7..8...54....1.6.....2.7.....4.5..83..    20     9
      2 ..............1..2..3.4..5.......4....63...7..1...2..5..4.6..3..2...8..15.....9..    20    10
      3 ..............1..2..3....4...4.5.6...2.3......7...6..1..8.4..3..6...9...1...2.7..    20    11
      1 ................12..3..45.......34...1..6..7.8..2.......4.7.6...9.......52.1...8.    20    12
      3 .................1....2345........2...3..46...7.8....9..2.5..7...61....84.....3..    20    13
      1 ...........1..2..3.4..5..6........47..2..89..3...6......8..32...9.4.....6...7....    20    17
----------------------
  22524 Number of UA61 generating pseudo-puzzles

1024029 .................1.....1234..1..5..6..5..4.....789......4..6....2..3..8.3..2..9..    21     2
 312748 .................1.....2.34..1.5..6..4...32..7..8.......59....8..6.1..7..2...43..    21     3
  49158 .................1.....234...1....5...6.7...8.4...92....8.1...6.3..2..7..5...49..    21     4
  21292 .................1.....234...1....5...3.6.7...8...4..9..75..6...4...3.2..9..1...8    21     5
   3187 .................1.....2.34..1.4.5...2.6....73....8.9...47..6....5.1....8....3.2.    21     6
   3652 .................1....23.4......5..6..1...7..78..4..3..4..9..8.3....75..6..1....2    21     7
    376 .................1..2..3.....3..4.2..1..5.6..7..8....9..4.6..3..6.1..5..5...9...6    21     8
    665 .................1.....234...1.3.5...2...4...6..7....8..31....7.4...6.2.8...5..9.    21     9
    181 .................1..2..3.4......2.3..1..5...64..7..8....3..7.2..8..9...57.91.....    21    10
    140 .................1.....234...1....5...3.6.7...8...4..2..75..6...2..1...8.4...3.9.    21    11
     18 ................12..3.14.......2...5...6......47..3.8...2.3.7...5.9....61....8.4.    21    12
     84 .................1....2345........2...16....7.3...48...2..5..9..8.1....64....73..    21    13
      7 ..............1..2..3.4..5.........6..57...3..1..82.....7.3..9..8...6..42...5.1..    21    14
     12 ..............1..2.34....5.....3.....652...4.7....4..1..15....4.8.6...3.9....7...    21    15
     10 ................12..3..4.......1..4...5.6.7...8.9....3..7..35...1..9...64...2..8.    21    16
     12 ..............1..2..3.4..5...6....3..1...24..5...7......7.6..8..4.3..9..2....51..    21    17
      5 ................12..3..45.......1..6..4..7.3..8..2.9...6...3.4.2..9....75.....8..    21    19
      2 ..............1..2..3.4.56....5..3....4.6..7..1...8..9..6......23...9.489........    21    21
      1 ........1.....2.3...4...5.......3.6...5.78....3.4..9.2....5.4...6.1...7.2.......8    21    22
      2 ..............1..2..3.4..5...6....3..1...24..5...7......7.6..8..4.3..1..2....59..    21    25
      1 ........1.....2.3...4.5........4......36....5.7...1.2...5.6...4.2...7.8.9..3..1..    21    26
      1 ........1..2..3....4..5..6.....4..5...3..71..2.......8..8..9..4.5..6....7..1..3..    21    33
----------------------
1415583 Number of UA60 generating pseudo-puzzles

======================
1438188 Collection size


There are 96 UA62. All sets have only one solution and identify the grid, givens and non-givens uniquely.

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Code: Select all

....12345.12.36.78394758612.46.752311.569348.78.2415.9.71329.562581.479.63958.1.4
....12345.13645728542.7896..6452387.2397.14.685749..13.78.645924.1859.3769.2371.4
....12345.34.67.18125843679.46.5819335962.4.78714.952..82394.6149.17.8526.72.5934
....12345.34.67.18159843672.46.5813732567.4.98714.952..87194.6349.72.8516.23.5794
....12345.34.67.81152843697.46.9817332967.45.8714.59.2.87129.3629.75.8146.53.4729
....12345.34678.19129.53768.47.9615338572.49.6915.48.2.62185.377.83.952495.24.681
....12345.36.78.19124953786.51789.3234726.5.89825.416..95126.7326.84.9517.83.5624
....12345.36.78.19125943768.72.5913434876.5.29512.468..89126.732.438.95676.4.5821
....12345.36.78.19125943786.41769.3238725.6.49628.415..98125.7325.48.9617.43.6528
....12345.36.78.19152943768.75.8912332876.5.49412.568..89326.712.485.93676.1.4852
....12345.367482.9412.39786.83.7592425189.63.7493.6.51.972534.836.9.15728.546.193
....12345134.65.78258734619.1238.7944.7529.3696.4.18523792.84.16.5.47.8384169.52.
...123456.12.457895647893.1.475312.812349.67.8952.6.43.86.175.443.85296.7.9364.12
...123456.12.47.89435896721.28419.371632.589.79436.2.5.79.81.4225.73496.8.69521.3
...123456.12.74.89435869721.28491.6715623.89.7946.52.3.79.18.4556.74293.8.39561.2
...123456.12.74.89453986712.27.691481367.82.598425.63..98.12.742.583.96176.4.5823
...123456.145.78.2265984173.478.25.119.37564.8.3641.29.812593.7539.16.8472643.91.
...123456.1456738935698.2.7.673958.2542.1697.8934.2.61.8973.6.56.1258.9472.64913.
...123456.1456738963589.27..4978.613381.59.247264.18.5.7831.96.1.2.4853795.2.6148
...123456.1456789335689.7.2.673852.9542.16.789834.216..9873.5.44.125968.72.648.31
...123456123.45789456879.21.48.31.6736945.8.27129.653..71.98.4323576.19.8943.26.5
...123456124..783936598.2.7.3184976.29763.5.484.275.914783.612.6.245.973953.12.48
...123456124.573895369487.1.68.915.23.2864.1797.23564..95.128.42475.6.9381347.26.
...123456124.578.3563894271.58.419.73465.9.8271926.34..71.825.449273.61.8354.6.29
...123456124.578.9536849172.17.869.546279.31.8593.2.64.85.316.76935.428.74126..93
...123456124.7.8.9563948721.48759.1337.81296.9.24.65.725139..784.65.7192897.6134.
...123456124.7.8393654987.2.58317.9447.86912.6.95.23.7.91734.687329.65.184.25197.
...123456124.758.9536.89172.179346.54687.2.1395386.24..95.187.468254.39.7413.6.28
...123456124.758.9536849172.58.169.746259.38.7193.2.64.71.386.56937.421.84526..93
...123456124.758.9536849172.58.312.724356.98.7912.4.63.72.186.546.79231.8.9356.24
...123456124.758.9563894172.47.183.53.674291.89.356.24.85.312.741926..837325.964.
...123456124.758.9563984172.59.167.448653.29.7124.8.63.71.493.523576..489483.261.
...12345612456.738563478.91296.5481.3579.16.248.63..756152.73.973.89..64948.1652.
...1234561457.8.293269.48712.8397.1449351.76.751.862.358263.1.7617.4593.9.42.1.85
..1.23.45.246.78.9693584271.16..2984247.9156385.3461.7138.65.9246527931.97.1.84.6
..1.23.45.674.839.324597168..9786.23736.52.1485.1.49762.5.41.3941836925769.27548.
..1.23.4524.5.678968.79.32113768.29.5.4179.368964.25.73...514724123679.875924816.
..1.23.4524.5.678976.89.32113927.86.5.4168.326824.95.73...5147845768219.9183472.6
..1.23.4526.1.78.9348569172.26.35.1419.68.3.7537491268.52.14.8341937852678.2.649.
..1.23.4526.478391843.95.6713658.72.5.4967.837982.14.63.9.4657245271.6.86873.291.
..1.23.4526.7.18.934759862115643.2987.8.1536493.2.61.748937251.5.2864.7367.1.94.2
..1.23.4526.78.31995.4.672813769.8.24.5178.636895.247.3...4158751836729.7428591.6
..1.23.4546257.8935938.6127.24.175381783.926.63548.7.925..34.813.72984.68.916537.
..1.23456.2456789.96514..37.976.5182583271.64612.9437.1367825.924.35..187.84.962.
..1.234562345.7.8968519.3.7.29.4176.3.8.5629474.289531.6247591.19763.8.54539.8.72
..1.2345624.7.18.9639485271.58614.2317.2.8.944.357961..6214.985517.9634.89.3521.7
..1.2345624.756189695.187.3.27395.643.986421.86..713.54365.297.57.1396.891864..32
..1.2345624.756318536.1897..25869.4338..7169.9.75342.14931.25.765839..2471.64583.
..1.234562435.7.8965819.3.7.6247591.4359.8.7271963.8.5.97.4126.1.6.8953438.256791
..1.2345627..48.1953419682718.952.644596.723.62783.1.53624.597.71826.5.394..71.82
..1.2345645.76812.326.14798.958362.42.7495.3184..7156.5346.29.767.14938.91835..42
..1.2345647.5.89.3563194287.1538264.2.9456.7184.9.753..5863.72439.2751.8627.41.95
..1234567.235.689465498713.13769.2.548.3.197.962.45.1824816..5937.8.942.519.726.3
..1234567.235861945467.98.3157.9243.26814..7593.8.76.231947.25.472.65.8168.3.17.9
..1234567.256.18944769582.3163.2748.59.8.31.684719..5221846.73.63.7.59.8759.82.41
..1234567.2561789336798.2.4179.5238.5381.6.4264.87.9.12543.817.79.54.6.8816.29.35
..123456723..581.965479.28..2894567.41.3.6.9279681.354.7956.42854.1.9.3686342791.
..123456723..851.946579.28.17..528966.394.72.9281.635434.867915589.136.27.652.43.
..1234567235.86.91746951832.7382.64.5.94.71.386..19.2531267.9.44581.327.69.542.18
..12345672538.69.1476591382.4576.29.3.8.15.7469.3.21.8512.8743.76942..1583.1.9726
.12.34.563.47.589.597682143.4816..2517542368962.8.947.23657..1448..965377.93.12.8
.12.34.563.517.48.67.52893118..625.3546319.277.348.61925.6.7.984.829317.937.51264
.12.34.563.517.48.67.52893118..625.3546319.277.384.61925.6.7.944.829317.937.51268
.12.34.563.517.84.67.52893114..625.3586319.277.348.61925.6.7.984.829317.937.51264
.12.34.563.571.48.67.5281391.348.697546397.2178..625.325.6.9.784.827391.937.51264
.12.34.563.571.48.67.5281391.384.697546397.2178..625.325.6.9.744.827391.937.51268
.12.34.563.571.84.67.5281391.348.697586397.2174..625.325.6.9.784.827391.937.51264
.12.34.563.578.1.9679521384.346.2.952.74986.198..53472.6324951849831.2.752..67.43
.12.34.563.718.4.969.257381.35.61.722413786957.859.1.4.76.25.434.971.5.8583649217
.12.34.563.72.589.68.197423.5361..4712.7.938.479583162.64.215.829.3.867.538476219
.12.34.563.728.14969.57138..481526371.679..242756.389..8941.2.3423867.1556.3.9478
.12.34.563.728.14969.57183..431625781.579..242783.569..8941.2.7426857.1373.6.9485
.12.34.563.728.14969.57183..431625781.579..242783.596..8641.2.7429857.1373.6.9485
.12.34.563.728.14969.57183..431625781.879..242753.869..8941.2.7426857.1373.6.9485
.12.34.563.728.14969.57183..431625781.879..242753.896..8641.2.7429857.1373.6.9485
.12.34.563.728.14969.57183..481526731.679..242756.398..6341.2.8429867.1558.3.9467
.12.34.563.728.14996.57183..431925781.576..242783.569..8941.2.7426857.1373.6.9485
.12.34.563.728.14996.57183..431925781.876..242753.869..8941.2.7426857.1373.6.9485
.12.34.563.75.28.948.697132.53461.98128.7356469.28.3.7.79.5642123.7.968.546128.73
.12.34.563.75.81.948.691273.34.76.216512834977.91.53.8.76.52.342934176855.83.971.
.12.34.563.75.81.948.691273.43.76.216512834977.91.53.8.76.52.342943176855.84.971.
.12.34.563.75.81.948.691273.53.76421641283.977.91.53.8.76.52.342943176855.84.971.
.12.34.563.75.81.968.291473.24.16.351.89.32.7593472681.5632..142.91.75.8471685392
.12.34.563.75.81.968.291473.24.56.311934726855.83.92.7.76.23.142.91.57.8451687392
.12.34.563.75.81.968.291473.34.76.122.91853.77514.3698.73.52.644963172855.86.97.1
.12.34.563.75.81.968.291473.34.76.122.91853.77514.3698.76.52.344936172855.83.97.1
.12.34.563.75.81.968.291473.36.72.144.91853.77516.3298.74.56.322934176855.83.97.1
.12.34.563.75.81.968.291473.56.23.842.18.95.7498657312.74.82635523416.988.937.2.1
.12.34.563.75.81.968.291473.56.23.842.18.95.7498675312.74.82635523416.988.93.72.1
.12.34.563.75.819.48.69.273.51482639236.17.488.935.71.174.63.255.81.93.7693275481
.12.34.563.75.829.48.692137.34165.82598.7346162.8.937..76.21549159486.232.39.76.8
.12.34.563.75.829.68.291473.5612..471.93.768.473685129.94.165322.89.371.531472.68
.12.34.563.75.84.958.691273.45.16.321.83.95.7693275184.76.52.412314876954.91.37.8
.12.34.563.75.84.959.671283.45.961321.97.35.8683215.74.76.52.412314876954.81.93.7
.12.34.563.758.91.48.691273.49253.68531.674296.81.973..73.2654119.37.68.256418.97
.12.34.563.78.529.69.17.438.34.561.21264835795782.936..5162..432893.761.4.3591827


There are 4 solution grids having 2 UA62. Sets in the third one don't share any given cell, the rest three are from common base.

Hidden Text: Show

Code: Select all

123456789457189236698237415276318594519674823834925167342791658781563942965842371
1.345.7.9457.89236.982.7.152.631.594.19.7482.834925.67.4279165878..63.4296584.3.1
1.34567.9457.8923..982.7.152.631.594.19.7482.834925.67.4279165878..63.4296584.3.1

123456789457189236698237415276318594539674821814925367342791658781563942965842173
1.345.7.9457.89236.982.7.152.631.594.39.7482.814925.67.4279165878..63.4296584.1.3
1.34567.9457.8923..982.7.152.631.594.39.7482.814925.67.4279165878..63.4296584.1.3

123456789457189263689273415241568397396742158578391642735814926864927531912635874
1.345..89.571.926.6892734.5241568397.967.215.5.839..427358149268.492..31.126.587.
12345678945..892.36.927..152.156..9739..421.85783916427.581..2686492753.91..358.4

123456789457189263689273415265938147394761528871524396512697834736842951948315672
.234.678.4571892.36.927.415.65.381.739.7.15288.1524.9651269..3473.8.29.1.48315672
.234.678.4571892.36.927.415.65.381.73947.15288.152..9651269..3473.8.29.1.48315672


MD

[JPF]

Three new UA62 (divergence 62)

In November 2012 dobrichev published his UA60+ collection: 81 pseudo-puzzles with 19 givens (70 of them with 2 solutions) generating 96 distinct UA of size 62, the collection being "closed up to {-2} and less than 3000 solutions for {-2} seed".

I redid the {-2} search on the 81 generators of size 62 (13851 seeds), without any limit on the number of solutions. It gives 3 new 19-given pseudo-puzzles with exactly 2 solutions, which differ in all 62 empty cells (divergence 62):

Code: Select all

G1 ...........1..2..3.4..5..6............2..3..7.5..6..9...3..8..2.6..4..5.7........
   936814725581672943247359168174925836692483517358761294413598672869247351725136489
   825136974671492583349857261436789125982513647157264398593678412268341759714925836

G2 ...........7..2..3.4..5..6............2..1..7.5..8..4.......1....3..7..2.9..4..5.
   926314875587692413341758269134975628862431597759286341675829134413567982298143756
   635178924917462583248359761379624815482591637156783249824935176563817492791246358

G3 .....6.........123..4..5.....1...7...2..8....3..9.......6..74...8.2.....9...3....
   172396845569748123834125976691453782725681394348972651256817439483269517917534268
   713826954658479123294315867861542739429783615375961248536197482187254396942638571


The corresponding UA62 (minlex form, the same for both solutions of each pair) are not among the 96 of the collection:

Code: Select all

G1 .12.34.563.457812979.26.48..27.53.1453814926764.78.39..56.17.3217932654828.49.67.
G2 .12.34.563.51.78.967829541..64.13.822914863758.75.96.1.86.52.341.93.85.7453671298
G3 ...123456124.57893536.981.7.197426.564893..127528.634..75.819.448356.27.9612.4.38


So there are at least 99 UA62. They were missed because of the 3000-solution cap: the seeds from which they come have 5629, 10110 and 185010 solutions.

No divergence 63 was found in the following searches:
Edit
- the full {-2} neighbourhood above;
- the full {-3} neighbourhood of the 84 generators (80185 seeds with 16 givens, adding 1 or 2 givens back; all seeds fully explored, the largest one having 50403326 solutions): no puzzle with 17 givens and 2 solutions, 13863 puzzles with 18 givens and 2 solutions, best divergence 58;
- all 18-clue puzzles "17-clue puzzle minus 1 clue plus 2 cells of its solution" (1.68 billion puzzles, best divergence 50).

All counts were checked with an independent solver.
Computations were done with the help of Claude(AI) and my own PCs.

JPF