I have been interested in manual-solving simulation software for so long.
Recently, I viewed some parts of the SudokuExplainer rating system. Then I found something which could be optimised.
Extended SE ratings
42 posts
• Page 1 of 3 • 1, 2, 3
Re: Extended SE ratings
by Alpxcx » Mon Dec 12, 2022 10:44 am
Naked/Hidden triples can be divided into a few cases:
1. intersected
demonstration: |* * *|T T T|* * *|
2. non-intersected: 2 zones
demonstration: |T * *|T T *|* * *|
3. non-intersected: 3 zones
demonstration: |T * *|* T *|* * T|
T means a cell included in the subset.
Triples make 84 combinations in total and there are 3 of case 1, 54 of case 2 and 27 of case 3, if in rows/columns.
It is quite obvious that case 1 appears much more frequently than 3/84(1/28) because it require less hints to form such a structure. Statistics agrees.
In blocks it's slightly different because there are 6 of case 1, but the frequency is still much more than 6/84(1/14).
HoDoKu is defining it as "locked triple", but SudokuExplainer does not make it a special case.
Case 3 is not rare, but indeed less than 27/84(9/28), if in rows/columns.
Case 3 in blocks is quite different because most of the times it's a case 2 in a different view, so I can't give a conclusion now.
In my point of view, these should be differentiated, because the further apart the clues, the harder to find.
1. intersected
demonstration: |* * *|T T T|* * *|
2. non-intersected: 2 zones
demonstration: |T * *|T T *|* * *|
3. non-intersected: 3 zones
demonstration: |T * *|* T *|* * T|
T means a cell included in the subset.
Triples make 84 combinations in total and there are 3 of case 1, 54 of case 2 and 27 of case 3, if in rows/columns.
It is quite obvious that case 1 appears much more frequently than 3/84(1/28) because it require less hints to form such a structure. Statistics agrees.
In blocks it's slightly different because there are 6 of case 1, but the frequency is still much more than 6/84(1/14).
HoDoKu is defining it as "locked triple", but SudokuExplainer does not make it a special case.
Case 3 is not rare, but indeed less than 27/84(9/28), if in rows/columns.
Case 3 in blocks is quite different because most of the times it's a case 2 in a different view, so I can't give a conclusion now.
In my point of view, these should be differentiated, because the further apart the clues, the harder to find.
- Alpxcx
- Posts: 25
- Joined: 09 December 2022
Re: Extended SE ratings
by Alpxcx » Mon Dec 12, 2022 10:55 am
Naked/Hidden quadruples can be divided into a few cases:
1. 2 zones: intersected+1
demonstration: |* * *|T T T|* T *|
2. 2 zones: 2+2 distribution
demonstration: |T T *|T T *|* * *|
if in blocks, this means 2+2 in both row/column view, for example:
|T * T| |T T *|
|T * T| |* * * |
|* * *| |T T *|
3. 3 zones: 2+1+1 distribution
demonstration: |T * *|T T *|* * T|
T means a cell included in the subset.
Quadruple make 126 combinations in total and there are 18 of case 1, 27 of case 2 and 81 of case 3, if in rows/columns.
In blocks there are 36 of case 1, 9 of case 2 and 81 of case 3.
Now it's obvious that case 3 appears less than 81/126(9/14).
I have a set of HoDoKu randomly generated puzzles which include at least 1 Naked/Hidden quadruples here.
(Conditions: HoDoKu - Mode - Learning... - Naked/Hidden Quadruple ticked, HoDoKu - Edit - Preferences... - Solver - all uniqueness techniques unticked)
Statistics show:
In rows/columns:
Case 1: 80/133 (60.2%)
Case 2: 24/133 (18.0%)
Case 3: 29/133 (21.8%)
In blocks:
Case 1: 56/83 (67.5%)
Case 2: 6/83 (7.2%)
Case 3: 21/83 (25.3%)
--Cross distribution around a given/solved*: 14/21 (66.7%) 14/83(16.9%)
--Case 3 after deduction: 7/83 (8.4%)
*I treat cross distribution as a special case because it's in a pattern:
|T G T| |* T *|
|* T *| |T G T|
|* T *| |* T *|
G means a given/solved here.
This sample may be still small, but it takes a lot of effort (not an automatic process). I may be able to run a larger test if there is a script. It's not accurate, but already says something.
Is this interesting enough? This means, if you are a programmer, writing the detection code as a lot of for-loops could be quite inefficient to run.
Here is my sample:
Update: Typo fixed
1. 2 zones: intersected+1
demonstration: |* * *|T T T|* T *|
2. 2 zones: 2+2 distribution
demonstration: |T T *|T T *|* * *|
if in blocks, this means 2+2 in both row/column view, for example:
|T * T| |T T *|
|T * T| |* * * |
|* * *| |T T *|
3. 3 zones: 2+1+1 distribution
demonstration: |T * *|T T *|* * T|
T means a cell included in the subset.
Quadruple make 126 combinations in total and there are 18 of case 1, 27 of case 2 and 81 of case 3, if in rows/columns.
In blocks there are 36 of case 1, 9 of case 2 and 81 of case 3.
Now it's obvious that case 3 appears less than 81/126(9/14).
I have a set of HoDoKu randomly generated puzzles which include at least 1 Naked/Hidden quadruples here.
(Conditions: HoDoKu - Mode - Learning... - Naked/Hidden Quadruple ticked, HoDoKu - Edit - Preferences... - Solver - all uniqueness techniques unticked)
Statistics show:
In rows/columns:
Case 1: 80/133 (60.2%)
Case 2: 24/133 (18.0%)
Case 3: 29/133 (21.8%)
In blocks:
Case 1: 56/83 (67.5%)
Case 2: 6/83 (7.2%)
Case 3: 21/83 (25.3%)
--Cross distribution around a given/solved*: 14/21 (66.7%) 14/83(16.9%)
--Case 3 after deduction: 7/83 (8.4%)
*I treat cross distribution as a special case because it's in a pattern:
|T G T| |* T *|
|* T *| |T G T|
|* T *| |* T *|
G means a given/solved here.
This sample may be still small, but it takes a lot of effort (not an automatic process). I may be able to run a larger test if there is a script. It's not accurate, but already says something.
Is this interesting enough? This means, if you are a programmer, writing the detection code as a lot of for-loops could be quite inefficient to run.
Here is my sample:
- Code: Select all
.....65..19..3.47...41...8.4.69...5...........8...76.2.4...39...51.6..34..32.....;NQ;R1;
9.4.8.3.......9...32.6....1732....1...9...5...4....9722....1.59...3.......7.5.1.6;NQ;R1;
2...........156..9..19..3...72.....5..67381..9.....68...5..12..1..364...........1;NQ;R1;
.....4.78..7..13.9...6.......6.....7.23...54.9.....1.......8...1.29..4..65.2.....;NQ;R1;
.143.....3278..5...........4....231..3..5..9..914....7...........8..5741.....768.;NQ;R1;
.........3.52716.8....561....16......53...72......75....478....6.25198.3.........;NQ;R1;
..1372.4.73.64..2..........3.....9..54.....38..8.....2..........9..23.51.2.4156..;NQ;R1;
.....746.....2.....91..6..7.7.34.....657.932.....65.8.2..6..57.....7.....361.....;NQ;R1;
..3..7..52...3..9..5.1.27..5.........86...12.........9..57.1.6..9..6...44..5..8..;NQ;R1;
49.863.5.......896.........3...57.4..7..2..8..6.98...2.........247.......8.275.34;NQ;R1;
3...6428.........42..9..35...3..946...........573..1...39..1..25.........8127...9;NQ;R1;
8.............2814..5.1...927.1.43....6.3.4....45.9.626...2.9..4123.............3;NQ;R1;
.1947.....67..1.5.2.......1.2.18...7.........4...92.8.8.......2.7.2..51.....6974.;NQ;R1;
284.1.6...........19...2..5...9....7.2.871.6.4....5...3..4...28...........2.6.749;NQ;R1;
.............8.75.2.71.96..49.5.13....8.2.1....36.8.92..14.69.7.34.1.............;NQ;R1;
...........31.486.175.....42.1879...............5314.28.....329.972.81...........;NQ;R1;
..8.9.45.........7...2.4.8986.........34.68.........2672.3.1...6.........81.5.9..;NQ;R1;
.7..56..4.46.978..2........615...2.............7...459........8..978.53.7..16..4.;NQ;R1;
72...643..9...........2..618..6......37.4.82......3..948..1...........4..654...87;NQ;R1;
1.28.94..79.2....1.....1.....4....3.8...4...9.6....2.....5.....2....6.87..97.83.6;NQ;R1;
7......82..34..6.9....5.....1...5..68...6...42..8...1.....7....3.9..41..42......3;NQ;R1;
8........541286....739......2..6.3.8...7.3...3.9.2..1......513....812574........2;NQ;R1;
..89..1.5.......4.....362..4168.......7...4.......4671..569.....7.......1.3..25..;NQ;R1;
.6.8...2.5..........25..4.6...42.751.7.....4.459.73...3.5..46..........7.8...6.9.;NQ;R1;
1..73..94..42.87.6...........21......45.7.16......53...........8.35.74..47..29..3;NQ;R1;
........68..96.5...7..18...46...2.....18734.....6...79...78..2...3.26..49........;NQ;R1;
......253...6......5..32..7.9....416.4..9..7.816....2.5..21..9......8...471......;NQ;R1;
..7..45...54..21.868.......9.8.45...............97.4.2.......818.54..97...31..2..;NQ;R1;
....25...7.93...5.........1.63...81...14.32...87...59.1.........9...16.8...87....;NQ;R1;
4628...........5...7.6.......1.96.47.2.....1.34.21.8.......5.8...9...........4176;NQ;R1;
12..74.38........787...3.2...7.65.9...........1.38.2...9.5...644........76.14..85;NQ;R1;
8.32......1.6345............49.2.....71.5.42.....7.35............4192.3......86.7;NQ;R1;
.73.68.54..159...8...........6..4.2...2.3.8...5.7..3...........6...295..12.38.49.;HQ;R1;
.....6.54..8...2.6....5.....5....42...71985...96....8.....6....6.5...7..41.3.....;NQ;R1;
6.........5.3....7.27.8.6...7.4182.............8729.5...9.5.31.4....2.7.........8;NQ;R1;
724.3...616..9.57...........7......5..91.32..2......4...........52.4..383...1.469;NQ;R1;
.........195..68..37.....9.9...87.1...39.16...8.26...9.4.....67..93..485.........;NQ;R1;
..........86.2.9..925.64.....7..648.6...8...7.983..5.....61.372..1.9.64..........;NQ;R1;
.....4.135219...4.......6...9...71.4....1....7.34...2...2.......3...257996.8.....;NQ;R1;
8..........6.18.37.346......1.9.42.............75.2.9......968.42.83.5..........2;NQ;R1;
.......1.67.3..5..13.5.96........7.949..6..255.7........16.4.38..2..1.56.6.......;NQ;R1;
....12..7......6...635...8.4...7.95...93.57...75.6...8.5...982...1......2..78....;NQ;R1;
.83.56...4..........974.3..9.5....4..6.....3..4....8.1..7.124..........6...39.75.;NQ;R1;
.5......64............8.519.8..132...7.8.5.3...249..5.135.4............42......7.;NQ;R1;
.........483..17...918...2..483.7..9..5.2.4..9..4.583..2...954...95..618.........;NQ;R1;
849..31............32...9..7....6...985.2.376...5....8..1...74............46..819;NQ;R1;
.1743.....9.1.7.2.8...............8213.279.5665...............7.2.6.5.3.....1324.;NQ;R1;
.......258.........69.37..4....12.9...29.34...8.67....1..39.87.........347.......;NQ;R1;
93...2...........2...41.368..7..3.2.3.91.76.4.8.5..7..124.75...8...........2...51;NQ;R1;
......2....978.......5.4.3..94...5.6....1....2.6...87..5.1.3.......926....8......;NQ;R1;
........7267..9....41.6......67..83...........93..12......3.42....8..7935........;NQ;R1;
75.48..........4...6.....3124.7..3.....614.....5..8.4797.....5...6..........62.94;NQ;R1;
6.49...87..............791...1.7..28...821...25..9.1...265..............37...86.2;NQ;R1;
91.3..5.2..........5..89.........87478..2..19691.........13..4..........1.5..7.68;NQ;R1;
7.4.53....63............8....71..3...4.368.1...6..92....1............62....23.5.7;NQ;R1;
.5...4132.283..5.7...........9.43.1...........3.26.4...........6.2..837.8947...5.;NQ;R1;
3...........284..9.54..3....734....18...1...69....627....9..86.4..132...........4;NQ;R1;
.26..4....73........5137.......213...8.973.5...145.......5869........57....7..82.;NQ;C1;
..4..6..5.9..1..8.8....3.6........129...4...713........8.9....3.7..6..5.4..1..8..;NQ;C1;
.84..5....9.4....5.6.....7...15.2..7.........8..3.12...4.....8.6....8.1....2..35.;NQ;C1;
1...4...7.....2..1..41...32.7.8...139.......536...1.9.25...43..7..9.....6...2...8;NQ;C1;
.............4827..4.2.9..1.1..7..4.42..8..93.9..5..2.9..1.7.8..5389.............;NQ;C1;
573....69.........61.5.....7....3..1.4..5..8.3..9....2.....1.98.........98....257;N1;C1;
..6........5.364.7...2....8..269..4...43.79...7..486..9....2...4.316.8........1..;NQ;C1;
.9381..2...4.......78..2..5.3.47..8...........8..56.7.3..1..95.......2...6..9713.;NQ;C1;
.8..14.5..5.7........3..4....1..679...8...2...792..8....4..5........9.2..9.47..8.;NQ;C1;
..19.......6..1.2..98.62.7..39......5...4...8......73..6.18.95..4.6..3.......54..;NQ;C1;
....183....3..967....3...2...9....85...9.4...75....9...1...7....382..7....564....;NQ;C1;
87.5....6..1..9..7.5.1........6....2.4..3..9.6....5........1.8.2..9..1..5....8.23;NQ;C1;
.6.1.8.9..98..67...37...........4..6..16859..6..3...........51...49..62..7.8.1.4.;NQ;C1;
.....5.342..71..5.....4...8.2....6..69..7..25..5....4.1...6.....7..81..946.5.....;NQ;C1;
.1..9.3...2.6....55...3..7.....8.71.2.......3.49.7.....5..4...63....5.9...7.6..2.;NQ;C1;
...7.6.5357....9.........8.25.3....81..2.8..58....4.69.4.........5....3772.8.3...;HQ;C1;
.7...2.642.86..5.79........3..2.78.............25.6..9........88.4..17.359.8...2.;NQ;C1;
..63..89.2.3.1....7...6......1.36.....71.49.....89.7......4...5....8.4.3.54..36..;NQ;C1;
..47....279..4..6.21.6....99...6.......1.8.......9...71....6.95.5..2..463....17..;NQ;C1;
.....5..6.3...8.4...5.2.1...94..3.6...1.7.4...6.8..95...6.3.7...4.9...1.2..4.....;NQ;C1;
8....5.692..9.853....7..........29.57.......84.68..........7....891.4..667.5....1;NQ;C1;
53..91..4...........97...818...1..6.3...6...7.4..2...527...35...........1..45..72;NQ;C1;
.1.....93..2..3.568..6......2...8....4.5.2.7....3...1......9..478.4..1..46.....3.;NQ;C1;
2...4.....735....8.8...........9..5691.257.8474..3...........1.6....984.....6...2;NQ;B1;
.7.9.....2.5.6......9.52...4.65.398...........928.63.1...79.8......1.7.3.....8.5.;NQ;B1;
....28.6...1...........18391....694.9.7...6.3.362....57196...........2...5.87....;NQ;B1;
9817.5...237...........1....9..7.81....5.9....65.1..3....3...........689...8.6743;NQ;B1;
...2..85.....534.1.8..7.2.9...1..6..1...3...2..2..5...8.7.4..2.2.931.....45..2...;NQ;B1;
26..9......94......5...3...83..615.4..2.4.3..5.138..67...8...1......64......3..98;NQ;B1;
472.....5..........6...28....71.4....34.8.96....9.73....58...9..........3.....756;NQ;B1;
..3.95...8....26..9.24.......1..42..7.......9..43..5.......69.1..97....6...53.4..;NQ;B1;
...7..54......6...3...891.7..7.....583.....716.....8..9.821...4...9......74..3...;NQ;B1;
.......43...23.8.7...4.8.162.1.....8...627...5.....7.973.1.5...4.9.63...18.......;NQ;B1;
..21.743......2.76...3....8.......64.53...79.64.......4....3...51.2......796.82..;NQ;B1;
72..8.53........7..4..3...2.....1.....36428.....9.....5...9..8..6........74.2..95;NQ;B1;
....6....1.4..23..95....7.1...517...7.......4...248...6.1....79..26..4.3....8....;NQ;B1;
...46.853.....52.........17.825913.............324859.94.........61.....318.54...;NQ;B1;
........1784...9..1.9.7..2..9...6...6..824..3...7...5..4..6.3.2..1...4872........;NQ;B1;
.4...3..71.86.....3.9...48....39......4.8.6......26....85...1.6.....28.42..4...5.;NQ;B1;
.7239.....84....2.63...8..53...........915...........77..4...36.2....47.....6198.;NQ;B1;
..175....2....95..7...624..16....9....7...8....3....16..697...3..56....9....216..;NQ;B1;
7..8............3945....2819..4.23......5......53.7..6326....7519............1..2;NQ;B1;
247.15...8.1.........6.......3.4..57..5.8.1..18..7.3.......9.........5.2...16.739;NQ;B1;
..1.25..43........84.39.7..47....2..1.......9..9....48..3.68.95........69..41.8..;NQ;B1;
1.........945..8.168294..5..4.3........692........4.8..6..392484.1..639.........6;NQ;B1;
82...7.....1.5.7..3.79......4...5..2.7823195.2..4...7......34.1..6.2.5.....7...89;NQ;B1;
4.8..2..3.1.84.....6...7...3......4..75...86..2......9...6...3.....59.2.5..2..1.8;NQ;B1;
95......8.6.74...9..23..7.....56..8....984....8..23.....3..28..5...79.4.6......57;NQ;B1;
3.5......47.98....69...1.....781.....6.2.9.7.....635.....6...43....32.97......8.6;NQ;B1;
.9.4...3......52.....69...191....8.3..8...6..3.2....144...69.....38......2...1.7.;NQ;B1;
.78.....9.9.5.14..1.......5.......6343..5..2181.......3.......4..18.9.7.7.....65.;NQ;B1;
...5.......6.1.4......365.78..1.5.4..1.....2..3.2.7..13.745......9.2.8.......3...;NQ;B1;
.2....9....9743.588...2...4...5......4.967.8......2...4...7...676.1384....8....2.;NQ;B1;
6...3...291........28....373..6........795........8..419....84........264...8...1;NQ;B1;
...........12..6...2.946....93..8.1..52...89..6.1..27....369.5...5..14...........;NQ;B1;
.9....3..6.43....153.41.......83.6......7......5.21.......83.798....75.4..1....6.;NQ;B1;
71..........3...49..4.....2...4.371...67812...875.9...2.....5..64...8..........63;NQ;B1;
.5.96..7....2.........582.9681......72..8..96......4828.659.........3....3..16.5.;NQ;B1;
....57.2..9......7..741...828....3..4...8...9..3....843...759..6......1..4.16....;NQ;B1;
..87......61.....434.612...9......7...2.4.3...8......2...365.488.....59......12..;NQ;B1;
.......3..9.6..2.57.1...4.65.782......9.4.8......597.44.8...1.31.5..2.7..7.......;NQ;B1;
.......12...4.........31759.31.5...7.7..1..9.6...9.18.52734.........7...89.......;NQ;B1;
7.8.........36....49...2.....2..4165....1....6315..2.....6...37....89.........6.1;NQ;B1;
....657.1..1.8936........92.7.1.....4.......6.....3.5.31........6953.8..8.497....;NQ;B1;
...8..4.7..4...5..73.....9..9...37.2....4....5.27...1..2.....49..7...1..3.8..2...;NQ;B1;
..3.68.........164...5....334.19.7....7...2....8.37.155....6...794.........75.9..;NQ;B1;
9.3....6.2549..3...7.....5.4..8.36......1......57.4..3.4.....8...2..6419.9....5.6;NQ;B1;
15..72..3..........9315......2.8..1.53..4..27.4..9.3......2943..........4..73..65;NQ;B1;
6.....532...9...67..7...1.......2.899...4...125.7.......3...9..78...3...549.....6;NQ;B1;
......5.....6...1....82..47..2.9.48....7.3....51.4.9..69..14....7...8.....4......;NQ;B1;
2..6..45.......9.23.5.......785.2...1.......4...1.782.......5.14.7.......39..1..8;NQ;B1;
........7...9.612.....719.4..762.8....4...5....2.357..4.359.....857.4...9........;NQ;B1;
.2.485...4.57.6.....7.........3...4.84..6..13.9...4.........2.....1.78.6...658.9.;NQ;B1;
..8....4132......6......52...4692...2...4...9...5184...46......5......3881....9..;NQ;B1;
.2.5.8.6..15...3......172.917.......8...7...4.......372.745......6...41..4.6.9.7.;NQ;B1;
.....5.925..3...........6.1..6.5..1.1.42937.6.9..6.2..9.8...........8..334.1.....;NQ;B1;
45.......1.763.........1...7.....69558..1..47629.....3...7.........581.9.......26;NQ;B1;
6...9317....41.68.2......3...7...2..82.....56..4...3...7......1.96.87....8263...5;HQ;B1;
.5.............362....4..18.8.3..9...4.7.9.5...9..6.4.89..7....426.............3.;NQ;B1;
....2......51...747......215..3......89.4.75......2..994......263...91......1....;NQ;R2;
........6...2.39....6...3479....1.53....2....53.4....2617...4....37.9...2........;NQ;R2;
...........234..17.7...59.....4..57.41.657.23.57..3.....15...8.29..783...........;HQ;R2;
.........14...7.....64..3.74...352.82.8.4.7.55.186...37.4..96.....5...79.........;NQ;R2;
61.8.......316..8.85.79.6..........6.7..8..2.9..........7.24.68.8..763.......8.59;NQ;R2;
15....3.....9.8..1.7..2.96..2841.................7289..47.8..3.2..7.4.....5....87;NQ;R2;
......3.....87.6244..63...........1938.2.1.4694...........56..1159.87.....7......;NQ;R2;
1........37....2..4..5.3..9..74...9..9.125.6..3...95..5..9.8..4..6....21........5;NQ;R2;
7....45....3..126...........3..2..78.8.753.2.27..1..3...........428..3....85....6;NQ;R2;
.........4.7.6...382..43...2..5....736.478.515....6..4...31..981...9.4.2.........;HQ;R2;
63.9.......9........2.63.5...1642..5....1....8..3597...1.43.9........6.......6.81;NQ;R2;
..9........634..811..5.846.......273.........731.......182.7..596..548........1..;NQ;R2;
.3.5.2.147..1.........935...89.....1.........5.....64...726.........8..612.9.5.7.;NQ;R2;
.1..25.....5..4......1..28..592....3..14.39..2....916..37..1......5..4.....39..7.;NQ;C2;
38...69.........1454........5..9...7...328...1...5..2........4863.........47...62;NQ;C2;
9..........3..1..657...931......7.3.7.93.86.2.6.5......572...832..9..7..........4;HQ;C2;
.85.1.4...4.2......17..3.......2.3...7.1.8.9...9.7.......7..15......1.4...2.3.68.;NQ;C2;
79.3........2.5....4....8.5267....4.....5.....8....6198.1....5....5.7........9.23;NQ;C2;
..3.562..4.63....789............2...6..147..5...5............835....46.2..163.7..;NQ;C2;
.....2.4....89...139...5..6.1..3....56.....32....6..1.2..9...784...58....3.1.....;HQ;C2;
68......94......8....578.....2..3.7..1.287.9..6.4..2.....351....5......78......45;NQ;C2;
..6..31.8.5.......4.76....9..58........742........56..6....92.1.......3.9.41..5..;NQ;C2;
......7....89...52.2.7....8.154......4.....6......839.1....3.7.75...12....4......;NQ;C2;
19...6..8...3...723.41......5.......9.3...7.5.......1......32.453...2...8..6...97;NQ;C2;
.......8....35...2...4.67.919.7......6.831.9......9.376.52.3...2...95....4.......;HQ;B2;
48.5..67...7.4....9...8....3......6..16...48..5......2....6...7....1.9...28..7.31;HQ;B2;
..56.....3..57.....26.1......4...73.63..4..25.89...1......9.21.....65..9.....18..;HQ;B2;
.9...2....6.....1.1.3.7.4.9.....1..8...783...6..9.....9.4.3.1.6.5.....4....2...3.;NQ;B2;
65..1.3.....25......18.....12.....6.4.5...1.8.9.....47.....56......49.....9.8..54;HQ;B2;
.....6527.......6.....9...1.2..7.....759.463.....3..8.7...2.....5.......8697.....;HQ;B2;
4321...8...7.....11..3549......32.......8.......41......4821..92.....5...6...9312;NQ;R3;
7...3.1589.62.......8......2....1.......4.......6....9......5.......78.2654.8...7;NQ;R3;
..59....3..8.73.4..34..8.7.6...3.4.............7.5...8.4.2..76..9.71.3..5....69..;HQ;R3;
89.7...5.....927.42.7.....8......5..6...8...7..2......7.....4.69.136.....6...5.92;NQ;R3;
75.....48........63..812.7......1.....15874.....6......9.263..52........53.....64;NQ;R3;
..2.348..9...6.1....59...2..1........7.4.9.5........6..3...85....1.9...4..412.6..;NQ;R3;
........232.57....9...827.......3....41...59....4.......216...4....97.816........;NQ;R3;
..28745...1......4.7.1..92.....97...............21.....43..1.7.8......5...65231..;NQ;R3;
5.9.2.3.........4..8.73..9.3.....7.4...913...2.1.....8.6..58.7..2.........5.9.6.1;NQ;R3;
.5......9.7..2..1.3.91.6.8.51...8...............7...34.8.4.95.1.9..6..2.6......7.;NQ;R3;
.....2.3....57.489......6..1..2..7.3..6.3.9..9.4..6..8..7......429.67....5.4.....;NQ;R3;
..823...4.........2....798.1.3.9287...........6957.1.2.846....1.........3...452..;HQ;R3;
1...93584.5...41.....5...3..3.........73.62.........1..1...5.....56...7.38412...5;NQ;R3;
.9...23.5..3...6......9..42.....6....178.429....2.....53..7......2...5..1.96...7.;NQ;R3;
1.4..268....7...3.........4..28.5.7.96..7..58.5.4.69..7.........8...9....196..8.5;NQ;R3;
4.3..82.1.7..4.........3...6.7....355.4.7.1.893....7.6...8.........5..8.2.84..3.7;NQ;R3;
..........3.4.87..8.7.5..3652...9.4....825....1.7...9578..3.1.4..91.6.7..........;NQ;R3;
4157.8...87.59......62.......96..1.............7..92.......67......17.42...4.2918;NQ;R3;
.9......54.397..1......6.......4.97...9.2.1...82.9.......3......5..183.73......4.;NQ;R3;
...........48...5..823.94...3.56..8..46.8.92..1..94.3...14.839..2...17...........;NQ;R3;
49.7....6..3.2..74.8..3..1......8.43.........37.6......3..8..6.52..1.7..8....7.51;NQ;R3;
81....6......9..12.....53...6893...7.........7...4892...47.....98..1......2....31;HQ;R3;
.......2...6..9..3.1.85.9...61.98.7.9.......4.4.62.81...5.71.3.7..3..6...3.......;NQ;R3;
....8.4.......5..3...6.387.9.8.57.....7...2.....16.7.9.435.8...5..7.......6.2....;NQ;C3;
....7....2.9..6..44..3.1.....5.....2..28679..1.....8.....7.2..15..9..2.3....5....;NQ;C3;
.5.3..9.4..8....3..1.2..5..2657.........9.........2758..2..6.7..9....8..3.1..9.6.;NQ;C3;
.9.215...2.........1376........92.4..2.....3..7.64........2861.........5...974.8.;NQ;C3;
......9..9.3...18..483........9.13.8..9.5.7..3.68.4........589..57...4.1..2......;NQ;C3;
...32....5..914.......753..8.....7.31.5...2.69.7.....8..159.......168..9....32...;NQ;C3;
1........75..8....93..25.......98.6...2.3.7...7.61.......45..71....6..84........3;NQ;B3;
.....7..36..23..9........629..5..4...189.462...5..8..953........4..59..61..4.....;NQ;B3;
71...3.....6598...9..7.....8.4...25...9...6...21...7.3.....4..8...1529.....6...12;NQ;B3;
64.......3..51......943...82......4..36...97..7......29...471......83..4.......86;NQ;B3;
...54.836.....19.....9...42......391.5.....8.893......14...8.....76.....268.14...;NQ;B3;
.8...569..2.9...81......52....491.7.....8.....9.357....16......97...8.1..346...5.;NQ;B3;
..4..7.3.21..3.57....14...9........8..7.6.1..5........1...84....82.7..15.7.9..6..;NQ;B3;
..8..6...4....2...2..9541...421....7.3.....2.1....354...5698..2...5....6...3..8..;NQ;B3*;
..637.5........74......5.61.3.4..15....526....85..3.7.89.6......63........7.382..;NQ;B3*;
.4.....6.....8..317.134.5......62.....74153.....83......4.538.939..7.....1.....4.;NQ;B3*;
...14...7.....85....5...48...97..1...6741295...4..96...56...8....13.....4...21...;NQ;B3*;
3....9.......85....6......7..24..9.84...7...21.3..26..9......3....25.......9....4;NQ;B3*;
56.........73..8.4..9..1......75.....1.623.4.....19......4..7..3.1..82.........89;NQ;B3*;
....79.....9.1.38.1.56....96........5.7.6.1.2........42....78.3.13.2.5.....85....;NQ;B3*;
.82.4.6.13.7............2...25.94...9...8...6...32.91...9............1.92.8.1.46.;NQ;B3*;
.......387........682.1...7..796541.....3.....514723..4...9.573........952.......;NQ;B3*;
....4.6....1..2.47......3.54.8.79......528......31.2.82.7......38.2..9....9.3....;NQ;B3*;
3...8.6...67.14.....9......5...264....8...3....684...5......2.....93.57...3.6...8;NQ;B3*;
..719...6831........6.23.........8..91..5..27..4.........51.9........7543...721..;NQ;B3*;
7.........3...98....657.....82.93...4...8...3...65.21.....651....47...5.........9;NQ;B3*;
........7.....816...8.24..9.94..63.5.........1.52..74.2..63.8...735.....5........;NQ;B3*;
Update: Typo fixed
- Alpxcx
- Posts: 25
- Joined: 09 December 2022
by Alpxcx » Mon Dec 12, 2022 11:52 pm
The further apart the clues, the harder to find. Also, the more areas a chain is made across, the harder to find.
Look at these two examples:
They are both a dynamic contradiction chain, but think of the graphical difference. It's stunning.
Do you think they should be rated the same? Seriously.
In my point of view, the second one is meaningless. Even though it can be found by a machine, it's never going to be found by a human without machines. It's more like brute force. Therefore, it needs an elevated rating.
p.s. I'm trying to figure out how to send images on this forum. If you can't see the images, I will update them.
Look at these two examples:
They are both a dynamic contradiction chain, but think of the graphical difference. It's stunning.
Do you think they should be rated the same? Seriously.
In my point of view, the second one is meaningless. Even though it can be found by a machine, it's never going to be found by a human without machines. It's more like brute force. Therefore, it needs an elevated rating.
p.s. I'm trying to figure out how to send images on this forum. If you can't see the images, I will update them.
- Alpxcx
- Posts: 25
- Joined: 09 December 2022
by Alpxcx » Tue Dec 13, 2022 9:59 pm
Here is my result from the first 48 puzzles in g162_ep54.txt:
- Code: Select all
.....1.23...2..45.....6.1.7.3.6.82....4..3...6..59.....439....298.......1.2...9..;HQ;B2;
.....1.23...2..45.....6.7.1.5.1.23....8..5...1..47.....239....498.......4.5...9..;HQ;B2;
.....1.23...3..45.....6.7.1.5.2.83....2..6...1..49.....239....598.......7.5...9..;HQ;B2;
.....1.23...3..45.....6.1.7.5.2.83....2..6...7..49.....239....598.......1.5...9..;HQ;B2;
.....1.23...2..45.....6.1.7.5.8.23....8..6...7..39.....739....298.......4.5...9..;HQ;B2;
.....1.23...4..51.....3.6.4.7.8.64....8..3...9..57.....876....254.......2.6...8..;HQ;B2;
.....1.23...4..51.....3.6.4.7.6.48....5..8...2..51.....618....942.......8.7...3..;HQ;B2;
.....1.23...4..51.....3.6.4.2.7.64....7..3...8..59.....486....297.......1.2...7..;HQ;B2;
.....1.23...4..51.....3.6.4.2.7.64....6..2...8..54.....746....116.......3.2...7..;HQ;B2;
.....1.23...4..51.....3.6.4.2.6.47....5..7...7..58.....427....695.......1.6...2..;HQ;B2;
.....1.23...4..51.....3.4.6.7.6.48....5..8...9..57.....478....969.......8.3...6..;HQ;B2;
.....1.23...4..51.....3.4.6.2.7.46....7..8...9..52.....746....959.......8.2...7..;HQ;B2;
.....1.23...4..51.....3.4.6.2.7.46....7..3...8..62.....725....498.......5.6...7..;HQ;B2;
.....1.23...4..51.....3.4.6.2.7.46....7..3...8..59.....746....118.......5.2...7..;HQ;B2;
.....1.23...4..51.....3.4.6.2.5.46....7..8...9..72.....746....939.......5.2...7..;HQ;B2;
.....1.23...4..51.....2.6.4.3.7.64....7..8...9..53.....736....116.......8.4...7..;HQ;B2;
.....1.23...4..51.....2.6.4.3.7.64....7..3...8..51.....786....554.......9.3...7..;HQ;B2;
.....1.23...4..51.....2.6.4.3.7.64....7..2...8..53.....436....857.......1.8...7..;HQ;B2;
.....1.23...4..51.....2.4.6.6.5.37....8..6...9..78.....376....589.......4.6...2..;HQ;B2;
.....1.23...4..51.....2.4.6.5.7.63....8..4...9..53.....756....949.......8.3...7..;HQ;B2;
.....1.23...4..51.....2.4.6.3.7.46....7..8...9..53.....746....559.......8.3...7..;HQ;B2;
.....1.23...4..51.....2.4.6.3.7.46....7..8...8..69.....765....458.......9.3...7..;HQ;B2;
.....1.23...4..51.....2.4.6.3.7.46....7..2...8..53.....436....857.......1.8...7..;HQ;B2;
.....1.23...4..15.....5.6.4.7.6.48....2..9...9..17.....478....669.......8.1...5..;HQ;B2;
.....1.23...4..15.....5.6.4.7.5.63....8..2...9..71.....376....549.......8.6...7..;HQ;B2;
.....1.23...4..15.....5.6.4.7.5.62....8..9...9..74.....276....589.......4.6...7..;HQ;B2;
.....1.23...4..15.....5.6.4.6.5.37....8..4...9..72.....376....589.......1.6...2..;HQ;B2;
.....1.23...4..15.....5.6.4.6.5.27....8..4...9..73.....276....589.......1.6...2..;HQ;B2;
.....1.23...4..15.....5.6.4.6.5.27....8..4...9..63.....267....589.......1.7...4..;HQ;B2;
.....1.23...4..15.....5.6.4.6.3.57....8..2...9..68.....367....589.......4.7...3..;HQ;B2;
.....1.23...4..15.....5.6.4.2.6.47....3..8...8..59.....417....268.......7.2...5..;HQ;B2;
.....1.23...4..15.....5.4.6.7.5.63....8..2...9..71.....376....449.......8.5...7..;HQ;B2;
.....1.23...4..15.....5.4.6.6.5.78....9..4...3..69.....768....513.......9.8...3..;HQ;B2;
.....1.23...4..15.....3.6.4.7.6.48....9..8...2..59.....478....662.......8.1...2..;HQ;B2;
.....1.23...4..15.....3.6.4.7.6.48....9..8...2..57.....238....146.......8.7...2..;HQ;B2;
.....1.23...4..15.....3.6.4.2.7.64....7..2...1..58.....746....196.......8.2...7..;HQ;B2;
.....1.23...4..15.....3.6.4.2.6.47....8..7...9..58.....427....969.......7.3...2..;HQ;B2;
.....1.23...4..15.....3.4.6.2.6.47....8..3...9..58.....627....489.......5.7...6..;HQ;B2;
.....1.23...4..15.....2.4.6.7.6.48....9..8...3..59.....378....146.......8.1...3..;HQ;B2;
.....1.23...4..15.....2.4.6.7.5.43....8..9...9..71.....976....483.......6.5...7..;HQ;B2;
.....1.23...4..15.....2.4.6.6.7.43....8..9...9..61.....935....487.......5.6...7..;HQ;B2;
.....1.23...4..15.....2.4.6.6.7.43....8..9...9..61.....735....489.......5.6...7..;HQ;B2;
.....1.23...4..15.....2.4.6.6.5.78....9..2...3..69.....368....517.......9.8...3..;HQ;B2;
.....1.23...4..15.....2.4.6.5.7.43....8..9...9..53.....936....487.......6.5...7..;HQ;B2;
.....1.23...4..15.....2.4.6.3.5.46....7..2...8..73.....836....597.......5.4...7..;HQ;B2;
.....1.23...3..41.....5.6.7.4.2.53....7..8...9..43.....935....265.......7.4...8..;HQ;B2;
.....1.23...3..14.....5.6.7.4.2.83....6..5...5..43.....536....218.......6.4...9..;HQ;B2;
.....1.23...3..14.....5.6.7.4.2.53....6..8...8..43.....835....215.......6.4...9..;HQ;B2;
I have tried to randomly pick up other puzzles from the text, but I got 10 same results. I would say the puzzle generating algorithm used by SudokuExplainer was nonsense as well, because it was very ordered instead of being random. Statistics won't mean anything here because the sample was very biased.
- Alpxcx
- Posts: 25
- Joined: 09 December 2022
by Alpxcx » Tue Dec 13, 2022 11:33 pm
I'm running a test with only hidden quads this time.
In rows/columns:
Case 1: 30/66 (45.5%)
Case 2: 27/66 (40.9%)
Case 3: 9/66 (13.6%)
In blocks:
Case 1: 13/50 (26%)
Case 2: 36/50 (72%)
Case 3: 1/50 (2%)
Here is my data:
It seems that naked quads and hidden quads are different in the ferquency of cases. It does make sense, if you treat these hidden quads as naked quintets. Then block case 2 can be seen as case 1 (cross distribution).
Well, my previous comment wasn't completely correct. Tests are quite crucial here.
In rows/columns:
Case 1: 30/66 (45.5%)
Case 2: 27/66 (40.9%)
Case 3: 9/66 (13.6%)
In blocks:
Case 1: 13/50 (26%)
Case 2: 36/50 (72%)
Case 3: 1/50 (2%)
Here is my data:
- Code: Select all
.72..385.....2574.........1....1867...........4126....8.........6389.....576..98.;HQ;R1;
..........5..9.16.9.67.153..19.....63.......24.....75..483.76.5.95.4..2..........;HQ;R1;
9.2..73.118..3.6.5.............68...3..5.2..4...94.............6.4.2..972.57..1.6;NQ;B1;HQ;R1;
5.71...82269..31............51.378.............294.35............83..51779...16.8;HQ;R1;
......3.62......8.4...5321.5.698...2.........8...367.5.2874...9.4......19.1......;HQ;R1;
4....27.95976..2.............94...15...9.3...71...59.............8..16476.35....8;HQ;R1;
24..67..1163.5.............71......8.54.7.12.6......94.............2.9155..39..42;HQ;R1;
43.5.........9.32..12..7..4.83.....6.........2.....71.8..3..69..56.7.........4.52;HQ;R1;
4.65...2..93...86.............7...4.98.6.4.57.3...8.............69...43..4...96.1;HQ;R1;
6....82...831.....4...5...8.9.6.45.............72.5.4.9...4...5.....762...63....7;HQ;R1;
8264..3.1......4......652.7....5987...........3874....9.217......7......1.3..8746;HQ;R1;
.725..3.1..............472.54.83......3.9.6......75.13.176..............8.9..157.;HQ;R1;
..56.1..7...3...4...8.2...55.1..6.9...........6.5..4.86...9.3...7...3...9..1.82..;HQ;R1;
.2...4..3..79.....9..7..61..15...9.2.........7.4...86..53..7..6.....52..6..8...5.;HQ;R1;
...........67.945..19..6...13...5..7..8.2.3..9..8...46...1..28..623.89...........;HQ;R1;
..........14.58..635.4......9..2...1..3...7..7...1..9......2.655..73.91..........;HQ;R1;
..14.8..7...........9637.8........73...249...86........5.1832...........4..7.29..;HQ;R1;
78...3.5..9....1...351...96..639.2.............8.213..84...962...9....8..6.7...14;HQ;R1;
2......5...7.92...9.41..2...5..4.1.2.........6.9.3..7...8..59.1...36.8...9......3;HQ;R1;
.........3....76.9..683.42..5.4.2...9.2...8.6...1.6.4..17.289..2.93....5.........;HQ;R1;
.............8.23..34.9..16.8961...7...5.8...2...7918.12..6.47..97.4.............;HQ;R1;
3.45.2....2..........7.6..8.4.1....79..6.3..48....7.2.1..2.5..........6....9.18.5;HQ;C1;
...1....71.27..3.8....84.....6..7..9..5.6.1..3..9..8.....57....2.3..87.14....2...;HQ;C1;
4.6258.....1..76..9.......58.2.7.................3.1.82.......1..96..5.....7859.3;HQ;C1;
.897..23..67..381..............2.3...5.9.6.4...8.5..............328..57..76..142.;HQ;C1;
6.79.5..2..5...3.8.1....6.....1..9.....3.8.....3..4.....4....1.5.2...7..9..4.38.6;HQ;C1;
..........4.83......64.581..8..6937...2...6...3957..2..546.27......13.8..........;HQ;C1;
5.28....9..37....1.416.......93....8.2.....3.4....91.......789.2....36..3....65.7;HQ;C1;
.6.8.7.494.7..38...2...61..718.....................517..23...8...56..4.218.2.9.5.;HQ;C1;
1.25..73..3.......9.68........4..89.2.4...1.5.97..2........59.7.......4..79..82.6;HQ;C1;
..........53..281.82.....4...845...33..2.7..15...314...7.....26.891..53..........;HQ;R2;
1.9..48...........624...91....6.5...7.5.1.2.8...4.2....32...579...........19..4.2;HQ;R2;
.2....397....6984............217.4...1.982.5...7.362............9485....135....8.;HQ;R2;
...........517.3....45.67.28....2..7..6...2..3..9....44.18.96....2.615...........;HQ;R2;
726.531..1.86...............51..9..3....6....3..4..21...............84.7..453.896;HQ;R2;
........1..6.9.328259...74..3.75.................26.7..71...564425.6.8..9........;HQ;R2;
..2.......89..165.....93.8.7.49...2...........3...45.8.4.17.....276..94.......1..;HQ;R2;
26..8.5..5.31...279......3.8...59...............67...8.8......479...56.2..2.6..75;HQ;R2;
.........2..5896.35..6.7.1......4.97....9....95.2......7.4.6..16.4931..2.........;HQ;R2;
.8.4...2.247.85.1..............283..32..9..75..976..............9.84.136.3...7.8.;HQ;R2;
.85.3.......76.2.87....8....2.41.9.............4.27.3....2....76.9.84.......7.86.;HQ;R2;
5....49.7...5..4.6..8.1.5..9...458.............739...4..4.6.3..2.5..3...6.39....2;HQ;R2;
...........48.6.5217......6.652.3..4....8....8..5.129.3......2949.3.27...........;HQ;R2;
............83652...8.5.14...17....437..2..819....83...59.8.6...23165............;HQ;R2;
5...2..93..849.15...........7...6...1...4...9...3...8...........61.327..38..7...2;HQ;R2;
6.9.8..7.32.5................53.1.4...72483...8.6.59................4.69.1..5.4.2;HQ;R2;
...2.......19.38....3.6.29..126.93.............67.254..98.7.4....74.61.......5...;HQ;R2;
.....43.7.932..........825...6....8...85.17...4....1...716..........251.3.41.....;HQ;C2;
31.5..4...6...9...4.5...........628.6..1.2..9.278...........3.6...7...2...8..3.41;HQ;C2;
94...6.5.1..35..62........7.....7.1....682....3.1.....2........76..41..5.9.8...26;HQ;C2;
1.........9...3..46.38..7.1..12.58.............74.86..3.8..64.22..5...7.........5;HQ;C2;
.....1.2..164.28.........961..2..6....95.82....8..6..374.........28.473..9.3.....;HQ;C2;
.......2362.1...4..8...4..6....42.6....891....3.75....9..2...1..6...3.5285.......;HQ;C2;
34.6.1.9.5...7..1..7...5.......92.64.........81.46.......7...3..8..1...6.6.3.8.29;HQ;C2;
...8.1..61..5...3.5....4.28.....5.4.6...8...1.1.4.....23.7....4.7...8..24..3.9...;HQ;C2;
..47..62..7...5....8124.....6.1..7......5......3..7.6.....2437....8...9..28..15..;HQ;C2;
81..6..327...1..6.3..5..........9.7.9...2...1.7.8..........5..6.2..7...815..4..27;HQ;C2;
...8....6....213.....69.1...61...4.583..5..615.7...23...2.39.....416....7....8...;HQ;B1;
3.85.7.1.9.......6.4.68.2.....17.......9.2.......56.....9.43.7.7.......2.2.7.58.9;HQ;B1;
.8..49...47..6......27.......54..318...6.1...817..36.......65......3..89...52..7.;HQ;B1;
34.69....6...2.....71..3...136....2.4.......9.5....186...2..37.....4...5....75.68;HQ;B1;
1.842.3....315...4.7.............9.3.6.....5.5.2.............4.7...135....1.462.7;HQ;B1;
..7......21.....6.5.....8.9.6.39.7.....628.....3.45.9.9.8.....2.3.....41......9..;HQ;B1;
5..937..4..7.6.5...6.1..7...25....9.1.......7.8....45...6..9.4...8.1.9..9..842..6;HQ;B1;
....2.7489....7.1.7..6.......1......4.5...3.6......8.......8..4.7.9....3128.3....;HQ;B1;
4..2.........75....938......76.4...91...9...72...5.61......172....56.........3..8;HQ;B1;
2....3.866...8.1.....6.27...1....2..34.....71..8....4...39.1.....5.7...476.3....5;HQ;B1;
.....7365...2.9.18....6...........3756.....4921...........9....47.8.1...1853.....;HQ;B1;
19.5......68943........6...827...9..5.......7..6...253...1........72813......4.95;HQ;B1;
7...5..98..98.2..56..9...........8..5.1...2.4..3...........7..28..1.57..14..8...9;HQ;B1;
.7..25.4...87.6.3.564.......89.....4.........7.....92.......865.4.5.13...2.39..1.;HQ;B2;
87.........39.....129.5.....913.4.2..4..7..1..8.1.579.....3.287.....86.........51;HQ;B2;
1..5.9...73.......6.9.3........1275.2.......6.7498........2.3.9.......45...8.1..7;HQ;B2;
...32...6.....49.......9..85.4..3.828...1...732.5..4.12..9.......51.....7...86...;HQ;B2;
........2..34...6.....9683..15.749.............935.17..6124.....9...74..8........;HQ;R2;
76..9.1....15.........36..2.4.....8.8.9...3.5.7.....1.9..68.........45....2.5..34;HQ;B2;
6472...5...93..........72...9.....2876.....4381.....9...15..........39...2...4876;HQ;B2;
...19.74...57.....9....6...37....4.6.........2.1....57...4....9.....21...98.35...;HQ;B2;
....8.6.4...5.729....2......84.9.7..2.6.3.8.9..3.2.46......3....394.8...4.5.7....;HQ;B2;
...8..3.5.5.6.....2...759....6...4.1..5...2..8.3...7....175...9.....8.4.6.7..9...;HQ;B2;
.....82.......76.5...63...159.....4...73.59...3.....721...42...9.87.......35.....;HQ;B2;
..394....56.........97.6...4.....95..8..6..1..57.....4...4.18.........73....851..;HQ;B2;
8592.....1..6..........5......5..36..72.1.54..68..3......4..........9..2.....8175;HQ;B2;
...7261..........2....5.79..296....8..7.4.2..4....935..16.9....3..........4832...;HQ;B2;
....24.5.......17......9.46..2.5..68...891...38..6.7..79.3......25.......6.21....;HQ;B2;
.5.........1.32...3.94.5.....834...5.43.7.62.7...218.....9.43.8...28.7.........1.;HQ;B2;
614........346.....8...1........984..7.314.5..958........1...8.....236........532;HQ;B2;
15..29.7.87....9....27.............94.9...6.12.............48....5....96.8.23..57;HQ;B2;
95..6.....76..4....143............12.98...73.62............264....1..38.....9..51;HQ;B2;
.1.49.....9...5...7.8.62.....2..87.5.........1.93..8.....92.1.6...5...7.....46.3.;HQ;B2;
6........7.956......1.87.4.1.....5...95...37...3.....2.7.83.6......217.5........4;HQ;B2;
2.1387....9.5.......7........3.7..467.2...3.948..1.7........5.......8.6....4391.8;HQ;B2;
.1.896............6.4.32.5.1.3....9.5.......4.2....6.7.9.25.8.1............713.2.;HQ;B2;
.1...9...9638.......2.6........547.153..9..844.138........2.8.......3527...7...9.;HQ;B2;
....793.....61.8.....4....9..9.4...3.47...56.5...2.9..7....5.....8.61.....398....;HQ;B2;
.....6.1....9..6.4....57..8.826..7....9...3....4..518.5..74....2.7..1....6.5.....;HQ;B2;
...15.4.3....4.8.1.....79.....56..47...7.2...25..14.....89.....1.3.2....6.5.81...;HQ;B2;
.....589....42..6.......2.7.697.....8.5.1.9.3.....461.4.7.......9..87....389.....;HQ;B2;
.........5.3.6....1283......3.6.9..76...4...24..1.8.9......4685....5.7.9.........;HQ;B2;
..4652...........9.5..19.6.......9.351.....869.3.......8.46..5.7...........2873..;HQ;B2;
.6..4.3.9..431..5..9.........7.....4.43...21.2.....8.........2..3..214..9.2.3..6.;HQ;B2;
...1.........82.1.....542.62.85..76...4...3...37..85.29.341.....7.36.........9...;HQ;B2;
..9.7.....1482....8.........8.39.51...25.68...65.18.9.........9....8723.....6.1..;HQ;B2;
7...25.9.9.83.41...3.1...........41.2.3...7.9.89...........3.4...64.85.7.7.95...1;HQ;B2;
3.79.1...4.2.83....5.2.......5...6.3....4....6.8...2.......7.5....62.3.1...1.89.6;HQ;B2;
5..427.....6.......98..1.....5....471.4...3.823....5.....9..48.......6.....738..2;HQ;B2;
.........26.....143.7..5...5...8324.62.1.7.58.8352...9...8..9.575.....21.........;HQ;R3;
.3...1...2...839....46.2..576.....9...........8.....129..2.68....739...6...7...2.;HQ;R3;
1.59.8.4...2..4.3.........6..7.932.............156.8..8.........2.7..6...7.2.63.9;HQ;R3;
.2..6..1..63..48..8.4.3....7..4..3.............2..3..1....7.6.8..81..79..7..2..5.;HQ;R3;
1...45.38.3....6.....3..21...67.34.............72.85...93..6.....5....2.26.83...5;HQ;R3;
.5.6.3.7989.4...5...6.2..........34...........18..........4.5...7...9.3463.1.7.8.;HQ;R3;
6.9..7.3.8..3...2.2...8419.......45...........91.......8412...3.6...5..7.5.4..2.8;HQ;R3;
1..5.38...5.8..3.1.4.......2.5....39.9.....1.86....4.5.......4.5.6..1.2...47.2..6;HQ;C3;
..........72..34.1.6...47..816....4.3.7...6.2.5....138..59...1.6.18..35..........;HQ;C3;
6.789......5......1..7.6...48.6.......9.5.4.......3.82...1.9..7......3......875.6;HQ;B3;
It seems that naked quads and hidden quads are different in the ferquency of cases. It does make sense, if you treat these hidden quads as naked quintets. Then block case 2 can be seen as case 1 (cross distribution).
Well, my previous comment wasn't completely correct. Tests are quite crucial here.
- Alpxcx
- Posts: 25
- Joined: 09 December 2022
by Pat » Wed Dec 14, 2022 5:21 am
- "Hidden Quad" come from various sources...
and probably not random
-
Pat - Posts: 4056
- Joined: 18 July 2005
by Alpxcx » Wed Dec 14, 2022 10:10 pm
Pat wrote:"Hidden Quad" come from various sources...
here was my attempt to restrict the difficulty
and probably not random
I just tried that, and there was no much difference. Sadly it wan't a random set of data for this statistical research.
Well, if there really isn't a set of data existing for my test, nor is existing script, it's not a big problem now.
If we calculate the confidence interval on an online calculator (such as https://www.mathsisfun.com/data/confidence-interval-calculator.html), we can see my previous manual dataset was actually accurate, at least close to what it should be.
It was already enough for my conclusion on "cases".
If at some point a larger sample is needed for better accuracy, I could write the codes. It's nothing urgent, I suppose.
- Alpxcx
- Posts: 25
- Joined: 09 December 2022
by Alpxcx » Thu Dec 15, 2022 10:06 pm
There is something more I wanted to say.
Most authors of those manual-solving simulation software make a common mistake.
They list simple techniques and tough techniques and put them in order, so they can scan puzzles technique-by-technique.
This is the easiest way to write codes, but they didn't realise things.
Sometimes an intermediate step (or multiple steps) can be skipped. Those steps are not the appliance of the hardest techniques used on each of the puzzles, but removing them don't affect the validity of all following steps.
Obviously, removing them do decrease the rating of those puzzles.
Did you get what I meant? Because it weren't the hardest techniques applied, they didn't care.
I have seen a lot of these cases, but I will just list some simple examples today:
72..96..3...2.5....8...4.2........6.1.65.38.7.4........3.8...9....7.2...2..43..18
Which is the example used by SudokuWiki for "Moderate".
Here are the solution paths on some solvers, at the time of this post:
SudokuWiki: Singles, Naked Triple, Hidden Single, Hiddle Pair (89r8c13), stte
SudokuExplainer (DiufSudoku): Singles, Direct Hiddle Pair/Hiddle Pair (89r8c13), stte
HoDoKu: Singles, Naked Triple, ..., Locked Candidates, stte
YZF_Sudoku625: Same with HoDoKu
The shortest path was the one SudokuExplainer gave us. Well, it wasn't because it was better, but they put hidden pairs more priotised.
Let's forget the priority thing for now and look at what SudokuWiki did.
SudokuWiki number the techniques they use and scan techniques in order of their corresponding number. It's not difficult to see this when you look at their solving page, even if you don't know how to program.
In this example, they scan naked triples first, then hidden pairs, and put both in the solution path. When we ignore the priority, we can see the biggest problem here, as applying the naked triple didn't avoid the hidden pair being applied. However, when the naked triple is removed, the hidden pair is still valid. When we only apply the hidden pair, it's still single-to-the-end! We know it works as SudokuExplainer did it in this way.
They do came with a rating system as well. The naked triple as an unnecessary step on the solution path increases the rating when it shouldn't! This generally decreases the credibility of the whole rating system.
You may be wondering why I said it was a common mistake when I only talked about SudokuWiki. Okay, there are enough words on SudokuWiki now.
Let's look at another example:
2....7..8.4.........91.5.2...5.93..2..28..5.9.....1.3..3...2.7.7...8...5..17.....
Here are the solution paths on some solvers, at the time of this post:
SudokuWiki: Singles, Pointing Pairs (Pointing), X-Wing, Naked Triple, Simple Colouring (on 7), stte
SudokuExplainer (DiufSudoku): Singles, Pointing, X-Wing, Hidden Pair, Two String Kite (on 7), stte
HoDoKu: Singles, Locked Candidates, X-Wing, Naked Triple, Skyscraper (on 7), stte
YZF_Sudoku625: Singles, Locked Candidates, X-Wing, Hidden Pair, Sashimi X-Wing (on 7), stte
Now Let's paste the text again into these solvers, and start again. After all the initial singles, we stop. Did you find why I emphasise "on 7" inside the brackets? We are going to find out anyway.
Now, apply any substraction among 7r3c2, 7r4c7 and 7r6c3. Did you see what happened? Wow, single-to-the-end!
The real thing is, the solution path can be expressed as: Singles, Two String Kite/Skyscraper/Sashimi X-Wing (on 7, whichever would work), stte
So, what's wrong with all these unnecessary steps? We need an exclamation mark here! They just destroy the whole rating system!
Let's look back again. The hidden pair, which can be expressed as 68r67c7, was dependent on the X-Wing (8r67c37)! How was this hidden pair better to observe than a general Two String Kite/Skyscraper? I would say no.
In my point of view, writing this kind of dependency-detection algorithm isn't rocket science. There are at least two ways of implementation:
1. Scan a few techniques further on each step, if a "higher" technique can be detected with substraction of candidates, then mark it. If the technique is used later, then go back and only apply this technique. If the puzzle rating gets decreased, then apply this technique at an earlier stage.
2. Add substraction of candidates done by simpler techniques back when a "higher" technique is applied. If the technique is still valid and decrease the puzzle rating, then apply this technique at an earlier stage.
Most authors of those manual-solving simulation software make a common mistake.
They list simple techniques and tough techniques and put them in order, so they can scan puzzles technique-by-technique.
This is the easiest way to write codes, but they didn't realise things.
Sometimes an intermediate step (or multiple steps) can be skipped. Those steps are not the appliance of the hardest techniques used on each of the puzzles, but removing them don't affect the validity of all following steps.
Obviously, removing them do decrease the rating of those puzzles.
Did you get what I meant? Because it weren't the hardest techniques applied, they didn't care.
I have seen a lot of these cases, but I will just list some simple examples today:
72..96..3...2.5....8...4.2........6.1.65.38.7.4........3.8...9....7.2...2..43..18
Which is the example used by SudokuWiki for "Moderate".
Here are the solution paths on some solvers, at the time of this post:
SudokuWiki: Singles, Naked Triple, Hidden Single, Hiddle Pair (89r8c13), stte
SudokuExplainer (DiufSudoku): Singles, Direct Hiddle Pair/Hiddle Pair (89r8c13), stte
HoDoKu: Singles, Naked Triple, ..., Locked Candidates, stte
YZF_Sudoku625: Same with HoDoKu
The shortest path was the one SudokuExplainer gave us. Well, it wasn't because it was better, but they put hidden pairs more priotised.
Let's forget the priority thing for now and look at what SudokuWiki did.
SudokuWiki number the techniques they use and scan techniques in order of their corresponding number. It's not difficult to see this when you look at their solving page, even if you don't know how to program.
In this example, they scan naked triples first, then hidden pairs, and put both in the solution path. When we ignore the priority, we can see the biggest problem here, as applying the naked triple didn't avoid the hidden pair being applied. However, when the naked triple is removed, the hidden pair is still valid. When we only apply the hidden pair, it's still single-to-the-end! We know it works as SudokuExplainer did it in this way.
They do came with a rating system as well. The naked triple as an unnecessary step on the solution path increases the rating when it shouldn't! This generally decreases the credibility of the whole rating system.
You may be wondering why I said it was a common mistake when I only talked about SudokuWiki. Okay, there are enough words on SudokuWiki now.
Let's look at another example:
2....7..8.4.........91.5.2...5.93..2..28..5.9.....1.3..3...2.7.7...8...5..17.....
Here are the solution paths on some solvers, at the time of this post:
SudokuWiki: Singles, Pointing Pairs (Pointing), X-Wing, Naked Triple, Simple Colouring (on 7), stte
SudokuExplainer (DiufSudoku): Singles, Pointing, X-Wing, Hidden Pair, Two String Kite (on 7), stte
HoDoKu: Singles, Locked Candidates, X-Wing, Naked Triple, Skyscraper (on 7), stte
YZF_Sudoku625: Singles, Locked Candidates, X-Wing, Hidden Pair, Sashimi X-Wing (on 7), stte
Now Let's paste the text again into these solvers, and start again. After all the initial singles, we stop. Did you find why I emphasise "on 7" inside the brackets? We are going to find out anyway.
Now, apply any substraction among 7r3c2, 7r4c7 and 7r6c3. Did you see what happened? Wow, single-to-the-end!
The real thing is, the solution path can be expressed as: Singles, Two String Kite/Skyscraper/Sashimi X-Wing (on 7, whichever would work), stte
So, what's wrong with all these unnecessary steps? We need an exclamation mark here! They just destroy the whole rating system!
Let's look back again. The hidden pair, which can be expressed as 68r67c7, was dependent on the X-Wing (8r67c37)! How was this hidden pair better to observe than a general Two String Kite/Skyscraper? I would say no.
In my point of view, writing this kind of dependency-detection algorithm isn't rocket science. There are at least two ways of implementation:
1. Scan a few techniques further on each step, if a "higher" technique can be detected with substraction of candidates, then mark it. If the technique is used later, then go back and only apply this technique. If the puzzle rating gets decreased, then apply this technique at an earlier stage.
2. Add substraction of candidates done by simpler techniques back when a "higher" technique is applied. If the technique is still valid and decrease the puzzle rating, then apply this technique at an earlier stage.
- Alpxcx
- Posts: 25
- Joined: 09 December 2022
Re: Extended SE ratings
by eleven » Thu Dec 15, 2022 10:18 pm
Alpxcx wrote:I have been interested in manual-solving simulation software for so long.
Recently, I viewed some parts of the SudokuExplainer rating system. Then I found something which could be optimised.
Pat's first puzzle is a good sample, that ratings basically are often subjectively bad.
It is rated after the "hardest step" hidden quad, but this is easy to spot:
- Code: Select all
+---------+---------+---------+
| . . . | . . 1 | . . . |
| . 2 9 | . *3 . | 4 . . |
| . . 4 | 5 *2 . | . 6 . |
+---------+---------+---------+
| . . 7 | x . x | . . . |
| . *6 *2 | . . . | *3 *8 . |
| 9 . . | x . x | 2 . . |
+---------+---------+---------+
| . 8 . | . *6 3 | 5 . . |
| . . 5 | . *8 . | . 4 . |
| 7 . . | 9 . . | . . . |
+---------+---------+---------+
9r8c2,1r7c3
quad 2368 b5
Then it could be solved this way, which is much harder to find:
hidden pair 45c6,9r3c6 (ok, can be directly spotted)
locked 2r9b9, NP79,
locked 7c6b3,r2b2,4r1c5
HP23c7,
(harder:)locked 7c5b5, HP79r5,NP79c9,9r1c7,7r3c7
Summary: It's a hard puzzle, not because of the quad, but because you still need 3 locked candidates and 4 pairs, which are harder to spot.
For me
- hidden subsets in most cases are easier to spot than naked ones
- a subset, which needs locked candidates to reveal it, is much harder to spot
- eleven
- Posts: 3164
- Joined: 10 February 2008
by Alpxcx » Thu Dec 15, 2022 10:27 pm
1to9only wrote:Been there. Done that. What you got?
On this topic, I would like to talk about my discoveries on relative algorithm. They are not about new manual techniques, but generally software improvement. At the moment, they are just ideas that I want to share, but not actual codes I can put. Probably there will be on the next year, but I won't make a promise here. You can look at what I commented if you are interested.
I wasn't trying to be rude by ingoring your comment. I'm still new to this forum and I was trying to explore how the functions work here.
Last edited by Alpxcx on Sat Dec 17, 2022 1:25 am, edited 1 time in total.
- Alpxcx
- Posts: 25
- Joined: 09 December 2022
Re: Extended SE ratings
by Alpxcx » Thu Dec 15, 2022 10:55 pm
eleven wrote:Alpxcx wrote:I have been interested in manual-solving simulation software for so long.
Recently, I viewed some parts of the SudokuExplainer rating system. Then I found something which could be optimised.
Pat's first puzzle is a good sample, that ratings basically are often subjectively bad.
...
For me
- hidden subsets in most cases are easier to spot than naked ones
- a subset, which needs locked candidates to reveal it, is much harder to spot
I agree with your conclusion here. A subset which you can find by just looking at given or solved cells is usually more friendly to a human.
If a subset is dependent on locked candidates, it would be harder, because you need to make more pencilmarks.
And even worse if they need tough techniques, because you may need to manually fill all candidates in.
If a rating system aims to reflect the real difficulty on a human view, all these should be considered.
- Alpxcx
- Posts: 25
- Joined: 09 December 2022
by Pat » Fri Dec 16, 2022 5:04 am
eleven wrote:
.....1....29.3.4....452..6...7.......62...38.9.....2...8..635....5.8..4.7..9.....
it is on the list
becuase it requires a Quad;
and yes, i put it at the top of my list
because it requires several more steps...
that's what makes it interesting
-
Pat - Posts: 4056
- Joined: 18 July 2005
42 posts
• Page 1 of 3 • 1, 2, 3
