## High clue tamagotchis

Everything about Sudoku that doesn't fit in one of the other sections

### Re: 2250+4+9+9+3+5+18+8+1+7+4+1+1+2=2322

dobrichev wrote:The number of 36s exeeded the number of grids, so most grids are expected to have a 36-given minimal puzzle.
Is this collection of 36s the largest systematic collection of sudoku puzzles ever done?

To my knowledge, yes. The biggest one i remember are the (unpublished) 1.2 billion 18 clues of ano1.
eleven

Posts: 3121
Joined: 10 February 2008

### Re: High clue tamagotchis

Well it certainly is a lot of puzzles - and it explains why we found a 36 in a random grid a way back ......
How do you keep tabs on all of them - my isomorph sorter runs out of memory at under a million grids...... ?

This first found 36 puzzle is from the MC grid [most canonical]
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`+---+---+---+|..3|..6|78.||..6|78.|12.||78.|12.|45.|+---+---+---+|.31|.64|8..||.64|8..|2..||8..|2..|5..|+---+---+---+|312|645|...||645|...|...||...|...|...|+---+---+---+`

Out of interest did you find a 37 in this grid ? !!!!
coloin

Posts: 2455
Joined: 05 May 2005
Location: Devon

### Re: High clue tamagotchis

coloin wrote:How do you keep tabs on all of them - my isomorph sorter runs out of memory at under a million grids...... ?

I explained the data model earlier in this thread. But let repeat it with some new details.

My generator uses as input a stream of subgrids with up to 40 givens (the seed). Then it strips them to 35 givens, sorts them in memory in minlex form, and adds givens. Any minimal puzzle of size 36+ is converted to minlex and added to a sorted list in memory.
The input size (batch size) is optimized to use the 64GB RAM. It is 70,000 puzzles for 37+ seed and takes about 4 hours and half to complete. For 36s the batch size is 10,000,000 puzzles and takes about 2 hours and half.
After all puzzles are processed, the sorted list is written to a file. A tag with number of givens is added at the end of each puzzle.
Then the puzzles from all batches for this generation are merged in a single ordered file.
Then the puzzles of size 37, 38, 39, 40 are filtered in a separate files, the known ones are removed by single pass over the known puzzles of the respective size. The file with all puzzles is kept for later extraction of 36s.
The new puzzles are checked for twins, and the minimal twins are added to the new puzzles of the respective size.
Then all new 37+ puzzles are used as a seed for the next generation.
New puzzles are added to the sorted list of known (and processed) puzzles with the respective size.
After the 37+ seed for the next generation is reduced to about 40,000 puzzles, the generated 36s are filtered, compared to the known 36s, checked for twins, and added to the seed. Comparing to the known 36s takes several hours. The known 36s are currently kept in 11 zipped files of sizes between 3 and 20 GB, each of them sorted. About 2/3 of the known 36s are "processed" (i.e. {-1+} is done). One or two files of known 36s are processed at once and after processing the files are renamed.
Recently a typical generation of 36+ puzzles consists of 60 batches and a 37+ generation starts from 8 batches gradually decreasing to a single batch.
Generation and filtering are automated, but adding the puzzles to the collections of knowns and processed puzzles is done manually, just for safety and for prevention of collections corruption. Manual work takes several minutes per generation when seeding with 37+ puzzles and almost one day for preparation and finalization of a generation with 36-givens seed.

For few times I also stripped out the 39s down to 34 givens and involved the so generated 36+ puzzles in the process.

coloin wrote:This first found 36 puzzle is from the MC grid [most canonical]

Interesting. I didn't know that.

coloin wrote:Out of interest did you find a 37 in this grid ? !!!!

After a run over the most of the 37s (those copied to my PC) I found no puzzle in MC grid.
dobrichev
2016 Supporter

Posts: 1859
Joined: 24 May 2010

### Re: 2250+4+9+9+3+5+18+8+1+7+4+1+1+2=2322

eleven wrote:The biggest one [collection] i remember are the (unpublished) 1.2 billion 18 clues of ano1.

I am open to publish 37s and 36s if there is interest. Most 38+ are already in public space.
dobrichev
2016 Supporter

Posts: 1859
Joined: 24 May 2010

### 2322+17+10+6+19+29+21=2424

102 more 39s
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`.............12.34123..4.56.617...8.27..68..338.12..675162.7.4873..81..58......7............1..2.34.5634...7..8..64...6..58.735.71348.6.15.237.8.8..1...27.2.853.1...........1.23.45.24.651.3.1.23..67.37..6...2.6.87..4.72.5843.143.72.585......7............1.23.45.2456.13...768..13.4.7..58.18..35.27.1237.854.7.2..3..4...5..7............1.23.4524..1563......7..61.6258.7447.1.658..185.2..762..7185.7...8...............1.23.4524..1563......7..61.6258.7447.1.658..285.1..761..7285.7...8...............1.23.45264.5..31..7.8...4.8...2.17412.37.86.463...721...75.6.7.8..41.3...........1.23.45462.5..31..7.8...4.8...2.17214.37.86.463...721...75.6.7.8..41.3..........12.34.56.35.2614...7..281..58.7....12..48.75.7..6358..8.2...675.6.8..31........1..1..2.3.34.15..26..7....6..36.45.8748..7...3.1..24.787.45.8.1282.71.6.5........1..1.23.4..5..1426.....37.82...4..37.73..524.6.1624875..7...5...58..71624........1..1.23.4..5..1462.....37.82...4..37.73..524.6.1624875..7...5...58..71264........1..1.2345.245.167.3..4..8.....86.2.4552..3.8.7.83..157.1...8...44523.7..8........1..1.2345.452.16.73..5..8.....86.25.424..3..87.83..174.1...8...55243.7..8........1..2.13.4.14..25637.....84..48.35..7.7.5.64.83.6.....182.7.8136.81..367..........1..2.3456.35..162......4.71.5...784.674.6.1.2..15.8367..7......383..67152.......12....1345...42.53......6..3..435.726.6.7.32584.31.2864..8...61..4.6.51.2.`

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`...........1..2.34.23.541.6.....76.8.165.8.47.874.6315..8.7.....7..438.11.28.5.73...........1..2.34.23.5416......768..165.8.47.874.6351..8.7.....7..4381.1.28.5.73...........1.23.45.245..631...3.7..8.17.8.354.8..45.67..8....7..7283.5161.6..2.83........1....12.3..12.34.56.2..78..5.47.25.838..4.3.7..6..8.5..27...6.1858.241.67........1....2345.245.16.73.1..8...53.8..174.4523.7..8.24.3..875....8...8.16.25.4........1..1.2345.452.16.73....8...5.83..174.5243.7..8..5..8....186.25.424..3..87........1..2..3.4...1.452.6..7...8...38.74.1221...8.74.2..8..63.83.561277.63.14.8........1..2..3.4...1.452.6..7...8...83.74.1221...8.74.2..8..63.38.561277.63.14.8........1.12.34.5.56.1.2.43..6..7.8..57.286.482.4.6..5.7..814...8.2435.72..7....8........1.12.34.56.3561.24...7.......583.6.2732.78..65.73..8.1..814.35..5..17..8.`

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`...........1..2.34..2.351....6..37.8.17.8..63.83.67415.28.4..5.1...568.26.5.28.41...........1.23.45243..5.16.371.2.681.63.8.5.4.8.671...728....43...7..8.8.4.36.7.........1..2.13.4..1354..2...5.6.27..714....62.637.1.4.2.73...5.3785.4625.8..47..........1..2.34.5..561.243....7..8...45.83.17.784.13.5.2...8.7..87.165.256...718.........1..2.34.5..561.243....7..8...45.83.17.874.13.5.2...8.7..78.165.256...718.........1..2.34.56.536.142...61.75....7.6..145.1.48.67.3548..72.7.......2.87.3.45`

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`...........1.23.45.2364.17..18.6.5...5..82.612.6.5..8..82...7..17..38..663527.81............1.23.45.245.6.31..7....83.387.54.224..38.17.1...7..8.76..2154.82.5..7............1.23.45.42.56731.....2.1..24.8.3.6.5863.42...7..8..4.85.6.17.41..75.83...........1.23.45236.457.1.2...1..81.3.8..6.6.83.21.4.672.48..3...78..68.2.3.4.7..........12.34.56.34.5612......7.18.2..8.7...78.612.5.4761.582.8..4.67.2...7..41........1..2.13.4..51674.32........8.85.3642727..486....7..1.8..18.65.7452..871..........1..2.13.4..51674.32........8.85.4632727..386....7..1.8..18.65.7352..871..........1..2.13.4.14...563...6.71.847.4.381.68..26.37...7..2..82.5.874.348..5.7..........1..2.1345..134..267...8......38.75.4227..34.85..7.8...4.2.5.1.7..81.47526........1..2.1345..134..267...8......78.35.4223..74.85..7.8...4.2.5.1.7..81.47526........1..2.1345..314..267...8......83.75.4227..34.85..7.8...4.18.47526.2.5.1.7.........1..2.34.5..3.1.542......67...7631824.2.34.7.16.2.5.3.64.6574....3..6.157.........1..2.3456.35.7.1.48..1.......271.3.8553..78.12.43..7.5626......47.54.6.23........1..2.3456.35.7.1.48..1.......271.3.8553..78.12.63..7.5424......67.54.6.23........1.12.34.5..3615.4.2..73....8.2..85..7.6847.52..73.48.15.81....7.2.571.8..........1.12.34.5..531.6.42..7..8....2.3.5.78.38.67.25.8.......2.1.835.4395.41.87........1.12.34.5..531.6.42..7..8....2.3.5.87.38.67.25.8.......2.1.835.4395.41.78........1.12.34.5..531.6.42..7..8....2.3.7.85.38.65.27.8.......2.1.835.4395.41.78........1.12.3456..561.274..318..6...68.731.55.7..1.8..75.4.8...84..7.566....84..`

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`.............12.34135....26..7.....3.13.754684563.8.71.6...7....74.5.6825218...47.............12345.13..4267....7.5...38.45726.5.2.8.34.7.....1..81.2.4.334..81672.............12345.13..4627....7.5...38.25764.5.4.8.32.7.....1..81.4.2.332..81476.............12345.13..4627....7.5...38.45762.5.2.8.34.7.....1..81.2.4.334..81276...........1..2.34.3415.2....6.753.8.782...453.58..72..1762.453.6.....7.4.3.17.62...........1.23.45.24.163.7..7..8....18.75463.45.3.7.8.5..6.8..1.6..25.4482.5..36...........1.23.45.241.5.36..7.826.3..87...5.2.6531.78.85..7..441.....677.23..58............1.23.45.241.5.36..7.826.3..87...5.2.6531.78.85..7..441..5..677.23...8............1.23.45.245..63...3.57.6...683157...72.6.8..1..7.....7238541.43.1.275............1.23.45.245.6.31..7....83.387.54.224..38.17.1...7..8.76.82154.82.5...............1.23.45.2465.3.1..7..25..24..651.765..7...4.7..3...83.6.874.248.2.67.3...........1.23.45.425.6713........8.2.8.743.4.83.2.71..46...57.162.5384.5...816............1.23.45245..1.36....37.6..371...2841.2.8.73.248....7.78.12.5415..7..8............1.23456245.6137...7.......2.37..4545..82.37.14....8.5.2.38.1487..1.56...........12.34.56.345.62.1....47.85..36.87.2.87.526....58.3..7.78.6....3.1.75.68..........12.34.56.3526.41...7..3.8..2..4..71.5.72.634.71...86.28.37.1455...8...7..........12.34.56.356.2741.....3..8.8.24.57.52.8.7.14..84.61...5...8.67.6137..8...........12.34.56.3562.741..148.56..8...7..45...63..8..73.6.85..8.7..1..5384.6.7........1..1.23...24..15.36.26.478..7.4.5..6.8....2..7.8..761..1.7234..8462.81.73........1..2.13.4..145.623...7..8....26.5738..8.36.7.2.48..51...6143.8..5.3.8142.........1..2.1345..134..267...8..7...78.35.4223..74.85..7.8...4.2.5.1....81.47526........1..2.1345..4125..3...6.......24.76.8387..32.64.1..658.2.5...1.46.6872..15........1..2.1345..4125..3...6.......74.62.8582..75.64.1..368.2.3...1.46.6872..13........1..2.34.5..631.5.24.....7...3865.2.177..3.1.82..87..2..2.7453..8634..8.75........1.12.34.5..56.1243...42......21.735..5.74.13....83.6.75.65.47.83.7...864.........1.12.34567.5316.248....1...2..1..865.28.6.3.14.2...6.75.387..42.5.7.4............1.12.34567.5316.428....1...2..1..865.28.6.31.4.2...67.5.387..24.5.7.4............1.23.14.565.1276.43....21468....6..1....4.85.7.7.....8.2...87.343.8642.75........1.23.14.565.1672.43....21468....6..1....4.85.7.7.....8.2...87.343.8246.75`

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`.............12.34.356...12..7126.85.5.4.8.71.8.75.42...827.143.138....77.4....58.............12.34123.45.67..1....86.38.5671.76..8134..82.7....3..5.4..85.4.28.73.............12.34123.45.67..2....863.8.5672.67..2834..3.5.4..8.54.81.738.1.7.................12345.13..4627....7..5..38.25476.5.4.82.3.7....1...81.4..6262..81734.............12345.13..4627....7..5..38.45276.5.2.84.3.7....1...81.2..6464..81732.............12345.13..4627....7.5...38.25764.5.4.8.32.7.....1..81.4.2.662..81473.............12345.13..4627....7.5...38.45762.5.2.8.34.7.....1..81.2.4.664..81273...........1..2.34.23.45..1.462.7.15312.54.765...6.4...68......1.4.28.6.235.761.8...........1..2.34.23.54..1.462.7.15312.45.765...6.4...68......1.4.28.6.235.761.8...........1..2.34.53164.27...6...83.3684.7.2.87.2546...8.5.....1.4...75.7521.348...........1.23.45.23.451.6.1..78.63.68.327.13.7.6..8..86..7..41...84..77.425...8...........1.23.45.23.451.6.1..78.63.86.327.13.7.6..8..68..7..41...84..77.425...8...........1.23.45.24.15.36..2....78.76.384..4.8.72361.1.3.7.84.47.81..38...5..1............1.23.45.245.6.13..7....38.387.512.21..38.74.4...7.8..76..2451182.....7...........1.23.45.245.6.13..7....38.387.542.24..38.71.1...7.8..76..2154482.....7..........12.34.56.3562.741..148.56..8...7..45...63.78..73.6.85..8.7..1..5384.6..........1....2345..24.163.7.45..8...2.8.6.57.67.2.58.4.57..21.8462.8173.8......4.........1..1..234..35.41672.....4....586.7.344.3.5..67.1.....2.3.2.1578658.2.6.13........1..1.23...24..15.36.26.478..7.4.5..6.8....2..7.8..761..1.72346.84.2.81.73........1..2.13.45.14.5236......7....87.2..3424..3..17.7826..534.6.75.8.52...8.76........1..2.13.45.4125..3...67...8..28.36.744.78.5.63.64.7.3..2......577.53.241.`

2 x 40
2 424 x 39
2 014 078 x 38
337 246 430 x 37
dobrichev
2016 Supporter

Posts: 1859
Joined: 24 May 2010

### 2424+9+7+14+2+8+30+9+4+5+6+13+23+14=2568

144 more 39s in order of their discovery
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`...........1..2.34.53164.27...6...8..3684.7.2.8732546...8.5.....1.4...75.7521.348...........1.23456.42.15.37........82...6834.8.43.26.5..8...7..1.6.37.844.7.81563...........1.23456.42.15.37........82...6854.8.45.26.3..8...7..1.6.57.844.7.81365...........1.23456.42.15.73.......8.2...685.48.45.263...8...7..1.6.57.484.7.81365...........1.23456.42.567.1..........2856.31441..826.5.3..4..68.8.6.51.31...385.7...........1.23456.45.1672...........186.234545..8126..3...4.82.8.26.53.5...3867.........1..1..234..35.41672.....4....586.7.344.3.8..67.1.....2.3.2.1875658.2.6.13........1..2.13.45.4125..3...67...8..28.36.744.78.5.63.6457.3..2.......77.53.241.........1.12.34.5..631.542...7.5..8..8...37.22368.7.45.28..1....513.82.43..5...18`

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`.............12.341345...26.278.1.4534125..875.8.7.....731...684....8.7.8..72.4.3...........1.23.45.2..41.63..713...82...78.5.81..52.37.72..5..418..94.7.34..1758............1.23456.42.5671...5.8..6..2...518..38612.7..13..8....84.67.3126..3.84...........12.34.56.34.561.2....78....485...73.7.4238.5.25..7..8.87.4.5.14.1.8..27..........12.34.56.35.6214.....78....286...37.7.25386..56..7.8..87.2.61.2.1.8..75........1..1..2.3..42.135.6.....7.6..87.36.454.6.587.3..4.8...7.1.7..352.75321.84........1..2..345..4.12.36...47.213.32.68174.7..3......7...65..2.65.78..45.21867.`

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`...........1..2.34.3514672...7.8.....18.27..6.436.187..54.1826..8.2.54..1...6458............1.23.45.23.45.61..7.8..5..1..36.87.84.721.6.46..75.8.7..5461.1....8.74...........1.23.45.456..273.....7..8.87..64214.62.8.57.3.1..58..5.3.2.141.48...32...........1.23.45.456..273.....8..7.86..74214.72.6.58.3.1..58..5.3.2.141.48...32...........1.23.45.456..273.....8..7.87..64214.62.7.58.3.1..58..5.3.2.141.48...32...........1.23456.457..823....8.....68.7.3144.736.58..2.1..6.5.5.23.14.1.46..23............1.23456.457..823....8..6..68.7.3144.736.58..2.1....5.5.23.14.1.46..23...........12.34.56.34.561.2....78....485...73.7.4238.5.25..7..8.87.4...14.1.85.27..........12.34.56.34.561.2..3.78....485...73.7.42.8.5.25..7..8.87.4...14.1.85.27..........12.34.56.34.561.2..3.78....485...73.7.42.8.5.25..7..8.87.4.5.14.1.8..27..........12.34.56.35.6214.....78....286...37.7.25386..56..7.8..87.2..1.2.1.86.75..........12.34.56.35.6214...3.78....286...37.7.25.86..56..7.8..87.2..1.2.1.86.75..........12.34.56.35.6214...3.78....286...37.7.25.86..56..7.8..87.2.61.2.1.8..75.....1..2..1.3..4.243.5.1...1.....6..621.3.57358.6721..253.648..3.8...258.4..56..`

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`...........1.23.45.426...31..7.....8.1857.32442..8...7.5.76..8..862.5..3274.38.56........1.12.34..56.3.5147...7.18..6.6142..872.8.7.1...25.876.4.7.....588.6.45...`

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`...........1..2.34.23154.67.18..5.7..4721..582..7.8.4..82.3...613.8....55.6421.8............1..2.34.3214..56.2.47...8.48921..71.78.5.4..83.1....2.43.8.7.71.25..83..........12.34.56.3526.41...17..86...7.281.4.8..4..75..8.7.641.764.258.1...8...7........1....2345..456.123...7...84..54.6871..8...75.3.7.1..32.4...82.7.52.7.6184........1.12.34....5316..42..1.7..8..8742.1.652.81.7.4.38.425.7.7.3.....2.5.8.4.3........1.12.34.5..356.1.24..71.3.82.8..7....2534.8.17.7...62..32..47..55.63...78........1.12.34.5..356.1.24..71.3.85.8..7....5234.8.17.7...65..2.63...7835..47..2........1.23.1456..14756.23....8.1...814.5.3643..71.58..85......4..6..8.37..486.5`

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`...........1..2.34..3.412.5..61.5.4..1...65.23..427.61..87...26.3..647.8.672.8453...........1..2.34.2..536.1....26..7.7.5.83.6.863.7125..87.451..172854.3.4..3.7.............1..2.34.23154.67.18....7..4721..582..7.8.4..8253...613.8....55.6421.8............1..2.34.5..3461.....78.53.7.5..84..85243.76.16.27.8..2..81367.38..5..1...........1..2.34.5..3461.....78.53.7.5..84..85243.76.16327.8..2..81.67.38..5..1...........1.23.45.2345..61..7.4...6.1637.5.4.3.5.6.72.782...5.1..73...83.2.85.17...........1.23.45234.567.1....8...7.12.758.4.87..215..26.....8.5823..161.3.685.............1.23.4524..1563..143.2.7676..5....8.2.7.45..26..7.8.17.2.8.644.8..1..7...........1.23.4524..1563..26..7.8.17.2.8.644.8..1..75143.2.7676..5....8.2.7.4.............1.23.45243..5.16.2.7....83.82...747...38.6.1...8...74325.7.818.7.1245............1.23.45263.4517...4...78.1.8.37.646.7.845.1.463.281.31...8...8.2.....6...........1.2345624..56.17.3...8.2.1.8.32.6442.61..833.4.81.7551......88....5.4...........12.34.56.35.2614......7..8..136.57..7..5861..27.8.46.1.8.4.7..54..73.81..........12.34.56.35.2641......7..8..136.57..7..5816..27.8.64.1.8.4.7..54..73.81..........12.34.56.35.2641......7..8..7.1856..5.26.17..73.8.64.1.4.72.8558..4.7............12.34.563.56.1427.....3...1.846..322.31.8564.278...4.5.....2.88.1.4..75..........12.34.563.56.1427.....3...1.846..355.31.8264.578...4.2.....5.88.1.4..72..........12.34.563.56.1427.....3...2.31.85648.146..32.278...4.1.8.4..755.....2.8..........12.34.563.56.1427.....3...5.31.82648.146..35.578...4.1.8.4..722.....5.8........1.....234....13..2...5..1.6..76384.1581.5.6473.6.84...2.8.2.563.52.6.3.84........1..1..234.23..14.56.1527.68.3.7.48.1.82...1.7..53...86..8...5..77.2.86.35........1..1.23..4..5.1426.....5.7...5837.4267.64821.5..7..8....84.3.6.26..2458.7........1..1.23.4..2415.673..281.4.6.48.65.121....2.5...758.3.4.83....6.4...36.87........1..2.13..4.41.2536..173.....284.7163.63..82.17.26..784..782....64....8.7.........1..2.1345.14.62573...7.68..362.53..8.8....25...1.3.687..76.813.5.8..5..1.........1..2.1345.14.62573...7.68..562.35..8.8....23...1.5.687..76.815.3.8..3..1.........1.12.34.5..3516.2.7....4..82.84...5..523.8..74..8..6....4681.7.5351.72.68........1.12.3456.5.3.71428....1..8...146...56.5.87.14..6.....2.27.4685..5.72..46........1.23.1456..1527643......285..5..6....2.4.58.76.4162.38..8...3.1.3.2.816.......1..2.13....4.25.46..31..274..83.37.862.4.8...3.7..21.74.68.7..184258..6.....`

Code: Select all
`...........1..2345.32.4561...5..783..185..7.43.74.85.1.86.....315...6.8.2.38.41.6...........1.23.45.645...27..2....18.1823.47664.18...2.56.7..8..8.3...544.385.76............1.23.452345.67.1..7.....84....7.166182..4.7.42..8.63.836.21.41.63..8............12.34.56.35.621.4.....76...68341.7..71.96.4..274138...8..7.4.21...28..7..........12.34.563.456.721....53172..76...3.1.34..5.8..1..6.852...8....6.8.45217..........12.34.563.56.1427.....3.8.1.846..322.31.8564.278...4.5.....2..8.1.4..75..........12.34.563.56.1427.....3.8.1.846..355.31.8264.578...4.2.....5..8.1.4..72........1.12.34.5..536.1.24..5.63..7.27.4856.3..7...1..78......2.1.86.7553.4.7.82........1.12.34.5..536.1.24..5.63..7.27.4856.3..7...1..78......23.4.7.855.1.86.72`

Code: Select all
`..............1.23.24.3..51..1.6..7..461.73.575..84.16.684.2537.72..6..84.58...62..........12.34.56.3516.42...7..3.8..63.1.27.128.47.35.71.865.2.8....7..2...7..68..........12.34.56.3526.41...73...6..26.47...1.3.2674..58.12.7..7..8....261.7358...........12.34.563.456.721....531.2..76...3.1.34..568..1..6.852...8....6.8.45217`

Code: Select all
`...........1.23.45.26.4173...2..5.8..5821.36.16..38....1537.8...8..5247.2...865.3...........1.23.45.26.4173...2..5.8..5821.36.16..38.5..1537.8...8..5247.2...86..3..........12.34.565.78.1423.....7....513...747.84.6.35....4..68..56.83.7.86.7354......1..2..1.3.45.243.5617...267.58..8....7..6.7..8.24..81...4..24.6581.1.6.8.2.5.....1..2..1.3.45.243.6517...267.58..8....7..6.7..8.24..81...4..24.5681.1.6.8.2.5`

Code: Select all
`..........12.34567.352.6481.....3..5.237..64.5.76.82.3..1..78...5..8...6.78.6.154........1..2..3.4..53146.27..1..8.....86.5.145..4.1.83.853.74.22.7564.383..8...7.........1.12.3456..536.124......71...7134..2523.1.547..2.7......874.36.23.6...75.........1.12.3456..536.124......71...7134..252381.547...74.36.2.2.7.....3.6...75......1..2..1.3245..4256..31..73....54.6.7.32.5...26.47.7..53.141......7.6.4.17.83.....1..2..1.3245..4256..31..73....54.6.7.32.5...26.47.78.53.141......7.6.4.17..3`

Code: Select all
`...........1.23.45.241...36..37.....2.73.84.14.85.2.73.462.158.1.28.5.648....6.1............1.23.45.241...36..73.....2.37.84.14.85.2.73.462.158.1.28.5.648....6.1............1.23.45234..5.16..7..4.3..4.2.8.575231.7.84.12.8..7..7.3....83.87.2.61...........1.23.45234..5.16..7..4.3..4.238.5752.1.7.84.12.8..7..7.3....83.87.2.61...........1.23.45234..5.61..7..4.3..4.2.8.575231.7.84.12.8..7..7.3....83.87.2.16...........1.23.45234..5.61..7..4.3..4.238.5752.1.7.84.12.8..7..7.3....83.87.2.16........1..1.23.4.254.613.......67..462.378.57..28...41.635.47.3.7.1..5.54..721..........1..1.2345..42.16.37..4.87....2.3.5..8.582.1.43.85.3..7.2.7.583.44....2.85........1..1.2345..42.16.37..4.87....2.3.5..8.852.1.43.58.3..7.2.7.583.44....2.85........1..2.13.4..51.64..7..5.8.....68..1.7471.42..58.2.6...83.36.487.2.87.3246.........1..2.13.4..51.64..7..5.8.....68..1.7471.42..58.26.487.3.3.6...82.87.3246.........1..2.13.4..51467.32.......8..26.783.4.8734..16..8..4...2..73..687.5.81423........1.12.34.5.5.31.624......7..6.2.64.7...7.3.8425..1....7..374.156226.7.31.4`

Code: Select all
`...........1..2.34.23.546.1..7.6..12.32..57.61.62.7345.187.6453.745..1..3.......7...........1.23.45.23.4561...7..48...46.18.573.8.5746..3..82.76.7.53..8.8.2.7.5.............1.23.45.24.516.3.172.45.8.48.3...72...78.64.763.28...8..1..7.1.2.87..6...........1.23.45.421...36...7.....2845...737.638.45..682.751.1.7..8.6.42.6.1.87...........1.23.45.451...23..4..637..5673.4.2.7.2...56.17.68234.38.12.6..6..7...8...........1.23.4524..15.63.....7..8.84.5..7.73..8145..13.7268..2.1.4.3747..38.2............1.23.4524..15.63.....7..8.84.5..7.73..8145..13.72684.2.1.4.37.7..38.2............1.23.4524..5631...6.72458..7.......8256.73.1.3.875.47.461..8.8...3.17............1.23.4526.4.137...........12534.8.7.8162.34.263.5..71.7..6.535...1746............1.23.4526.41.37...........18542.3.7.2136.84.2635...71.7.6..535...7146...........12.34.56.35.2641...1.73....7.2.1.8.2.346.17...7.8..4..2...7.68.5864273.........1....2345..24156.37.....8......26517.26..14.85.4..3271..8..4...337.68154.........1....2345..24156.37.....8......26571.26..14.85.4..3217..8..4...337.68154.........1..2.13.4..51467.32.....6.8..26.783.4.8734..1...8..4...2..73..687.5.81423........1..2.13.45.13.5627......14....1362.5.3.75.41.6.38.2..64.746358.22....8...........1..2.13.45.136457.2....8.....87.342.632...68.4..1..7..823.4581.77...614..........1..2.13.45.136457.2....8.....87.362.432...48.6..1..7..823.4581.77...614..........1..2.13.4513..546...4..3.7.6263.75..87....8....8..47.6.3.75.6..442.3815.7........1..2.13.4513..546...4..3.7.6263.75..87....8....8..47.6.3.75.6.8442.3.15.7........1.12.34.5..635.1.2...47...8..284.37.5.3..85....76.581...81.4657.3..1.7.68........1.12.34.5.5.3.162.4..4.7..8..57.834.23.8.427.5.3...8..7.7536..288.1..7..........12..1.234...25.16378...3....1.1..6854.5.8.41.63..6..2..4.4268..3585..3..2........12..1.2345..25.16378...3....1.1..6854.5.8.41.63..6..2..4.4268..3.85..3..2.`

Code: Select all
`...........1..2.34.321456.7..62518...284.6...1...38..6.875.43..213.874..5...2.7.8...........1..2345.32.45.6...7.....432..7485.4.5.28.37.53.87.16.7..1.58.1.8..6.73...........1.23.45243..5.61....5...71.2.475867..2.8.1..18.746.24......786.78.2.54...........1.23.45243..5.61....5...71.2.475867..8.2.1..18.746.24......786.72.8.54...........1.2345624..5137..67..58..4...38...8...6.54..74.862.55.8.726.462....78...........12.34.56.345.621...1.57....47.136.53..6.217...8.7..62.23.6578..7...85..........1....2345..24156.37.....8......26517.26..14.85.4..32718.8..4...337.6.154.........1....2345..24156.37.....8......26571.26..14.85.4..32178.8..4...337.6.154.........1..2..3..4.13.4526...1..78...2.4.8.17.87..1642.5..7.....785.4.262348.6.75........1..2.13.45.5124.3....6..78.4.1863.7..5.7.28.36.25.81.63.6.3.25.8.8..6............1..2.13.4513..54.26.53.781.2.7...1...21.53..74.8..4.2..3...8..5772.3.54.8........1.12.34.5..35.164.2..3..784..584.31.7.7..8.....276.85...81..27.454..712..........1.12.34.5..35.164.2..3..784..584.31.7.7..8.....276485...81..27..54..712..........1.12.34.5.6.317..48....2..1..31457.262.631.4.5....83.64..8...5..36.74..82`

The source code is available at https://github.com/dobrichev/sudoku35plus
dobrichev
2016 Supporter

Posts: 1859
Joined: 24 May 2010

### 2568+8+3+1+2+2+1=2585

The next batch.
Hidden Text: Show
Code: Select all
`...........1..2345.32.45.6...7.....43...748514.5.28.37.53.87.16.7..1.58.1.8..6.73...........1.23.4523.4.5.16.17234.585....71..8.35.1.74.7.3...8..8...2..73.27.846............1.23.4523.4.5.61.17234.585....71..8.35.1.74.7...2.8..8.3....73.27.84.6........1..1.23..4.521.4.3....6.1....652371.81.7.486.3.864..3..2.43.6.855...82..6........1..1.23.4524..15.36..2.7..584.85.23.77...3.4..1.425..8352..871.48....1...........1.12.34.5..3617.428..8....1..2571...4.71.48.62.534...8..8.65.2432...8...5........1.12.34.5.65.2.1.43.....75...2...3.76.75.2613..87.6....2.37.8..5561.42.87........1.12.3456.5.62.143....7..68...5..8..3.684.3.75..13.27....7.4..1.2.41.7356`

Code: Select all
`...........1..2.34.3..56.21..67...82..7..814..48215.67.7..8...6.856.7.136.352..78........1..2.13.4..5162473......6.8..86237.542.5.48.76..83..4...2..81.6.5..4.281.........1..2.13.4..5162473......6.8..86247.532.5.38.76..84..3...2..81.6.5..3.281.`

Code: Select all
`...........1..2.34.3456..27..8..5.4.3..6....86452.8.13.8...6.711.38.746.47.15..82`

Code: Select all
`........1.....2.3.123.45.67..8......245.8..7331.52..4846..583..5312.6.848.24....6........1....2345..45..623..576..8..4.2..8.7.86.7.25.4.71.8.3...8.2.71.55243.1.8.`

Code: Select all
`...........1.23.45.2..64.31..23.6.74..5.72..373.41...8.18.47.56.7...1.8.25.6.8.17...........1.23.45.2..64.31..24.6.73..5.72..474.31...8.18.37.56.7...1.8.25.6.8.17`

Code: Select all
`........1..2.34.5..631.5.24.....7...3865.2.177..3.1.82..84..27.2.4.53..8637..8.45`

It is harder and harder to do more 39s.
Discovering of more 40-givens puzzles has less chance than discovering of green creatures living on Mars.
There are still much 36s to discover. The derivative 37s and 38s are exhausted quickly.
dobrichev
2016 Supporter

Posts: 1859
Joined: 24 May 2010

### 2585+9+24+14+6+5+3+2+1+1=2650

The next batch.
Hidden Text: Show
Code: Select all
`..............1.23..1..2.45.36.1..57215.7346.4.7..6.3..68.27..41436.8.727.21...8............1..2.34.5..34.16..7..8..351..43.878.3.75142.2.....7..75.86.211.8.2746............1..2.34.5..34.16..7..8..351..43.878.3.75142.25.86.71.7.....2.1.8.2746............1..2.34.5..34.61..7..8.4.51..43.788.4.75123.2......7.75.86.121.8.273.6...........1..2.34.5..34.61..7..8.4.51..43.788.4.75123.25.86.17.7......21.8.273.6...........1..2345.341652.7...5..7.8.8..2..3.7.3.1852...6.5.8....82.16.3.17.86452...........1..2345.341652.7...5..7.8.8..2..3.7.3.1852...62.18.3..8.5.6...17.86452...........1.23.45.421...63..73.84...8..16..713.2.7.86..87.1..441.532.787.38...5............1.23456.45.172.3.....1845.1..5....4.6.7813...2.8..64.64.325.858...632.`

Code: Select all
`..............1.23124..3.56..1..6.782.7.8.3.14.81.756264..58..77......8.8.27.4635.............12.34.135..627....7..82..7..845..81245.76..8.23..5.3.457.68.7.8.1.43.............12.34123.45.67.38.21..66.......871..683.2.8...4.7.2.4.57.8337..864.5.............12345.13.467.2..1.842.3.82...45.3...25..8.36..8..7.78.615341.5.7.8.............1..2.34.23.145.6..762...8.1.4.8.57.38.71642.72...46.1.52.6.733....7..5...........1..2345.23.45.1...6.....7.35..746.2.76.4531.62....7.31..7865.7.84.61.3...........1..2345.23.451....6.....7.35..746.2.76.4531.62...7..31..7865.7.84.6.13...........1.23.45.24.153.6..7..28...1..876.4.4813...7.7..5846..85.6..734...715.8...........1.23.45.24.5..63.......7..17.8653448.73..21.723.8..61.8.62..764.57...2...........1.23.45.245.6.31..23...67..62.54.3.4..67.5..18.5237..6713...82....8.14...........1.23.45.2465..31..2....7..7623.1.441..675...47.8....1.83.2.5723..76.18...........1.23456.45.172.3.....184..1..5....456.7813...2.8..64.64.325.858...632...........12.34.56.35.6742....6.158..81.4..7.52..78..4..87...4515..832672....68............12.34.56.3526.4.1..1.7..8..5.8..7.4.7842.615.2......81..34.5625.3.8.1.7..........12.34.56.3526.4.1..1.7..8..5.8..7.4.7842.615.2......81.3.8.5.75..34.162..........12.34567.345.6812..8..5.71.2.7.865..7....2...4..83125.83.5...62....738.........1.....2.3..34.15.2...6..7.58.48.5617.7.51.8.64.638.471..8..7...64.7.61.83........1..1..2.3..3...4256..7.83..518.4.7.2334.2...87.74.21.6861..48.728..7.6...........1..1.23.4..42.51367..4.82..6.1856.432.6..1...8..7..8....8.23..7442..75.83........1..2.13.4..1354.2....6.78.52.2835..675.7.6.81..846.....2.143..8.36..8..24........1..2.13.4..14.5.236..7..8.6..4653..78.8376.452.2.37..14.71.8..2.43......7........1.12.34..5.356.124......7....28345.76.731..4.2..7...6...867.35.435.4.6.27........1.12.34.5..6351.247..1.57.26.2.1.....6.74..1.5.36..57...7834.5622...7...3.....1..2..2.3.45.34..521.6..4.735.1.7.....6..8316.7.4.2731..45.365..2.74...27...`

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`...........1..2.3425.36..17..7.4..2.4.8..5.76526.37.4.175.26.836...8....8.2.53.61...........1..2.3425.36..71..7.4..2.4.8..5.67526.37.4.175.26.836...8....8.2.53.16...........1.23.45234.56.71.....1.8..42.685.78.32.541..27.8....3.86.27.44.6.3...8...........1.23.45234.56.71.....1.8.142.685.78.32.54...27.8....3.86.27.44.6.3...8..........12.34.56.35.2614...7.824...2...7.681..64..7..732.1.84.8..73...2.1.6873...........12.34.56.3526.4.1..1.7..8..5.8..7.4.7842.615.2......81..34.56.5.3.821.7..........12.34.56.3526.4.1..1.7..8..5.8..7.4.7842.615.2......81.3.825.75..34.16...........12.34567.345.6812..8..5.71.2.7.86...7..6.2...4..83125.83.5...62....738...........12.34567.345.6812..8..5.71.2.7.865..7..6.2...4..831.5.83.5...62....738.........1....12.3..14.536.2....7..8...73.82...83.257.6..1..79...985361.77.5.91368........1..1.23.4..541.6.32.....2.7..45.37.26.726.53.4..7......4.8.61.575.6.78413........1..1.23.4..541.6.32.....2.7..45.37.26.726.54.3..7......4.8.61.575.6.78314........1..1.23.4..541.6.32.....7.2..45.32.76.726.53.4..7......4.8.61.575.6.78413........1..1.23.4..541.6.32.....7.2..45.32.76.726.54.3..7......4.8.61.575.6.78314`

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`..............1234..2.3.5.6..7.864...461.7..3.8134.6.7.2.7....8.584137.2.74.283.5........1.12.34..5.36.51.2...3.17.48.483.25.7.6..482...8....7..3...75.8667..831.2........1.12.34.5.36..51.42....7..1..314.5.87.76.124.5..7.4..28.2358..74.8...75..........1.12.34.5.6.31.52.7.....3..5.2584.....365.7428..1.7..8...74.81.22.83.1.74........1.12.34.566.5.12347..1.6.47..7634.1.55....1..3..8..7.34.5..2.....6748.5.2.....1..2..1.3..4.45..6..3...6....78.8567.4.374..1826..1875.324.7..8....5.412..87`

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`.............12.34.13.456.2.4..5.7.3.71.8.4..3.6.74.28.87.2.3.613..682.76....7.81.............12.34.13.456.2.41.7.8...8..5.4.33.6.84.27.78.2.3.613..672.86....8.71...........1..2345.3456172......8.7..836.751.7.61.583...8.1425..428.....1..2.648.........1..2.34..5.36.51.2...3.17.48.483.25.7.6..482...8....7..32..75.8667..831.2........1.12.34.566.5.1234...1.6.47..7634.1.55....1..3..8..7.34.5..2.7...6748.5.2`

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`........1....23.4..25.413....6..47..2...76.347.4238.16.62.85.73.8..6..5.5.73.2.68........1..2.13.4.14..52.36....783.4.74531.688..2...57.17.2..8..25.876.3.8...5.7.........1..2.13.4.14..52.36....783.4.74531.688..2...57.1732..8..25.876...8...5.7.`

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`.............12.34.153...26....7..4..4123...776.1.4.53..67....815486..7287.421.65..........12.34.56.35.267.1.24.8.5.7.586.7.121.7..2..8.43.681.5.8.4.....5....3.84`

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`.....1..2..3.4.56..2536.41...76..1...61.73.2423..1467..5...7.4..7..3.2..3.248.75.`

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`........1..2.13.4.14..523.6.26.7143.3.426.1.77...3.....6....7..2.5.876.44.7.2658.`
dobrichev
2016 Supporter

Posts: 1859
Joined: 24 May 2010

### Minimal 40-clue Puzzles

Just a note to advise that one of dobrichev's 40-clue minimal puzzles (still the highest known number of clues for a minimal puzzle) also has an 18-clue puzzle on the same grid:

Code: Select all
`..........12.34567.345.6182..1.582.6..86....1.2...7.5...37.5.28.8..6.7..2.7.83615   40-clues5........81....5.......6..2...3...9.3..6.2.7.......8...6..1......5....3.....8...5   19-clues......34.81...4...9.................3...9...1.....7.5..6..1.9.8..5........7.8....   18-clues576821349812934567934576182741358296358692471629147853463715928185269734297483615`

Coincidence?

Note: I have not excluded the possible existence of a 17-clue puzzle on this grid, perhaps someone might do that?

Mathimagics
2017 Supporter

Posts: 1926
Joined: 27 May 2015
Location: Canberra

### Re: Minimal 40-clue Puzzles

Mathimagics wrote:Coincidence? ?

unfortunately not
.... maybe one in three solution grids have an 18, almost all solution grids have at least one 19 ....
the MC grid doesnt have a 19 and only has one ED 20-puzzle
coloin

Posts: 2455
Joined: 05 May 2005
Location: Devon

### Re: High clue tamagotchis

Ok, no big deal then.

Thanks coloin!

Mathimagics
2017 Supporter

Posts: 1926
Joined: 27 May 2015
Location: Canberra

### New 39C minimal

I believe this is a new 39-clue minimal puzzle:

In puzzle minlex form:
Code: Select all
`..........12.34567.345.6128..1.582.6..86....1.2...7.5...37.5..2.8..6.7..2.7.83615576821349812934567934576128741358296358692471629147853463715982185269734297483615`

In grid-canonical form:
Code: Select all
`1..4....9.5..8..2..981.2..4..1..5.9.58.2....7.798412.5.67518.4281.924.76.........123456789456789123798132564231675498584293617679841235367518942815924376942367851`

This was found by processing one of Mladen's famous 40C minimal puzzles with his sudoku35plus tool (https://github.com/dobrichev/sudoku35plus). I am trying to establish whether or not the only known grid with a 40C also has a 39C, and this seemed like a relatively quick way to find one ...

But no, because the 40C grid and the 39C grids differ ever so slightly (by a UA4):
Code: Select all
`123456789456789123798132564231675498584293617679841235367518942815924376942367851 # CF soln to the 39C above123456789456789123798132564231675498584923617679841235367518942815294376942367851 # CF soln to the 40C                                       **                         **`

So, I have not actually demonstrated that the 40C grid has a 39C, but neither can I say that it doesn't. This question remains open.

If it could be proven that there is no 39C minimal puzzle on the 40C grid, then this would be significant for the (notional) "High Clue Threshold" project, at least as far as any "minimal puzzle continuity" conjecture" is concerned. This refers to whether or not all grids have minimal puzzles of EVERY size, from the least-clues case throught to the most-clues case.

Mathimagics
2017 Supporter

Posts: 1926
Joined: 27 May 2015
Location: Canberra

### Re: High clue tamagotchis

Only to mention that your puzzle is very close to one published on page 10 of this topic and to the one on line 1545 in this file.
dobrichev
2016 Supporter

Posts: 1859
Joined: 24 May 2010

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