The New Sudoku Players' Forum

by **coloin** » Thu Jun 07, 2007 10:56 pm

A while ago we wondered what was the maximum number of clues in a minimal sudoku puzzle.

Dukuso started with a randomly generated 32 clue puzle - this is what you get if you generate several million puzzles !

Gradually Ocean worked the way up to a 35 clue puzzle in the MC grid.

I found a chameleon clue 36 clue puzzle, and a few more to go along with it in the MC grid.

Code: Select all: *-----------* |..3|..6|78.| |..6|78.|12.| |78.|12.|45.| |---+---+---| |.31|.64|8..| |.64|8..|2..| |8..|2..|5..| |---+---+---| |312|645|...| |645|...|...| |...|...|...| *-----------*

plus 5 more

Code: Select all: ..34.678.78.12.45...678.12..31.648...648.....8..2..5..3126.5...645....1.......... ..3.5678.78.12.45...678.12..31.648...648.....8..2..5..3126.5...645....1.......... ..3..678.78.12.45...678.12.231.648...648.....8..2..5..3126.5...645....1.......... ..3..678.78.12.45...678.12..315648...648.....8..2..5..3126.5...645....1.......... ..3..678.78.12.45...678.12..31.648..5648.....8..2..5..3126.5...645....1..........

I had a grid which revealed more and more 35s - eventually it yielded a 36 clue.

Subsequently over time my program has chanced over 2500 35s and eventually 30 different 36 clues in this grid.

Code: Select all: ....567....71...36..83.251.....3......9..56...4..2.953.1.79..6..74.6319.9..5.13.7 ....567....71...36..83.251.....3......9..56...41.2.95..1.79..6..74.6319.9..5.13.7 ....567....71...366..37.5142..9....1.....5....41...95...279..65.7..6319.9.65.1..7 ....567....71.9.366..37.514...93...1....15....4....95...279..65.74.6319...6..1..7 ....567....71.9.366..37.514..593...1....1.....4....95...279..65.7..6319...65.1..7 ....567....71.9.366..37.514..593...1....1.....4....95...279..65.74.6319...6..1..7 ....567....71.9.366..37.514..593...1....15....4....9....279..65.7..6319...65.1..7 ....567....71.9.366..37.514..593...1....15....4....9....279..65.74.6319...6..1..7 ....567....71.9.366..37.5142..93...1....15....4....95...279..65.7..63.9...65.1..7 ....567.9..71.9.366..37.51....93...1....15....4....95...279..65.74.6319...6..1..7 ....567.9..71.9.366..37.51...593...1....1.....4....95...279..65.74.6319...6..1..7 ....567.9..71.9.366..37.51...593...1....15....4....9....279..65.74.6319...6..1..7 ....567.9..71.9.366..37.514..593...1....1.....4....95...279..65.7..631....65.1..7 ....567.9..71.9.366..37.514..593...1....15....4....9....279..65.7..631....65.1..7 ....567.9..71.9.366..37.5142..93...1....15....4....95...279..65.7..63.....65.1..7 ..3.567....71...366..37.5142...3...1..9.15....4....953...79..65.7..6..9.9.65.1..7 ..3.567.9..71...366..37.5142...3...1..9.15....4....953...79..65.7..6....9.65.1..7 ..3.567.9..71...366..37.5142..93...1....15....4....953...79..65.7..6....9.65.1..7 ..3.567.9..71...366..37.5142..93...1..9.15....4.....53...79..65.7..6....9.65.1..7 1...567....7.....66...7.5142...3........15.........9533..79..65.74.6319.9.65413.7 1...567....7.....66...7.5142..93........15.........9.33..79..65.74.6319.9.65413.7 1...567....71....66...7.5.42..93........15.........9.33..79..65.74.6319.9.65413.7 1...567....71...36..83.251.....3......9..56...4....953.1.79..6..7426319.9....13.7 1...567....71...36..83.251.....3......9..56...4..2.953...79..6..74.6319.9..5.13.7 1...567....71...36..83.251.....3......9..56...41.2.95....79..6..74.6319.9..5.13.7 1...567....71..236...37.51.....3......9...6...4.6..95..1.79..6..7426319.9..5.13.7 1...567.9..7.....66...7.5142...3........15.........9533..79..65.74.631..9.65413.7 1...567.9..7.....66...7.5142..93........15.........9.33..79..65.74.631..9.65413.7 1...567.9..71....66...7.5.42..93........15.........9.33..79..65.74.631..9.65413.7 12..567....71....6..837.51............9..56...4.6..953.1.79.465.74.6.19.9....13.7

one of them

Code: Select all: ....567.9..71.9.366..37.51...593...1....1.....4....95...279..65.74.6319...6..1..7 SE 8.9 !

I have no idea where the grid came from - I believe it was a randomly chosen grid from one puzzle.

Untill today making these high clue - and paradoxically dificult puzzles was very difficult. Adding a clue tended to lose the minimality.

Today I tried gsf's program to see if any progress could be made.............

I didnt get any more 36s but I did get a couple more 35s !

C

by **coloin** » Thu Jun 07, 2007 11:01 pm

Generated from other puzzles .......a lot of puzzles are formed ...only a few are minimals - from an initial run - here are just under 400 minimal 35s from over 85 different solution grids.

123456789456789123789132564217398456345261897968547231532974618671823945894615372 12.45.....5..89.2...91.2..421..984...452.189....54.2..5.....6..671...9...9..1..7.
123456789456789123789132564217398456345261897968547231532974618671823945894615372 12.45...9.5..89.2...91.2..421..984...45.6189....54.2..5.....6..671.......9..1..7.
123456789456789123789132564217398456345261897968547231532974618671823945894615372 12.45...9.5..89.2...91.2..421..984...452.189....54.2..5.....6...718......9..1..7.
123456789456789123789132564217398456345261897968547231532974618671823945894615372 12.45...9.5..89.2...91.2..421..984...452.189....54.2..5.....6..671.......9..1..7.
123456789456789123789132564217398456345261897968547231532974618671823945894615372 12.45..8..5..89.2....1.2..421..984...452.1.9.9..54.2..5.....6..671...9...9..1..7.
123456789456789123789132564217398456345261897968547231532974618671823945894615372 12.45..8..5..89.2...91.2..421...84...452.1.9....54.2..5..9..6..671...9...9..1..7.
123456789456789123789132564217398456345261897968547231532974618671823945894615372 12.45..8..5..89.2...91.2..421..984...45.61.9....54.2..5.....6..671...9...9..1..7.
123456789456789123789132564217398456345261897968547231532974618671823945894615372 12.45..8..5..89.2...91.2..421..984...452.1...9..54.2..5.....6..671...9...9..1..7.
123456789456789123789132564217398456345261897968547231532974618671823945894615372 12.45..8..5..89.2...91.2..421..984...452.1.9....54.2..5.....6..671...9...9..1..7.
123456789456789123789132564217398456345261897968547231532974618671823945894615372 12.45..89.5..89.2....1.2..421..984...45.61.9.9..54.2..5.....6..671.......9..1..7.
123456789456789123789132564217398456345261897968547231532974618671823945894615372 12.45..89.5..89.2....1.2..421..984...452.1...9..54.2..5.....6..671...9...9..1..7.
123456789456789123789132564217398456345261897968547231532974618671823945894615372 12.45..89.5..89.2....1.2..421..984...452.1.9.9..54.2..5.....6..671.......9..1..7.
123456789456789123789132564217398456345261897968547231532974618671823945894615372 12.45..89.5..89.2...91.2..421..984...45.61.9....54.2..5.....6..671.......9..1..7.
123456789456789123789132564217398456345261897968547231532974618671823945894615372 12.45..89.5..89.2...91.2..421..984...452.1.9....54.2..5.....6..671.......9..1..7.
123456789456789123789132564217398456345261897968547231594873612671925348832614975 12.45..89.5..89.2....1.2..421..984...452.1.9.9..54.2..5..8..6..671..........1..7.
123456789456789123798132546231894675564271398879365214382647951615928437947513862 1...56.89......1...9.1.25.62.18946.55..2.1..8....6521....6.......5..84.794....86.
123456789456789123798132546231894675564271398879365214382647951615928437947513862 1...56.89......1...9.1.25.62.18946.55..2.1..8..9.6.21....6.......5..84.7.4.5..86.
123456789456789123798132546231894675564271398879365214382647951615928437947513862 1...56.89......1...9.1.25.62.18946.55..2.1..8..9.6521....6.......5..84.7.4....86.
123456789456789123798132546231894675564271398879365214382647951615928437947513862 1...56.89....8.1...9.1.25.62.189.6.55..2.1..8..9.6521....6.......5..84.7.4....86.
123456789456789123798132546231894675564271398879365214382647951615928437947513862 1...56.89.5..8.1...9.1.25.62.189.6.5...2.1..8..9.6521....6.......5..84.7.4....86.
123456789456789123798132546231894675564271398879365214382647951615928437947513862 1...56.89.5..8.12..9.1.25.62.189.6..5..2.1..8..9.6521..........6....84.7.4....86.
123456789456789123798132546231894675564271398879365214382647951615928437947513862 1...56.89.5..8.12..9.1.25.62.189.6..5..2.1..8..9.6521....6.....6....84.7.4....8..
123456789456789123798132546231894675564271398879365214382647951615928437947513862 1...56.89.5..8.12..9.1.25.62.189.6.55..2.1..8..9.652...........6....84.7.4....86.
123456789456789123798132546231894675564271398879365214382647951615928437947513862 1...56.89.5..8.12..9.1.25.62.189.6.55..2.1..8..9.652.....6.....6....84.7.4....8..
123456789456789123798132546231894675564271398879365214382647951615928437947513862 1..4.6.89....8.1...9.1.25.62.189.6..5..2.1..8..9.6521....6...5...5..84.7.4....86.
123456789456789123798132546231894675564271398879365214382647951615928437947513862 1..4.6.89....8.1...9.1.25.62.189.6.55..2.1..8..9.6521....6.......5..84.7.4....86.
123456789456789123798132546231894675564271398879365214382647951615928437947513862 1..456.8.......1...9.1.25.62.18946.55..2.1..8..9.6521....6.......5..84.7.4....86.
123456789456789123798132546231894675564271398879365214382647951615928437947513862 1..456.8.....8.1...9.1.25.62.189.6.55..2.1..8....6521....6.......5..84.794....86.
123456789456789123798132546231894675564271398879365214382647951615928437947513862 1..456.8.....8.1...9.1.25.62.189.6.55..2.1..8..9.6521....6.......5..84.7.4....86.
123456789456789123798132546231894675564271398879365214382647951615928437947513862 12..56.89.5..8.12..9.1.25.62..89.6..5..2.1..8..9.6521..........6....84.7.4....86.
123456789456789123798132546231894675564271398879365214382647951615928437947513862 12..56.89.5..8.12..9.1.25.62..89.6..5..2.1..8..9.6521....6.....6....84.7.4....8..
123456789456789123798132546231894675564271938879365214315928467647513892982647351 1...5678..5..8.1...9.1.25.62.189.6.55..2.1..8..9.6521......8467.4....8.....6.....
123456789456789123798132546231894675564271938879365214315928467647513892982647351 1...56789.5..8.1...9.1.25.62.189.6.55....1..8..9.652.......8467.4....8.2...6.....
123456789456789123798132546231894675564271938879365214315928467647513892982647351 1...56789.5..8.1...9.1.25.62.189.6.55..2.1..8..9.65........8467.4....8.2...6.....
123456789456789123798213564214538697385697241679124835541362978867945312932871456 .23.5..8.45.78....7..2.35.4....3..9.3..6972...7.......54.3.....8.7.45..293287.4..
123456789456789123798213564214538697385697241679124835541362978867945312932871456 .23.5..8.45.78....7..2135.4....3..9.3...972...7.......54.3.....8.7.45..293287.4..
123456789456789123798213564214538697385697241679124835541362978867945312932871456 .23.5..8.45.78..2.7..2.35.4....3..9.3..697....7.......54.3.....8.7.45..293287.4..
123456789456789123798213564214538697385697241679124835541362978867945312932871456 .23.5..8.45.78..2.7..2.35.4....3..9.3..6972...7.......54.3.....8.7.45...93287.4..
123456789456789123798213564217598346589364217364172958835627491671945832942831675 12.4....94.6.8.12..9821..6421...8.46.89.6..1...41..95.8..6.7.9..........9......75
123456789456789123798213564217598346589364217364172958835627491671945832942831675 12.4.6..94.6.8.12..9821..6421...8.46.89....1...41..95.8..6.7.9..........9......75
123456789456789123798213564217598346589364217634172958345627891871945632962831475 12.4....94...8.12..9821..6.21...8.46.89..421.6.41..95....6.7.9..........96.....75
123456789456789123798213564217598346589364217634172958345627891871945632962831475 12.4....94...8.12..9821..6421...8.46.89..4.1.6.41..95......7.9.......6..96.....75
123456789456789123798213564217598346589364217634172958345627891871945632962831475 12.4....94...8.12..9821..6421...8.46.89..4.1.6.41..95....6.7.9..........96.....75
123456789456789123798213564217598346589364217634172958345627891871945632962831475 12.4....94.6.8.12..9821....21...8.46.89..421.6.41..95....6.7.9.......6..9......75
123456789456789123798213564217598346589364217634172958345627891871945632962831475 12.4....94.6.8.12..9821..6.21...8.46.89..421.6.41..95....6.7.9..........9......75
123456789456789123798213564217598346589364217634172958345627891871945632962831475 12.4....94.6.8.12..9821..6421...8.46.89..4.1.6.41..95....6.7.9..........9......75
123456789456789123798213564217598346589364217634172958345627891871945632962831475 12.4....94.6.8.12..9821..6421...8.46.89.6..1.6.41..95....6.7.9..........9......75
123456789456789123798213564217598346589364217634172958345627891871945632962831475 12.4...894.6.8.12..9821..6.21...8.46.89..421.6.41..9.....6.7.9..........9......75
123456789456789123798213564217598346589364217634172958345627891871945632962831475 12.4.6..94...8.12..9821..6421...8.46.89....1.6.41..95....6.7.9..........96.....75
123456789456789123798213564217598346589364217634172958345627891871945632962831475 12.4.6..94.6.8.12..9821...421...8.46.89....1.6.41..95....6.7.9.......6..9......75
123456789456789123798213564217598346589364217634172958345627891871945632962831475 12.4.6..94.6.8.12..9821..6421...8.46.89....1.6.41..95....6.7.9..........9......75
123456789456789123798213564239871456541362897687945231364128975815697342972534618 123...7..45.78....7..2.3..4.3.87.4..54.36.8.7..7.452..3....8....156.....9..53.6..
123456789456789123798213564239871456541362897687945231364128975815697342972534618 123.5.7..45.78....7..2.3..4.3.87.4..54.36.8.7..7..52..3....8....156.....9..53.6..
123456789456789123798213654249137865375648291681592437564321978817965342932874516 .23.56....5.789..37....36..2....78...75.....1..159....56.3....8817.6.3.2.32.7...6
123456789456789123798231564215897346379645218684123957547962831831574692962318475 12....7.94.67.91...9.2...6421...7346.79.4.21.6.....9.7........1831..46...6.3.....
123456789456789123798231564215897346379645218684123957547962831831574692962318475 12.4..7.94.67.91...9.2...6421...7346.79...21.6.....9.7........1831..46...6.3.....
123456789456789123798231564215897346379645218684123957547962831831574692962318475 12.4..7.94.67.91...9.2...6421...7346.79.4.21.6.....9.7........1831...6...6.3.....
123456789456789132789123546248961357315872694697534218571248963832695471964317825 1..4.6..9.56.8.1.2.8.1....6.48......3......9....5342..5.1.48.6.8326.5..1.6431....
123456789456789132789123546248961357315872694697534218571248963832695471964317825 1..4.6..9.56.8.1.2.8.1....6.48......3..8...9.....342..5.1.48.6.8326.5..1.6431....
123456789456789132789123546248961357315872694697534218571248963832695471964317825 1.34.6..9.56.8.1.2.8.1....6..8......3..8...94....342..5.1.48...8326.5..1.6431....
123456789456789132789123546248961357315872694697534218571248963832695471964317825 1.34.6..9.56.8.1.2.8.1....6..8......3..8...94....342..5.1248...8326.5....6431....
123456789456789132789123546248961357315872694697534218571248963832695471964317825 1.34.6..9.56.8.1.2.8.1....6.48......3......9....5342..5.1.48...8326.5..1.6431....
123456789456789132789123546248961357315872694697534218571248963832695471964317825 1.34.6..9.56.8.1.2.8.1....6.48......3..8...9.....342..5.1.48...8326.5..1.6431....
123456789456789132789123546248961357315872694697534218571248963832695471964317825 1.34.6..9.56.8.1.2.8.1....6.48......3..8...94....3.2..5.1.48...8326.5..1.6431....
123456789456789132789123546248961357315872694697534218571248963832695471964317825 1.34.6..9.56.8.1.2.8.1....6.48......3..8...94....3.2..5.1248...8326.5....6431....
123456789456789132789213645215938467398674251674125398531842976867391524942567813 .2.4.6.89....891...8921.64.2.....46..9.6.4.516..12..985...4.....6.3.1.24.......1.
123456789456789132789213645215938467398674251674125398531842976867391524942567813 .2.4.6.89....891...8921.64.2.....46..9.6.42516..1...985...4.....6.3.1.24.......1.
123456789456789132789213645215938467398674251674125398531842976867391524942567813 .2.4.6.89..6.891...8921.64.2.....46..9.6.4.51...12..985...4.....6.3.1.24.......1.
123456789456789132789213645215938467398674251674125398531842976867391524942567813 .2.4.6.89..6.891...8921.64.2.....46..9.6.4251...1...985...4.....6.3.1.24.......1.
123456789456789132789213645217398456564127398938564271392675814645831927871942563 .2.4.6.894...891.2.8.21....2...9.45.5..12..98..85.42.13......1..4..319...7.9.....
123456789456789132789213645217398456564127398938564271392675814645831927871942563 .2.4.6.894...891.2.8.21....2...9.45.5.412..98..85.42.13......1.....319...7.9.....
123456789456789132789213645217398456564127398938564271392675814645831927871942563 .2.4.6.894...891.2.8.21..4.2...9.45.5.412..98..85.42.13......1.....31....7.9.....
123456789456789132789213645217398456564127398938564271392675814645831927871942563 .2.4.6.894...891.2.8.21..4.2...9.45.5.412..98..85.42.13......1.....319...7.......
123456789456789132789231546215897364398645271674123895532974618841362957967518423 12.....8.4.6..91.2.892.1.4621..9..64..8.4...16.41..89.....746..8......57.6.5.....
123456789456789132789231546215897364398645271674123895532974618841362957967518423 12.....8.4.6..91.2.892.1.4621..9..64.9..4...16.41..89.....74..88......57.6.5.....
123456789456789132789231546215897364398645271674123895532974618841362957967518423 12.....8.4.6..91.2.892.1.4621..9..64.9..4...167.1..89.....74..88......57.6.5.....
123456789456789132789231546215897364398645271674123895532974618841362957967518423 12.....8.4.6..91.2.892.1.4621..9..64.98.4...16.41..89.....74...8......57.6.5.....
123456789456789132789231546215897364398645271674123895532974618841362957967518423 12.....8.4.6..91.2.892.1.4621..9..64.98.4...167.1..89.....74...8......57.6.5.....
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123456789457189236986273154275931648348567921619824573532698417764312895891745362 1234.6.8.45.1....6.86..3........1...3.85...2..1.8.4.7.53.6.8..7.6431.8....1..5.6.
123456789457189236986273154275931648348567921619824573532698417764312895891745362 1234.6.8.45.18...6..6..3........1...3.85...2..1.8.4.7.53.6....7.6431.8..8.1..5.6.
123456789457189236986273154275931648348567921619824573532698417764312895891745362 1234.6.8.45.18...6.86..3........1...3.85...2..1.8.4.7.53.6....7.6431.8....1..5.6.
123456789457189236986273154375921648648537921219864573532698417764312895891745362 1234.6.8.45.1....6..6..3........1.....853..2..1.8.4.7.53.6.8..7.6431.8..8.1..5.6.
123456789457189236986273154375921648648537921219864573532698417764312895891745362 1234.6.8.45.1....6..6..3.....5..1.....853..2..1...4.7.53.6.8..7.6431.8..8.1..5.6.
123456789457189236986273154375921648648537921219864573532698417764312895891745362 1234.6.8.45.1....6.86..3........1.....853..2..1.8.4.7.53.6.8..7.6431.8....1..5.6.
123456789457189236986273154375921648648537921219864573532698417764312895891745362 1234.6.8.45.18...6..6..3........1.....853..2..1.8.4.7.53.6....7.6431.8..8.1..5.6.
123456789756983124894172536231849675567231948489765213978614352615328497342597861 12..56.89.5..8.12..9.1.25.62..8..6..5..2.1..8..9.6521....6.....6....8497.4....8..
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123456789756983124894172536231894675567231948489765213372649851615328497948517362 12..56.89.5..8.12..9.1.25.62..89.6..5..2.19.8..9.6521....6.....6....84.7.4.......
123456789756983124894172536231894675567231948489765312378649251615328497942517863 1...56.89.5..8.12..9.1.25.62.189.6.55..2.1..8..9.65......6.....6....84.7.4...78..
123456789756983142489127356248519637317862594695734218571248963832695471964371825 1.34.6..9.56.831.2.8.1....6..8......3..8...94....342..5.1.48...8326.5..1.643.....
123456789756983142489127356248519637317862594695734218571248963832695471964371825 1.34.6..9.56.831.2.8.1....6.48......3..8...9.....342..5.1.48...8326.5..1.643.....
123456789756983142489127356248519637317862594695734218571248963832695471964371825 1.34.6..9.56.831.2.8.1....6.48......3..8...94....3.2..5.1.48...8326.5..1.643.....
123456987456789213789123645915842736674391852238567194391674528562938471847215369 1.........56..92..7.91....5.158.....67..918....856...4.9167...85....8...8.7215.69
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123465789456789123789231546215897364398546271674123895561972438832614957947358612 12.4...8.4.6..91...892.1.4621..9..64.98.4...16.4..389.....7...88.2....57......6..
123465789456789123798213564215978346389546217674132958832657491547891632961324875 12.4....94...8.12..9821..6421...8.46.89....1.6.41..95.8..6.7.9..........96.....75
123465789456789123798213564215978346389546217674132958832657491547891632961324875 12.4....94.6.8.12..9821..6421...8.4..89....1.6.41..95.8..6.7.9.......6..9......75
123465789456789123798213564215978346389546217674132958832657491547891632961324875 12.4....94.6.8.12..9821..6421...8.46..9....1.6.41..9588..6.7.9..........9......75
123465789456789123798213564215978346389546217674132958832657491547891632961324875 12.4....94.6.8.12..9821..6421...8.46.89....1.6.41..95.8..6.7.9..........9......75
123467589456839172789251346215698734398745261674123895931576428862314957547982613 12.4...8.4.6..91.2.892.1.4621..9...4.98.4...16.41.38..9...7...88......57......6..
123486759487159236659372814231798465745263198968541327396827541572614983814935672 .2...67.94.71.9.366...7..1....7...657...6319..6.5413.7........15...1.9.3..49.5...
123496785457182396986753241375921468648537129219864573532648917764319852891275634 1234.6.8.45.1....6..6.53........1.....853..2..1.8.4.7.53.6.8..7.6431.8..8.1..5...
123496785457182396986753241678921534349567128215834679532648917764319852891275463 1234.6.8545.1....6.86..3........1...3..5...2..1.8.4.7.53.6.8..7.6431.8....1..5.6.
123546789456789123798213564215978346389465217674132958832657491547891632961324875 12......94.6.8.12..9821..6421...8.46.89.6..1.6.41..95.8..6.7.9..........9......75
123546789456789123798213564215978346389465217674132958832657491547891632961324875 12...6..94.6.8.12..9821..6421...8.46.89....1.6.41..95.8..6.7.9..........9......75
123645789456789132789231546215897364398456271674123895532974618841362957967518423 12.....8.4.6..91.2.892.1.4621..9..64.9.4....16.41..89.....74..88......57.6.5.....
123645789456789132789231546215897364398456271674123895532974618841362957967518423 12.....8.4.6..91.2.892.1.4621..9..64.9.4....167.1..89.....74..88......57.6.5.....
123645789456789132789231546215897364398456271674123895532974618841362957967518423 12.....8.4.6..91.2.892.1.4621..9..64.984....16.41..89.....74...8......57.6.5.....
123645789456789132789231546215897364398456271674123895532974618841362957967518423 12..4..8.4.6..91.2.892.1.4621..9..64.9......16.41..89.....74..88......57.6.5.....
123645789456789132789231546215897364398456271674123895532974618841362957967518423 12..4..8.4.6..91.2.892.1.4621..9..64.9......167.1..89.....74..88......57.6.5.....
123645789456789132789231546215897364398456271674123895532974618841362957967518423 12..4..8.4.6..91.2.892.1.4621..9..64.98.....16.41..89.....74...8......57.6.5.....
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123954876456781329798263514685432197314697285279518643541329768867145932932876451 .23.5.8..45.78..2.7..2.35.4....3..9.3..697....7.......54.3.....8.7.45..293287.4..
123954876456781329798263514685432197314697285279518643541329768867145932932876451 .23.5.8..45.78..2.7..2.35.4....3..9.3..697....7...8...54.3.....8.7.45..2932.7.4..
125436789486759123397821564218597346579643218643182957752968431831274695964315872 12.4..7.94.67.91...9.....64.1...7346.79.4.21.6....29.7..2.....1831...6...6.3.....
125436789486759123397821564218597346579643218643182957752968431831274695964315872 12.4..7.94.67.91...9.....6421...7346.79.4.21......29.7.....8..1831...6...6.3.....
125436789486759123397821564218597346579643218643182957752968431831274695964315872 12.4..7.94.67.91...9.....6421...7346.79.4.21.6....29.7........1831...6...6.3.....
126453987457986231983127645214895376578362419639741528362578194895214763741639852 .............8.2.1.8.127....1.8.5..65.8.6.4..63..415..36...8..48.5.14.63.4163..5.
126453987457986231983127645214895376578362419639741528362578194895214763741639852 .............8.2.1.8.127...21.8.5..65.8.6.4..63..415..36...8...8.5.14.63.4163..5.
126453987457986231983127645214895376578362419639741528362578194895214763741639852 1............8.2.1.8..27....1.8.5..65.8.6.4..63..415..36...8..48.5.14.63.4163..5.
126453987457986231983127645214895376578362419639741528362578194895214763741639852 1............8.2.1.8..27...21.8.5..65.8.6.4..63..415..36...8...8.5.14.63.4163..5.
127456389356987124894132576271893645563241798489765213738614952915328467642579831 1...56.89...98.1...9.1.25.62.189.6.55..2.1..8....6521....6.......5..8467.4....8..
127456389356987124894132576271893645563241798489765213738614952915328467642579831 1...56.89...98.1...9.1.25.62.189.6.55..2.1..8..9.6521....6.......5..84.7.4....8..
127456389356987124894132576271893645563241798489765213738614952915328467642579831 1...56.89.5.98.1...9.1.25.62.189.6.5...2.1..8..9.6521....6.......5..84.7.4....8..
127456389356987124894132576271893645563241798489765213738614952915328467642579831 1..4.6.89...98.1...9.1.25.62.189.6.55..2.1..8..9.6521....6.......5..84.7.4....8..
127456389456983172398172546271894635564231798839765214712648953685319427943527861 1...56.89...98.1...9.1.25.62.189.6.55..2.1..8..9.6521....6.......5...4.7.4....86.
127456389456983172398172546271894635564231798839765214712648953685319427943527861 1...56.89.5.98.1...9.1.25.62.189.6.5...2.1..8..9.6521....6.......5...4.7.4....86.
127456389456983172398172546271894635564231798839765214712648953685319427943527861 1..4.6.89...98.1...9.1.25.62.189.6.55..2.1..8..9.6521....6.......5...4.7.4....86.
127456389653987124894132576271893645536241798489765213768314952915628437342579861 1...56389....8.1...9.1.25.62.189.6.55..2.1..8..9.6521............5..84.7.4....86.
127456389653987124894132576271893645536241798489765213768314952915628437342579861 1...56389.5..8.1...9.1.25.62.189.6.5...2.1..8..9.6521............5..84.7.4....86.
127465983436789512589231746215897364398546271674123895952674138863912457741358629 12.4..98.4.6..9..2.892.1.4621..9..64.98.4...16.41.38......7...88......57......6..
129463785456789132387251946213978564578634291694125873742596318865317429931842657 12.4..78.4.6.8.1.2.8.2...4621..78.64.78...2.16.....87........1..6.3.....931..26..
129463785456789132387251946213978564578634291694125873742596318865317429931842657 12.4..78.4.6.8.1.2.8.2...4621..78.64.78..42.16.....87........1..6.3.....93...26..
129463785456789132387251946213978564578634291694125873742596318865317429931842657 12.4..78.4.6.8.13..8.2...4621..78.64.78..42.16.....87........1..6.3.....93...26..
153426789486759231729183645215847396674391852938562174391674528562938417847215963 1..........6.592..7.91....5.158.....67..918..9.856...4.9167...85....8...8.7215.6.
153426789486759231729183645215847396674391852938562174391674528562938417847215963 1..........6.592..7.91....5.158...9.67...18..9.856...4..167...85..9.8...8.7215.6.
153426789486759231729183645215847396674391852938562174391674528562938417847215963 1..........6.592..7.91....5.158...9.67..918....856...4.9167...85....8...8.7215.6.
153426789486759231729183645215847396674391852938562174391674528562938417847215963 1..........6.592..7.91....5.158...9.67..918..9.856...4..167...85....8...8.7215.6.
153426789486759231729183645215847396674391852938562174391674528562938417847215963 1..........6.592..7.91....5.158.7.9.6...918..9.856...4..167...85....8...8.7215.6.
153426789486759231729183645215847396674391852938562174391674528562938417847215963 1..........6.592..7291......158...9.67..918..9.856...4..167...85....8...8.7215.6.
153426789486759231729183645215847396674391852938562174391674528562938417847215963 15.........6..92..7.91....5.158.....67..918..9.856...4.9167...85....8...8.7215.6.
153426789486759231729183645215847396674391852938562174391674528562938417847215963 15.........6..92..7.91....5.158...9.67...18..9.856...4..167...85..9.8...8.7215.6.
153426789486759231729183645215847396674391852938562174391674528562938417847215963 15.........6..92..7.91....5.158...9.67..918....856...4.9167...85....8...8.7215.6.
153426789486759231729183645215847396674391852938562174391674528562938417847215963 15.........6..92..7.91....5.158...9.67..918..9.856...4..167...85....8...8.7215.6.
153426789486759231729183645215847396674391852938562174391674528562938417847215963 15.........6..92..7.91....5.158.7.9.6...918..9.856...4..167...85....8...8.7215.6.
153426789486759231729183645215847396674391852938562174391674528562938417847215963 15.........6..92..7291......158...9.67..918..9.856...4..167...85....8...8.7215.6.
173426589456983172289157436648279315327561894915834267591748623832695741764312958 1.34.6..9.56.831.2.8.1....6.4.......3......9....8342..5.1.48...8326.5..1.6431....
173426589456983172289157436648279315327561894915834267591748623832695741764312958 1.34.6..9.56.831.2.8.1....6.4.......3..5...9.....342..5.1.48...8326.5..1.6431....
173426589456983172289157436648279315327561894915834267591748623832695741764312958 1.34.6.89.56.831.2.8.1....6.4.......3......9.....342..5.1.48...8326.5..1.6431....
173426859456983172289157436645279318327861594918534267591748623832695741764312985 1.34.6..9.56.831.2...1....6.4.......3..8...9....5342..5.1.48...8326.5..1.6431....
173426859456983172289157436645279318327861594918534267591748623832695741764312985 1.34.6..9.56.831.2.8.1....6.........3..8...94....342..5.1.48...8326.5..1.6431....
173426859456983172289157436645279318327861594918534267591748623832695741764312985 1.34.6..9.56.831.2.8.1....6.4.......3......9....5342..5.1.48...8326.5..1.6431....
173426859456983172289157436645279318327861594918534267591748623832695741764312985 1.34.6..9.56.831.2.8.1....6.4.......3..8...9.....342..5.1.48...8326.5..1.6431....
173426859456983172289157436645279318327861594918534267591748623832695741764312985 1.34.6..9.56.831.2.8.1....6.4.......3..8...94....3.2..5.1.48...8326.5..1.6431....
173426859456983172289157436645279318327861594918534267591748623832695741764312985 1.34.6..9.56.831.2.8.1....6.45......3......9.....342..5.1.48...8326.5..1.6431....
213457689456189237978362514132798465564213798897546123349625871725831946681974352 ..345..8945..8.23.9..3.2..4.3..984.55..213.98...54..2.....2.871...8.......1.....2
263457189475189236819362754632798415547213698198546327356924871924871563781635942 ..345..894.5.8.23...93.2..4.3..984.55..213.98...54..2.....2.871...8.......1.....2
321456789457189236698372514213798645745263198869541327936827451582614973174935862 .2..567.94.71.9.366...7..1....7....57...6319..6.5413.7.......51....1.9.3..49.5...
321456789457189236698372514213798645745263198869541327936827451582614973174935862 .2..567.94.71.9.366...7..1....79...57...6319..6.5.13.7.......51....1.9.3..49.5...
321456789487129536695378214138792465742563198569841327273984651856217943914635872 .2..567.94.71.9.366...7..1....79..657...6319..6...13.72......51....1.9.3..4..5...
321456879457189236698372514213798465745263198869541327936824751582617943174935682 .2..56..94.71.9.366...7..1....7...657...6319..6.5413.7.......51....1.9.3..49.5...
321456879457189236698372514213798465745263198869541327936824751582617943174935682 .2..56..94.71.9.366...7..1....79..657...6319..6.5.13.7.......51....1.9.3..49.5...
321456879487129536659378214813792465745863192296541387932684751568217943174935628 .2..56..94.7129.366...7..1....79..657...6319....5.13.7.......515...1.9.3..49.....
321456879487129536659378214813792465745863192296541387932684751568217943174935628 .2..56..94.7129.366...7..1....79..657.5.6319......13.7.......51....1.9.3..49.5...
328456719457129836619378542841793265735862194962541387293687451586214973174935628 .2..567.94.71.9.366...7.......7...657...6219..6.5413.7.......51....1.9.3..49.5...
328456719457129836619378542841793265735862194962541387293687451586214973174935628 .2..567.94.71.9.366...7.......79..657...6219..6.5.13.7.......51....1.9.3..49.5...
623457189457189236819362754236798415574213698198546327365924871942871563781635942 ...45..8945..8.23...93.2..4.3..984.55..213.98...54..2.3...2.871...8.......1.....2
623457189457189236819362754236798415574213698198546327365924871942871563781635942 ..345..8945..8.23...93.2..4....984.55..213.98...54..2.3...2.871...8.......1.....2
623457189457189236819362754236798415574213698198546327365924871942871563781635942 ..345..8945..8.23...93.2..4.3..984.55..213.98...54..2.....2.871...8.......1.....2
623459817451786923798213564264138795385697241179524638547362189816945372932871456 .23.5.8..45.78..2.7..2.35.4....3..9.3..697....7.......54.3...8.8...45..293287.4..
823456719457129836691378524138792465745863192962541387379684251586217943214935678 .2..567.94.71.9.366...7.......7...657...6319..6.5413.7.......51....1.9.3..49.5...
823456719457129836691378524138792465745863192962541387379684251586217943214935678 .2..567.94.71.9.366...7.......79..657...6319..6.5.13.7.......51....1.9.3..49.5...
823456719457129836691378524138792465745863192962541387379684251586217943214935678 .23.56..94.71.9.366...7.......7...657...6319..6.5413.7.......51....1.9.3..49.5...
823456719457129836691378524138792465745863192962541387379684251586217943214935678 .23.56..94.71.9.366...7.......79..657...6319..6.5.13.7.......51....1.9.3..49.5...

And easy success, starting ftom those 30 36s......a 1off/2on/1off gives new minimal 36s.

Code: Select all: 12.4....94....9.2..89.23.6.23.9.8....913472..8.4.12.9.34.....1....83...7..8..46.. 12.4....94....9.2..89.23.6.23.9.8....913472..8.4.12.9.34.....1....83...7.18...6.. 12.4....94....9.2..89.23.6.23.9.8....913472..8.4.12.9.34.....1....831..7..8...6.. .2.4.6...4.6.....178..2....2..5.8..383...2..7..73.....34..675..5782.43.66.283...4 .2.4.6...4.6.....178..2....2..5.8..383.6.2..7..73.....34...75..5782.43.66.283...4 .2.4.6...4.6.....178..2....2..578..383...2..7...3.....34..675..5782.43.66.283...4 .2...6...4.....236..93..5...4..6137..7.5.31.2.3127.465.....5....9.7..6.17...1295. .2..56...4......36..932.....4..6137..7.5.31.2.3127.465.....5....9.7..6.17...1295. .2..56...4.....236..93......4..6137..7.5.31.2.3127.465.....5....9.7..6.17...1295. ..3.5.7.9..7189.366..37.51.2..79..657...6.19..6...1..7.8.9.5.........9.1..2.1..53 ..3.567.9..7189.366..37.51.2...9..657...6.19..6...1..7.8.9.5.........9.1..2.1..53 ..34...89.5....23..983.2514..........6.8.495........413.2..84..5..2.3.989..54132. ..34...89.5....23..983.2514..........6.8.495........413.2..84.55..2.3.989...4132. ..34...89.5..8.23..983.2514..........6.8.495........413.2...4..5..2.3.989..54132. ..34...89.5..8.23..983.2514..........6.8.495........413.2...4.55..2.3.989...4132. ..34....94..1.9..6.9..3..4.28.3..6...31..........21.5.3.29.8..4.1924.8..84.5139.2 ..34....94..1.9..6.98.3..4.2.....6...31.....8...821.5.3.29.8..4.1924....84.5139.2 ..34....94..1.9..6.98.3..4.2..3..6...31.....8....21.5.3.29.8..4.1924....84.5139.2 ..34....94..1.9..6.98.3..4.28....6...31.....8....21.5.3.29.8..4.1924....84.5139.2 1.34567.94..1.9..6..9.7.51...17..3.5..65.14.7....631....893..........953...6.5.7. 1.34567.94..1.9..6..937.51...17..3.5..65.14.7....6.1....893..........953...6.5.7. 1.34567.94..1.9..6..937.51...17..365..65.14.7......1....893..........953...6.5.7. 1.34567.94..1.9.36..9.7.51...17....5..65.14.7....631....893..........953...6.5.7. 1.34567.94..1.9.36..9.7.51...17...65..65.14.7.....31....893..........953...6.5.7. 1.34567.94..1.9.36..937.51...17....5..65.14.7....6.1....893..........953...6.5.7. 1.34567.94..1.9.36..937.51...17...65..65.14.7......1....893..........953...6.5.7.

C

by **Havard** » Fri Jun 08, 2007 6:50 am

coloin wrote:And easy success, starting ftom those 30 36s......a 1off/2on/1off gives new minimal 36s.
Code: Select all
12.4....94....9.2..89.23.6.23.9.8....913472..8.4.12.9.34.....1....83...7..8..46.. 12.4....94....9.2..89.23.6.23.9.8....913472..8.4.12.9.34.....1....83...7.18...6.. 12.4....94....9.2..89.23.6.23.9.8....913472..8.4.12.9.34.....1....831..7..8...6.. .2.4.6...4.6.....178..2....2..5.8..383...2..7..73.....34..675..5782.43.66.283...4 .2.4.6...4.6.....178..2....2..5.8..383.6.2..7..73.....34...75..5782.43.66.283...4 .2.4.6...4.6.....178..2....2..578..383...2..7...3.....34..675..5782.43.66.283...4 .2...6...4.....236..93..5...4..6137..7.5.31.2.3127.465.....5....9.7..6.17...1295. .2..56...4......36..932.....4..6137..7.5.31.2.3127.465.....5....9.7..6.17...1295. .2..56...4.....236..93......4..6137..7.5.31.2.3127.465.....5....9.7..6.17...1295. ..3.5.7.9..7189.366..37.51.2..79..657...6.19..6...1..7.8.9.5.........9.1..2.1..53 ..3.567.9..7189.366..37.51.2...9..657...6.19..6...1..7.8.9.5.........9.1..2.1..53 ..34...89.5....23..983.2514..........6.8.495........413.2..84..5..2.3.989..54132. ..34...89.5....23..983.2514..........6.8.495........413.2..84.55..2.3.989...4132. ..34...89.5..8.23..983.2514..........6.8.495........413.2...4..5..2.3.989..54132. ..34...89.5..8.23..983.2514..........6.8.495........413.2...4.55..2.3.989...4132. ..34....94..1.9..6.9..3..4.28.3..6...31..........21.5.3.29.8..4.1924.8..84.5139.2 ..34....94..1.9..6.98.3..4.2.....6...31.....8...821.5.3.29.8..4.1924....84.5139.2 ..34....94..1.9..6.98.3..4.2..3..6...31.....8....21.5.3.29.8..4.1924....84.5139.2 ..34....94..1.9..6.98.3..4.28....6...31.....8....21.5.3.29.8..4.1924....84.5139.2 1.34567.94..1.9..6..9.7.51...17..3.5..65.14.7....631....893..........953...6.5.7. 1.34567.94..1.9..6..937.51...17..3.5..65.14.7....6.1....893..........953...6.5.7. 1.34567.94..1.9..6..937.51...17..365..65.14.7......1....893..........953...6.5.7. 1.34567.94..1.9.36..9.7.51...17....5..65.14.7....631....893..........953...6.5.7. 1.34567.94..1.9.36..9.7.51...17...65..65.14.7.....31....893..........953...6.5.7. 1.34567.94..1.9.36..937.51...17....5..65.14.7....6.1....893..........953...6.5.7. 1.34567.94..1.9.36..937.51...17...65..65.14.7......1....893..........953...6.5.7.

C

That's very interesting, Coloin, congratulations on finding so many minimal 36! With this kind of "reverse" off/on search, you would have to throw in a "is the sudoku minimal" check as well I guess. If we could make enough 36's, maybe a minimal 37 would pop out?

Havard

by **coloin** » Fri Jun 08, 2007 11:10 pm

I think that with this sideways technigue there is a very good chance to get a 37-puzzle, There are many more grids out there with 36s, and it seems I can generate new ones very easily.

Of course there it is incrementally more difficult to squeeze in an extra clue - worse, not only is there an extra clue there is one less space for the unavoidables to have a solitary clue [minimal].

Amazingly after about the 100th puzz...
This appeared, Havard's prophecy came true. :!:

Code: Select all: +---+---+---+ |.23|4..|..9| |45.|.8.|2..| |8.9|3..|4.5| +---+---+---+ |28.|713|...| |3..|..2|1..| |...|8..|...| +---+---+---+ |54.|23.|.9.| |73.|.98|5..| |9.8|5.4|.2.| +---+---+---+ 37 clues SE 8.5

Eight in total !

Code: Select all: .234....945..8.2..8.93..4.528.713...3....21.....8.....54.23..9.73..985..9.85.4.2. # 95180 FNXK C37.m .234....945..8.2..8.93..4.528.713...3....21.....8.....54..3..9.732.985..9.85.4.2. # 95180 FNXK C37.m .234....945..8.2..8.93..4..28.713...3....21.....8.....54.23..9.73..9854.9.85.4.2. # 95271 FNBYK C37.m .234....945..8.2..8.93..4..28.713...3....21.....8.....54..3..9.732.9854.9.85.4.2. # 95271 FNBYK C37.m ..34....945..8.2..8.932.4.528.713...3....21.....8.....54.23..9.73..985..9.85.4.2. # 95180 FNXK C37.m ..34....945..8.2..8.932.4.528.713...3....21.....8.....54..3..9.732.985..9.85.4.2. # 95180 FNXK C37.m ..34....945..8.2..8.932.4..28.713...3....21.....8.....54.23..9.73..9854.9.85.4.2. # 95271 FNBYK C37.m ..34....945..8.2..8.932.4..28.713...3....21.....8.....54..3..9.732.9854.9.85.4.2. # 95271 FNBYK C37.m

by **Havard** » Fri Jun 08, 2007 11:13 pm

Congratulations!
It seems everyone is bending old "rules" nowadays!

Now find me a 38!

Havard

by **Mauricio** » Fri Jun 08, 2007 11:39 pm

Wow, a minimal 37. That is the next to last thing I expected to hear, besides finding a minimal 16.

36 was a nice number, but hey, 37 is prime.

by **udosuk** » Sat Jun 09, 2007 3:57 am

Mauricio wrote:36 was a nice number, but hey, 37 is prime.

38 is my favourite number.

So let's gun for 38 (but not 38!=5.23...x10^44).

PS: On 2nd thought there's something special about 37 here. Currently 17 is the conjectured minimum number of clues in a minimal puzzle. If 37 is the maximum, then the median of them, 27, is exactly 1/3 of the number of cells. And are there evidences suggesting that 27-clue minimal puzzles are at the peak of the "normal distribution" (i.e. more such puzzles than 26- or 28-clue ones)?

So, perhaps we can "justify" the numbers like this:

On 9x9 minimal Sudoku puzzles,

most frequently occured #clues
= (#cells)/sqrt(#symbols) = 81/3 = 27

min #clues
= (#cells)/sqrt(#symbols) - #symbols - 1 = 81/3 - 9 - 1 = 17

max #clues
=(#cells)/sqrt(#symbols) + #symbols + 1 = 81/3 + 9 + 1 = 37

Neat!

by **Havard** » Sat Jun 09, 2007 6:55 am

Here are 8 more:

Code: Select all: .234....945..8...28.93..4..28.713...3....21.....8.....54.23..9.73..9854.9.85.42.. .234....945..8...28.93..4..28.713...3....21.....8.....54..3..9.732.9854.9.85.42.. ..34....945..8...28.932.4..28.713...3....21.....8.....54.23..9.73..9854.9.85.42.. ..34....945..8...28.932.4..28.713...3....21.....8.....54..3..9.732.9854.9.85.42.. .234....945..8...28.93..4..28.713...3....21.....8.....54.23..9.73..985.49.85.42.. ..34....945..8...28.932.4..28.713...3....21.....8.....54.23..9.73..985.49.85.42.. .234....945..8...28.93..4..28.713...3....21.....8.....54..3..9.732.985.49.85.42.. ..34....945..8...28.932.4..28.713...3....21.....8.....54..3..9.732.985.49.85.42..

Havard

by **ravel** » Sat Jun 09, 2007 1:17 pm

udosuk wrote:And are there evidences suggesting that 27-clue minimal puzzles are at the peak of the "normal distribution" (i.e. more such puzzles than 26- or 28-clue ones)?

I dont think so, it should be somewhere between 24 and 26 clues, but it is hard to say, because it very depends, how you "randomly" calculate minimal puzzles (some methods tend to give lower clues than others and the distribution is different for different - fixed - grids).

Coloin and Havard,
congratulations on the 37's !

by **udosuk** » Sat Jun 09, 2007 2:52 pm

ravel wrote:I dont think so, it should be somewhere between 24 and 26 clues, but it is hard to say, because it very depends, how you "randomly" calculate minimal puzzles (some methods tend to give lower clues than others and the distribution is different for different - fixed - grids).

According to this study by Ocean (posted last December), 41.6% of a huge sampling set of random minimal puzzles have 27 clues, much higher than all other #clues. :idea:

From what I read from the thread above, all the previous studies which gave the range of the 24-26 clues were likely to be biased when picking the sampling grids. :?:

But then again it's difficult to determine if the one above done by Ocean wasn't a bit biased itself. Too bad the guys stop working on this problem since January.

by **ravel** » Sat Jun 09, 2007 3:34 pm

Thanks for the link, udosuk.
I should have known that, after all it was me, who started this thread

(but this was the time, when i was abroad and too busy to read it carefully).

by **Smythe Dakota** » Sun Jun 10, 2007 5:05 pm

Is it possible to have an N-clue minimal pseudoku (multiple solutions) where every successful attempt to turn it into an actual (N+1)-clue sudoku (unique solution) by adding 1 clue, results in a clue set which is no longer minimal (because one of the earlier clues now becomes redundant)?

By "minimal" when applied to a pseudoku, I guess I mean that the removal of any clue would generate still more solutions.

Bill Smythe

by **Ocean** » Mon Jun 11, 2007 11:13 am

coloin wrote:Amazingly after about the 100th puzz...
This appeared, Havard's prophecy came true.

Code: Select all
+---+---+---+ |.23|4..|..9| |45.|.8.|2..| |8.9|3..|4.5| +---+---+---+ |28.|713|...| |3..|..2|1..| |...|8..|...| +---+---+---+ |54.|23.|.9.| |73.|.98|5..| |9.8|5.4|.2.| +---+---+---+ 37 clues SE 8.5

Eight in total !

Incredible! Congratulations!

by **Havard** » Mon Jun 11, 2007 12:28 pm

here is another load of minimal 37s:

Code: Select all: 12.4...79...1.982...9.23.6.23.9.8....9134728.8.4.12.9.34..........83.....18..46.. 12.48..79...1.982..89.23.6.23.9......9134728...4.12.9.34..........83.....18..46.. 12.48..79...1.982...9.23.6.23.9......9134728.8.4.12.9.3...........831....18..46.. 12.4...79...1.982..89.23.6.23.9.8....9134728...4.12.9.34..........83.....18..46.. 12.4...79...1.982...9.23.6.23.9.8....9134728.8.4.12.9.3...........831....18..46.. 12.48..79...1.982..89.23.6.23.9......9134728...4.12.9.3...........831....18..46.. ...4.....4.6.8...17....6...2...78..383.5.26....73....234..67.255.82.43.66.283..74 ...4.....4.6.8...17....6...2..678..383.5.26....73....234...7.255.82.43.66.283..74 .8....6..4.6.....17...8.4..2..5781.383...2.....73..2..34..67.2.5782.43.66.28.5..4 .8.4..6....6.....17...8.4..2..5781.383...2.....73..2..34..67.2.5782.43.66.28.5..4 .8...16..4.67....1....8....2..5781.38....2....573..2..34..67.2.5782.43.66.283...4 ..3.867.98.7159.36..637....2.879..657...6.19..6......7.81935...........1..2.1..53 ..3.867.98.7159.36..637.5..2.879..657...6.19..6......7.81935...........1..2.1...3 12.4...79...1.982..89.23.6.23.9.8....9134728...4.12.9.3...........831....18..46.. 12.48..79...1.982...9.23.6.23.9......9134728.8.4.12.9.3.8..........31....1.8.46.. 12.4...79...1.982...9.23.6.23.9.8....9134728.8.4.12.9.3.8..........31....1.8.46.. 12.48..79...1.982..89.23.6.23.9......9134728...4.12.9.3.8..........31....1.8.46.. 12.4...79...1.982..89.23.6.23.9.8....9134728...4.12.9.3.8..........31....1.8.46.. 12.48..79...1.982...9.23.6.23.9......9134728.8.4.12.9.3.8..1.......3.....1.8.46.. 12.4...79...1.982...9.23.6.23.9.8....9134728.8.4.12.9.3.8..1.......3.....1.8.46.. 12.48..79...1.982..89.23.6.23.9......9134728...4.12.9.3.8..1.......3.....1.8.46.. 12.4...79...1.982..89.23.6.23.9.8....9134728...4.12.9.3.8..1.......3.....1.8.46..

Havard

by **coloin** » Mon Jun 11, 2007 12:49 pm

Thanks to all.

In retrospect, it probably wasnt a good idea to restrict a search for a max clue in one specific grid.

When we were at the 35 clue level I was able to find a big puzzle eventually in a random grid - but there will be many other regions with big puzzles in any grid - so it would be extrmely difficult to find the biggest puzzle in any one grid. [much more difficult than finding the smallest !]

Why there should be as many 35s and 36s in the random grid that I obsessivly studied is a mystery.

To find similar 36s using the off/on technique is only obvious when we see it work - You have to realize that you probably only get another different 36 puzzle this way by searching through tens of thousands of combinations - i had assumed that all these other combinations of clues in different grids would always give non minimal puzzles - but not the case !

Once we demonstrated many 36s in many grids...a 37 was always possible - Ive not had a chance to look for more 37s, Havards furthur 8 look strangely similar [but not] !

Once gsf improves the inner loop in the off/on program it would be easier, although the lack of furthur 37s from havard possibly means the limit is reached...........but there are so many grids and each grid has billions of possible regions that just might allow a 38 to fit in.

EDIT - he has just posted some more !

Some how I doubt there will be a 38 - the step up at each clue level is very steep.

With one more clue you have to fit one more unavoidable set into an [empty] clue set made smaller by one !

C

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