The New Sudoku Players' Forum

by **coloin** » Thu Feb 17, 2011 12:22 am

This puzzle has a diagonal pattern in every box [27 clues]

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

Many of the patterns in the patterns game[which produce puzzles with ED > 9.2 ] have 3 clues diagonally placed in a box

So if all the boxes have the diagonal pattern then minlex versions of the puzzles all have similar B12347

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

Here are some 27 clue "all diagonal" patterns - there may well be a few more

Code: Select all: 001002003020030040400500100006001007080060090200900800008003004050080070300200500 001002003020030010400500600002005007080090040700600900005080090040200500900003008 001002003020010040300500600002006001040030070500800400004200800030060007900003020 001002003020030040300500600002007008030010060600300700007100400080060010100004009 001002003020010040300400500002006004040030200700100080006009007050070900100200060 001002003020010040300500100004006002070100080100020300009005004040090050200400700 001002003020030040300500600002003004070600500800070090003006001090200300700050060 001002003020010040500600100002004001070800900600050030007006500080070006400900070 001002003020030040300500600003007080050040001800900700009008050070060004100400900 001002003020030040500600700002005060050040100800300009007004030090080005400900200 001002003020030040300500600003007100050010020200800009008060400040005007600900010 001002003020010040500600700002060080030007400900300007004070030010008200700100009 001002003020010040500600100002040070060003800400500002009080200010007006300900050 001002003020010040500600700002080600030004009600100050004200300060050090800009006 001002003020030040500100600004010700060400080200009006006900100090020008300005070 001002003020030040400500100003600007060007080100050200006003010070900004900040300 001002003020040050300600700002100080070006002400090600006070090030009001900500800 001002003020010040300500600007300060030007100400020008008700200040005030100080009 001002003020030040500600700002800090080040100400007006003004070090200600700050009 001002003020010040300500600002100700050007008900040050003008004010090070800600300 001002003020010040300500200003600400070005080600040009009004007040700600200030050 001002003020010040300500600005100200040070001200008030009600070060040300800007004 001002003020010040500600100004500700080060030100007005007800400030050090400009006

There are 6 ways to complete a diagonal and 4 boxes to complete.

How many of these all diagonal patterns with 21+ clues can be made by isomorphic swapping to have symmetry [S2 and above] which qualifies it for the game ?

And here is a few - from the non-minimal puzzles above

Code: Select all: .....1.2.....2...1..75..6....6..2..8.9..3..4.5..6..1....3..42..9...6...5.6.8...9. # 11 FN C25.m/S2.d ..1..3....2..4..3.4..1..5....6..7..1.8..9..6.2..8..9....8..4..3.5..7..8....5..2.. # 758 FNP C25.m/S4.da/M1.3.30 ..1..3..2.2.....3.4..1..5....6..7..1.8..9..6.2..8..9....8..4..3.5.....8.3..5..2.. # 1078 FNP C25.m/S2.p/M1.2.54 ..1.2.3...2...3..44..5...1..5...8.....8.3.4.....2...5..8...6..92..9...8...6.1.7.. # 1160 FNP C25.m/S2.p/M1.4.27 ..1.3...2.2...4.3.5..7..6....7.....4.9..5..8.4.....9....2..6..5.5.1...4.8...9.3.. # 293 FNP C25.m/S2.p/M1.6.1 ..21...3......2..45...3....6..3..4....5..7..8.4..6..9....9...7.7....46...3..2...5 # 500 FNP C24.m/S2.d/M1.14.2 ..28....9.8...4.1.4...7.6...2...3..4....2....5..6...7...3.4...7.9.2...6.7....59.. # 415 FNP C25.m/S2.p/M1.10.4 .1.3..2..2...5..4......7..63..1..9...6.....7...9..8..57..2......2..8...1..4..6.9. # 378 FNP C24.m/S4.da/M1.10.6 .2...1.3.1...2.......3....6..1..2..7.7..5..8.4..9..5.......3.4.9...1.7....68....3 # 729 FNP C24.m/S2.d/M1.2.52 .3...1.2.4...2......75..6....6..2..8.9..3..4.5..6..1....3..42..9...6...5...8...9. # 469 FNP C25.m/S2.d/M1.18.5 .6...7..18..9...6...2.8.9...1......2..4.1.5..2......3...3.5.2...8...4..35..7...8. # 720 FNP C25.m/S4.da/M1.5.11 1..2..3....2..1..4.3..5..1.4..6..2....7.....8.1...2.3.9..5..4....4..9..5.2..4..7. # 194 FNP C26.m/S2.d/M1.3.27 1..2..3...2..1..4...5..6...4....5..7.8..6..3...17..5..7....8..4.3..5..9....9..6.. # 515 FNP C25.m/S2.d/M1.22.5 1..3.......2.....3.4..1..5.6..7..1....8..9..6....8..9....4..3....5..7..8.3..5..2. # 1824 FNP C23.m/S2.d/M1.2.26 2...1...3..3..2....5.4..1....6..8.9.1...6...7.9.2..8....8..5.7....3..5..3...8...4 # 845 FNP C25.m/S4.da/M1.6.10 2..1...3...3..2..4.5....6..7..3..1.......5..2.8..2..9...68..4..5....4.7..9..6.... # 519 FNP C24.m/S2.d/M1.20.3 3..2....1..1..3.2..6..5.4..7..5....2..4..9.8..9..6......9.....5.5..2....8..3..9.. # 780 FNP C24.m/S2.d/M1.4.35

C

by **ronk** » Thu Feb 17, 2011 10:52 am

coloin wrote:Here are some 27 clue "all diagonal" patterns - there may well be a few more

Code: Select all
001002003020030040400500100006001007080060090200900800008003004050080070300200500 001002003020030010400500600002005007080090040700600900005080090040200500900003008 001002003020010040300500600002006001040030070500800400004200800030060007900003020 001002003020030040300500600002007008030010060600300700007100400080060010100004009 001002003020010040300400500002006004040030200700100080006009007050070900100200060 001002003020010040300500100004006002070100080100020300009005004040090050200400700 001002003020030040300500600002003004070600500800070090003006001090200300700050060 001002003020010040500600100002004001070800900600050030007006500080070006400900070 001002003020030040300500600003007080050040001800900700009008050070060004100400900 001002003020030040500600700002005060050040100800300009007004030090080005400900200 001002003020030040300500600003007100050010020200800009008060400040005007600900010 001002003020010040500600700002060080030007400900300007004070030010008200700100009 001002003020010040500600100002040070060003800400500002009080200010007006300900050 001002003020010040500600700002080600030004009600100050004200300060050090800009006 001002003020030040500100600004010700060400080200009006006900100090020008300005070 001002003020030040400500100003600007060007080100050200006003010070900004900040300 001002003020040050300600700002100080070006002400090600006070090030009001900500800 001002003020010040300500600007300060030007100400020008008700200040005030100080009 001002003020030040500600700002800090080040100400007006003004070090200600700050009 001002003020010040300500600002100700050007008900040050003008004010090070800600300 001002003020010040300500200003600400070005080600040009009004007040700600200030050 001002003020010040300500600005100200040070001200008030009600070060040300800007004 001002003020010040500600100004500700080060030100007005007800400030050090400009006

When the 23 patterns are canonicalized .. gsf-solver -f%#xc infile.dat ... there exist only 10 essentially different patterns.

Code: Select all: ..X..X..X.X..X..X.X..X..X....X..X..X.X..X..X.X..X..X....X..X..X.X..X..X.X..X..X.. ..X..X..X.X..X..X.X..X..X....X..X..X.X..X..X.X..X..X....X..X..X.X..X.X..X..X...X. ..X..X..X.X..X..X.X..X..X....X..X..X.X..X..X.X..X..X....X..X.X..X..X.X..X..X....X ..X..X..X.X..X..X.X..X..X....X..X..X.X..X..X.X..X..X....X..X.X..X.X....XX...X.X.. ..X..X..X.X..X..X.X..X..X....X..X..X.X..X.X..X..X...X...X.X...X.X...X.X.X..X..X.. ..X..X..X.X..X..X.X..X..X....X..X..X.X..X.X..X..X...X...X.X...X.X.X...X.X....XX.. ..X..X..X.X..X..X.X..X..X....X..X..X.X..X.X..X..X...X...X.X..X..X...XX..X..X....X ..X..X..X.X..X..X.X..X..X....X..X..X.X..X.X..X..X...X...X.X..X..X.X....XX....XX.. ..X..X..X.X..X..X.X..X..X....X..X.X..X..X.X..X..X....X..X.X...X.X.X..X..X....X.X. ..X..X..X.X..X..X.X..X..X....X..X.X..X.X....XX...X.X....X.X.X...X.X...X.X....X..X

by **coloin** » Thu Mar 03, 2011 12:09 am

Thanks ronk for alerting me to an error

I did a bit more searching found only - 15 in total.

EDIT ... there are 18 will update at end of thread page 3

Code: Select all: # 1 ..X..X..X.X..X..X.X..X..X....X..X..X.X..X..X.X..X..X....X..X..X.X..X..X.X..X..X.. # 2 ..X..X..X.X..X..X.X..X..X....X..X..X.X..X..X.X..X..X....X..X..X.X..X.X..X..X...X. # 3 ..X..X..X.X..X..X.X..X..X....X..X..X.X..X..X.X..X..X....X..X.X..X..X.X..X..X....X # 4 ..X..X..X.X..X..X.X..X..X....X..X..X.X..X..X.X..X..X....X..X.X..X.X....XX...X.X.. # 5 ..X..X..X.X..X..X.X..X..X....X..X..X.X..X.X..X..X...X...X..X..X.X.X...X.X...X.X.. # 6 ..X..X..X.X..X..X.X..X..X....X..X..X.X..X.X..X..X...X...X..X.X..X.X....XX...X.X.. # 7 ..X..X..X.X..X..X.X..X..X....X..X..X.X..X.X..X..X...X...X.X...X.X...X.X.X..X..X.. # 8 ..X..X..X.X..X..X.X..X..X....X..X..X.X..X.X..X..X...X...X.X...X.X.X...X.X....XX.. # 9 ..X..X..X.X..X..X.X..X..X....X..X..X.X..X.X..X..X...X...X.X..X..X...XX..X..X....X #10 ..X..X..X.X..X..X.X..X..X....X..X..X.X..X.X..X..X...X...X.X..X..X.X....XX....XX.. #11 ..X..X..X.X..X..X.X..X..X....X..X.X..X..X.X..X..X....X..X.X...X.X.X...X.X....XX.. #12 ..X..X..X.X..X..X.X..X..X....X..X.X..X..X.X..X..X....X..X.X...X.X.X..X..X....X.X. #13 ..X..X..X.X..X..X.X..X..X....X..X.X..X.X....XX...X.X....X.X...X.X...XX..X..X...X. #14 ..X..X..X.X..X..X.X..X..X....X..X.X..X.X....XX...X.X....X.X...X.X.X..X..X....X.X. #15 ..X..X..X.X..X..X.X..X..X....X..X.X..X.X....XX...X.X....X.X.X...X.X...X.X....X..X #16 ..X..X..X.X..X..X.X..X..X....X..X.X..X..X.X..X..X....X..X.X..X..X.X..X..X....X..X##NEW1 #17 ..X..X..X.X..X..X.X..X..X....X..X..X.X..X..X.X..X..X....X.X.X...X.X....XX....X.X.##NEW2 #18 ..X..X..X.X..X..X.X..X..X....X.X.X...X.X....XX....X.X...XX...X..X...XX..X...X...X##NEW3

Here is a representative of each. Interestingly only one pattern cant be made symetrical with the 27 clues.

Code: Select all: # 1 ..1..2..3.2..1..4.5..6..1....2..4..1.5..6..7.7..2..3....7..5..8.8..7..9.9..3..2.. # C27/S4.da/M1.16.3 Patterns Game 16 ED = 10.6/10.6/9.8 # 2 2...4...6..4..2.3..7.8..1....24...1.1...3...2.3...54....5..9.7..1.6..2..6...7...9 # C27.M/S4.da/M1.31.2 Patterns Game 150 ED = 10.7/10.7/8.9 # 3 ..2..3.1..3..1.2..5..6....4..5..7.2..9..4.8..6..9....7.8..9..5.2..5..4....3..8..9 # C27/S2.d/M1.33.1 # 4 ..1.2.3...2...1..43..5...6...42...8.9...3...2.3...67...4...3..75..8...4...2.6.1.. # C27.M/S2.p/M1.13.4 # 5 1....2..3.9..4..1...73..5....21....9.6..2..5.9....56....3..41...7..8..2.2..6....8 # C27.M/S4.da/M1.11.6 # 6 2...3.1....14...2..5...6..3.6.2..4..3...5..7...7..3..65..8..7...9..1..4...6..2..9 # C27/S2.d # 7 .2..7...84..6..9....5..4.7..1.2..3..2...1...4..3..5.6..9.5..6....1..7..37...3..5. # C27.M/S4.da/M1.16.1 # 8 1..3..2...2..4..1...3..6..52...8..7..7.5..3....9..1..67...9.5...4.1....8..8..2.6. # C27/S2.d # 9 ..2.1.3...1...2.4.5..3....2..5..7.8.6...3...4.4.6..9..7....4..6.3.2...5...4.9.7.. # C27.M/S4.da #10 ..1..2..3.2..1..4.3..5..6....51..2...4..7...12....8.3...96...7..6..4.3..8....7..4 # C27 [asymmetric] #11 ..1..3..2.2..4..3.4..6..5....23...1..4...57..5...9...8..6.8..7..9.1..6..7....2..1 # C27/S2.d #12 2..1....3..1..2.4..5..3.6..5..7...9...6.8.2...8...4..1..7.6..8..6.4..1..3....7..5 # C27/S4.da #13 2...3.1....14...2..5...6..3.6.2..4..3....4.7...7.8...65..8..7...9..1..4...6..2..9 # C27/S2.d #14 6....2.7...8.1...5.9.5..3....2..1..3.1..2..4.5..3..2....4..8.9.1...9.8...3.4....7 # C27.M/S4.da #15 ..1.2...3.2...34..5..1...6...4..1.7.2...9...6.6.4..8...9...2..8..69...1.3...5.7.. # C27.M/S4.da

And furthur work .....copied from another post in the hardest thread

I suppose it helps to clarify the valid/invalid patterns of the "diagonal" 123 clues.
Boxes 1,2 and 4 can always be morphed to this pattern

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

There are 6 ways to add 3 diagonal clue patterns to box 5

Here are representatives of the possible valid patterns

Code: Select all: +---+---+---+ +---+---+---+ +---+---+---+ |1..|3..|...| |1..|3..|...| |1..|3..|...| |.2.|.1.|...| |.2.|.1.|...| |.2.|.1.|...| |..3|..2|...| |..3|..2|...| |..3|..2|...| +---+---+---+ +---+---+---+ +---+---+---+ |3..|1..|...| |3..|.2.|...| |3..|..1|...| |.1.|.2.|...| |.1.|..3|...| |.1.|2..|...| |..2|..3|...| |..2|1..|...| |..2|.3.|...| +---+---+---+ +---+---+---+ +---+---+---+ |...|...|...| |...|...|...| |...|...|...| |...|...|...| |...|...|...| |...|...|...| |...|...|...| |...|...|...| |...|...|...| +---+---+---+ valid +---+---+---+ valid +---+---+---+ valid

Here are representatives of the invalid patterns

Code: Select all: +---+---+---+ +---+---+---+ +---+---+---+ |1..|3..|...| |1..|2..|...| |1..|2..|...| |.2.|.1.|...| |.2.|.3.|...| |.2.|.3.|...| |..3|..2|...| |..3|..1|...| |..3|..1|...| +---+---+---+ +---+---+---+ +---+---+---+ |3..|1..|...| |2..|.1.|...| |2..|..3|...| |.1.|..3|...| |.3.|X..|...| |.3.|.1.|...| |..2|.X.|...| |..1|..2|...| |..1|X..|...| +---+---+---+ +---+---+---+ +---+---+---+ |...|...|...| |...|...|...| |...|...|...| |...|...|...| |...|...|...| |...|...|...| |...|...|...| |...|...|...| |...|...|...| +---+---+---+ invalid +---+---+---+ invalid +---+---+---+ invalid

For comepleteness
of the 18 ED ways to form a 27 clue pattern with 3 "diagonal" clues per box
there are only 3 out of the 18 which have valid template

Code: Select all: +---+---+---+ +---+---+---+ +---+---+---+ |1..|3..|2..| |1..|3..|..2| |1..|3..|2..| |.2.|.1.|.3.| |.2.|.1.|3..| |.2.|.1.|.3.| |..3|..2|..1| |..3|..2|.1.| |..3|..2|..1| +---+---+---+ +---+---+---+ +---+---+---+ |3..|2..|1..| |3..|2..|1..| |2..|1..|..3| |.1.|.3.|.2.| |.1.|.3.|.2.| |.3.|.2.|1..| |..2|..1|..3| |..2|..1|..3| |..1|..3|.2.| +---+---+---+ +---+---+---+ +---+---+---+ |2..|1..|3..| |.3.|1..|2..| |3..|2..|.1.| |.3.|.2.|.1.| |..1|.2.|.3.| |.1.|.3.|..2| |..1|..3|..2| |2..|..3|..1| |..2|..1|3..| +---+---+---+ +---+---+---+ +---+---+---+

C

by **coloin** » Tue May 17, 2011 10:58 am

From these 15 27 clue templates I removed 3 clues and found 8099 different 24 clue templates.

Of these only 18 had an empty box

Code: Select all: .....X..X....X..X....X..X....X..X..X.X..X..X.X..X..X....X..X..X.X..X..X.X..X..X.. .....X..X....X..X....X..X....X..X..X.X..X..X.X..X..X....X..X..X.X..X.X..X..X...X. .....X..X....X..X....X..X....X..X..X.X..X..X.X..X..X....X..X..X.X.X..X..X...X..X. .....X..X....X..X....X..X....X..X..X.X..X..X.X..X..X....X..X.X..X..X.X..X..X....X .....X..X....X..X....X..X....X..X..X.X..X..X.X..X..X....X..X.X..X.X....XX...X.X.. .....X..X....X..X....X..X....X..X..X.X..X..X.X..X..X....X..X.X..X.X..X..X...X...X .....X..X....X..X....X..X....X..X..X.X..X..X.X..X..X....X.X..X..X.X..X..X....X..X .....X..X....X..X....X..X....X..X..X.X..X..X.X..X..X....X.X.X...X.X....XX....X.X. .....X..X....X..X....X..X....X..X..X.X..X.X..X..X...X...X..X..X.X.X...X.X...X.X.. .....X..X....X..X....X..X....X..X..X.X..X.X..X..X...X...X..X.X..X.X....XX...X.X.. .....X..X....X..X....X..X....X..X..X.X..X.X..X..X...X...X..X.X..X.X..X..X...X...X .....X..X....X..X....X..X....X..X..X.X..X.X..X..X...X...X.X..X..X...XX..X..X....X .....X..X....X..X....X..X....X..X..X.X..X.X..X..X...X...X.X..X..X.X....XX....XX.. .....X..X....X..X....X..X....X..X..X.X..X.X..X..X...X...X.X.X...X...X..XX..X...X. .....X..X....X..X....X..X....X..X..X.X..X.X..X..X...X...X.X.X...X...X.X.X..X....X .....X..X....X..X....X..X....X..X..X.X..X.X..X..X...X...X.X.X...X.X...X.X....X..X .....X..X....X..X....X..X....X..X.X..X..X.X..X..X....X..X.X...X.X.X...X.X....XX.. .....X..X....X..X....X..X....X..X.X..X..X.X..X..X....X..X.X.X...X.X....XX....X.X.

C

by **coloin** » Wed Nov 09, 2011 4:35 pm

been thinking about the 27-puzzles with all "diagonal" patterns.

im still surprised about only 15 ED patterns.

I had sort of assumed that the more total ED puzzles a pattern had the bigger the range in the ratings.

Removing clues from a 27-puzzle - might make a puzzle be formable from another of the 15 ED 27-patterns.

Except this can only happen when you remove 2 clues from a box.

Therefore there may well be more puzzles if a pattern has one box with only one clue.

I might look at patterns with 25 clues with 2 clues removed from one box

C

by **coloin** » Wed Nov 23, 2011 3:19 pm

Going back to the 15 ED patterns with all 27 clues in a potentially diagonal pattern.

I am wondering what the incidence is of these patterns.

Essentially there are 6 ways to have a "diagonal" pattern in a box - trivially this is 6^9 patterns

Given that B1B2B3B4B7 can always be fixed - there are at most 6^4 [/2] ways to complete B5B6B8B9

Can anyone show what the incidence of the 15 ED patterns ?

Can anyone estimate the approx total number of puzzles in the 15 ED patterns ?

C

by **coloin** » Sun Dec 13, 2015 1:48 pm

Regarding the diagonal patterns .... and hard puzzles..... Maybe the obvious answer is the correct one.

Given that a set pattern has n puzzles, and some patterns will have more puzzles than others , although by nature symmetrical patterns will have less ed puzzles.

Do diagonal patterns have less puzzles with ED x/x/1.2 than other patterns with a box with 3 clues in a non-diagonal pattern ?

Or do diagonal patterns just have more puzzles than other non-diagonal patterns ?

C

by **champagne** » Sun Dec 13, 2015 4:47 pm

So far I start a search for hardest in the n clues space starting from seeds of size n-1 rating 10.0 and more

Starting from your 15 ED for 26 or 27 clues never searched (as far as I know) could be another way to launch a new 'n'

by **coloin** » Thu Dec 17, 2015 9:36 pm

From the 15 ED Patterns with a representative puzzle.
Removing 3 clues from them - gave 43571 puzzles/pseudopuzzles .....
Of which 3455 could be morphed to be symmetrical .....
Of which 567 had an essentially different pattern.
Those with a box distribution of 222333333 will come from a unique stem of the 15.
Those with other distributions may share a stem
- here are the 567 [24 clue] minlex patterns - which can be made symmetrical

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by **coloin** » Mon Dec 21, 2015 3:27 pm

And further removing of clues

23 clues - 1488 ED patterns which can be made symmetrical

Code: Select all: ........X.......X...X..XX....X..X..X.X..X..X.X..X..X....X..X.X..X..X...XX..X..X.. ........X.......X...X..XX....X..X..X.X..X..X.X..X..X....X..X.X..X..X.X..X..X....X ........ .....X..X..X....X..X..X.X....XX......X..X.X..X....X..X..XX...X..X..X.X..X....X... .....X..X..X....X..X..X.X....XX......X..X.X..X....X.X...XX....X.X..X.X..X....X...

22 clues - 2772 ED patterns which can be made symmetrical

Code: Select all: ..............X..X....X..X...X..X..X.X..X..X.X..X..X....X..X..X.X..X..X.X..X..X.. ..............X..X....X..X...X..X..X.X..X..X.X..X..X....X.X..X..X.X..X..X....X..X ........ .....X..X..X....X..X..X.X.....X..X....X.X....X....X.X...XX....X.X...X...X...X.X.. .....X..X..X....X..X..X.X.....X..X...X...X..XX...X..X...X.X...X.X.X.....X.....X..

by **m_b_metcalf** » Mon Dec 21, 2015 4:43 pm

Coloin,
Are you planning to submit thousands of patterns to the Patterns Game?

Mike

by **coloin** » Mon Dec 21, 2015 9:55 pm

not really - i just wondered how many patterns there were, and perhaps how many had been used ......

by **Pat** » Thu Jan 07, 2016 4:10 pm

coloin wrote:

i just wondered---how many had been used

for a report of all 297 past patterns

31 early un-numbered,
+ 266 numbered games;
game 267 not yet

see post 248795.

diagonality information is not provided.

almost

by **coloin** » Sat Jan 09, 2016 10:26 pm

interesting slant
your pattern with 5 clues in one of the boxes made up to 29 clues

Code: Select all: +---+---+---+ |..1|2..|.3.| |.7.|..4|5..| |5..|.6.|..7| +---+---+---+ |2..|7.6|.4.| |..7|.3.|8..| |.8.|5.2|..6| +---+---+---+ |4..|.2.|..8| |..6|9..|.5.| |.9.|..3|1..| +---+---+---+

with 5 clues in a box there are 3 ways to make it up to 5 and have 2 diagonal equivs in the box
at most there will be 3 * 9 * 15 patterns with clue box dist of 533333333
reductions for non symmetry and isomorphs.
could do it easily - is this what you are thinking ?

patterns like yours with 25 clues would have clue box dist of 533332222
removing a clue from a box with 3 clues retains the original pattern stem.
of these some would be symmetrical in some way
C

by **Pat** » Sun Jan 10, 2016 3:00 pm

Pat (2008.Nov.6) wrote:

in # 49,
with only 20 cells given
and poor diagonality ( only 3 boxes ),
highest rating = 9.1/2.6/2.6
( and players un-happy for lack of "diamonds" )
results

in # 57,
also only 20 givens
but full diagonality ( all 9 boxes ),
highest rating = 10.4/6.7/6.7
results

could be interesting to re-visit these two
with better software (and stronger computers)

# 49 wrote:
Code: Select all
. . . . . . O O . . . . O O . . . . . . O . . . O O . . O . . . . . . O . O . . O . . . O . . . . . O . . . O . O . . . O . . O . O . . . . . . . . . O O . . . .

# 57 wrote:
Code: Select all
. . O O . . . . . . O . . . O O . . O . . . . . . O . O . . O . . . O . . . . . O . . . . . O . . . O . . O . O . . . . . . O . . O O . . . . . . . . . . O O . .

The New Sudoku Players' Forum

Diagonal Patterns in the "Patterns Game"

Diagonal Patterns in the "Patterns Game"

Re: Diagonal Patterns in the "Patterns Game"

Re: Diagonal Patterns in the "Patterns Game"

Re: Diagonal Patterns in the "Patterns Game"

Re: Diagonal Patterns in the "Patterns Game"

Re: Diagonal Patterns in the "Patterns Game"

Re: Diagonal Patterns in the "Patterns Game"

Re: Diagonal Patterns in the "Patterns Game"

Re: Diagonal Patterns in the "Patterns Game"

Re: Diagonal Patterns in the "Patterns Game"

Re: Diagonal Patterns in the "Patterns Game"

Re: Diagonal Patterns in the "Patterns Game"

Re: Diagonal Patterns in the "Patterns Game"