Analysis of zz-www.sudokuoftheday.co.uk-20060827-absurd-base.sdk
Contents
Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Aug&YEAR=2006
level: medium
position: .1......98..5.92...974..5...8......3......4.5...7..19..68.....1..9.56..4...3.2... initial
Autosolve
position: .1......98..5.92...974..5...8......3......485...7..192.689..3.1..9.56..4...3.29.. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* PRF # A1: 3,4 => SOL * DIS # C1: 3,4 => CTR => C1: 2,5,6 * PRF # H2: 3,4 => SOL * DIS # B6: 3,4 => CTR => B6: 5 * PRF # H2: 3,4 => SOL * PRF # A1: 3,4 => SOL * DIS # C1: 3,4 => CTR => C1: 2,5,6 * DIS # G1: 8 => CTR => G1: 6,7 * DIS # I9: 8 => CTR => I9: 6,7 * PRF # H2: 4 => SOL * DIS # E3: 1,3 => CTR => E3: 2,6,8 * DIS # G1: 7 => CTR => G1: 6,8 * PRF # E3: 6,8 => SOL * DIS # I9: 7 => CTR => I9: 6,8 * DIS # D5: 1,2 => CTR => D5: 6 * DIS # E5: 1,2 => CTR => E5: 3,6,9 * PRF # A4: 1,2 => SOL * PRF # E5: 1,3 => SOL * DIS # A5: 1,3 => CTR => A5: 2,6,7,9 * DIS # F3: 8 => CTR => F3: 1,3 * DIS # G1: 8 => CTR => G1: 6,7 * DIS # A4: 2,5 => CTR => A4: 1,4,9 * DIS # E3: 1,8 => CTR => E3: 2,3,6 * DIS # I9: 7,8 => CTR => I9: 6 * DIS # G1: 7,8 => CTR => G1: 6 * DIS # A8: 2,7 => CTR => A8: 1,3 * CNT 26 HDP CHAINS / 63 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* PRF # A1: 3,4 => SOL * STA A1: 3,4 * CNT 1 HDP CHAINS / 1 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| .1......98..5.92...974..5...8......3......4.5...7..19..68.....1..9.56..4...3.2... | initial |
| .1......98..5.92...974..5...8......3......485...7..192.689..3.1..9.56..4...3.29.. | autosolve |
| 415827639836519247297463518184295763972631485653748192568974321329156874741382956 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (17) B2: 3,4 H1: 3,4 I2: 6,7 H3: 1,3 I3: 6,8 D4: 1,2 F5: 1,3 G4: 6,7 H4: 6,7 A7: 2,5 E7: 4,7 F7: 4,7 D8: 1,8 E9: 1,8 H7: 2,5 G8: 7,8 H8: 2,7 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) H2,H3: 1.. / H2 = 1 => 17 pairs (_) / H3 = 1 => 0 pairs (*) D8,E9: 1.. / D8 = 1 => 14 pairs (_) / E9 = 1 => 0 pairs (X) E2,H2: 1.. / E2 = 1 => 0 pairs (*) / H2 = 1 => 0 pairs (X) A8,D8: 1.. / A8 = 1 => 0 pairs (X) / D8 = 1 => 14 pairs (_) H7,H8: 2.. / H7 = 2 => 21 pairs (_) / H8 = 2 => 23 pairs (_) A3,E3: 2.. / A3 = 2 => 0 pairs (*) / E3 = 2 => 0 pairs (X) A7,H7: 2.. / A7 = 2 => 23 pairs (_) / H7 = 2 => 21 pairs (_) B5,B8: 2.. / B5 = 2 => 23 pairs (_) / B8 = 2 => 21 pairs (_) A8,B8: 3.. / A8 = 3 => 17 pairs (_) / B8 = 3 => 0 pairs (X) H1,H2: 4.. / H1 = 4 => 17 pairs (_) / H2 = 4 => 0 pairs (*) E7,F7: 4.. / E7 = 4 => 0 pairs (X) / F7 = 4 => 17 pairs (_) A1,C1: 5.. / A1 = 5 => 23 pairs (_) / C1 = 5 => 21 pairs (_) F4,F6: 5.. / F4 = 5 => 17 pairs (_) / F6 = 5 => 0 pairs (X) H7,H9: 5.. / H7 = 5 => 23 pairs (_) / H9 = 5 => 21 pairs (_) A7,H7: 5.. / A7 = 5 => 21 pairs (_) / H7 = 5 => 23 pairs (_) B6,B9: 5.. / B6 = 5 => 18 pairs (_) / B9 = 5 => 0 pairs (X) G4,H4: 6.. / G4 = 6 => 0 pairs (X) / H4 = 6 => 14 pairs (_) H9,I9: 6.. / H9 = 6 => 0 pairs (X) / I9 = 6 => 14 pairs (_) D1,D5: 6.. / D1 = 6 => 0 pairs (X) / D5 = 6 => 18 pairs (_) G1,G4: 6.. / G1 = 6 => 14 pairs (_) / G4 = 6 => 0 pairs (X) H4,H9: 6.. / H4 = 6 => 14 pairs (_) / H9 = 6 => 0 pairs (X) G1,I2: 7.. / G1 = 7 => 0 pairs (X) / I2 = 7 => 18 pairs (_) A5,B5: 7.. / A5 = 7 => 19 pairs (_) / B5 = 7 => 0 pairs (*) G4,H4: 7.. / G4 = 7 => 14 pairs (_) / H4 = 7 => 0 pairs (X) E7,F7: 7.. / E7 = 7 => 17 pairs (_) / F7 = 7 => 0 pairs (X) E2,I2: 7.. / E2 = 7 => 0 pairs (X) / I2 = 7 => 18 pairs (_) F1,F7: 7.. / F1 = 7 => 17 pairs (_) / F7 = 7 => 0 pairs (X) I2,I9: 7.. / I2 = 7 => 18 pairs (_) / I9 = 7 => 0 pairs (X) G1,I3: 8.. / G1 = 8 => 0 pairs (X) / I3 = 8 => 14 pairs (_) E6,F6: 8.. / E6 = 8 => 0 pairs (X) / F6 = 8 => 18 pairs (_) D8,E9: 8.. / D8 = 8 => 0 pairs (X) / E9 = 8 => 14 pairs (_) G8,I9: 8.. / G8 = 8 => 14 pairs (_) / I9 = 8 => 0 pairs (X) D8,G8: 8.. / D8 = 8 => 0 pairs (X) / G8 = 8 => 14 pairs (_) E9,I9: 8.. / E9 = 8 => 14 pairs (_) / I9 = 8 => 0 pairs (X) D1,D8: 8.. / D1 = 8 => 14 pairs (_) / D8 = 8 => 0 pairs (X) G1,G8: 8.. / G1 = 8 => 0 pairs (X) / G8 = 8 => 14 pairs (_) I3,I9: 8.. / I3 = 8 => 14 pairs (_) / I9 = 8 => 0 pairs (X) A4,A5: 9.. / A4 = 9 => 17 pairs (_) / A5 = 9 => 0 pairs (*) E4,E5: 9.. / E4 = 9 => 0 pairs (*) / E5 = 9 => 0 pairs (X) A4,E4: 9.. / A4 = 9 => 17 pairs (_) / E4 = 9 => 0 pairs (*) A5,E5: 9.. / A5 = 9 => 0 pairs (*) / E5 = 9 => 0 pairs (X) * DURATION: 0:00:51.851884 START: 02:07:09.312854 END: 02:08:01.164738 2019-05-01 * CP COUNT: (41) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A7,B2,D4,D8,E7,E9,F5,F7,G4,G8,H1,H3,H4,H7,H8,I2,I3) * .1......98..5.92...974..5...8......3......485...7..192.689..3.1..9.56..4...3.29.. * PAIR B2: 3,4 BLK 1 A1: 3,4,2,5,6 # reduction candidate for 3,4 A1: 3,4 => SOLVED * 415827639836519247297463518184295763972631485653748192568974321329156874741382956 A1: 2,5,6 # 17 pairs C1: 3,4,2,5,6 # reduction candidate for 3,4 C1: 3,4 => CTR * 51......98..5.92..2974..5...8......3......485...7..192.689..3.1..9.56..4...3.29.. C1: 2,5,6 # 17 pairs C2: 3,4,6 # reduction candidate for 3,4 C2: 3,4 # 19 pairs * PAIR B2: 3,4 ROW 2 H2: 3,4,1 # reduction candidate for 3,4 H2: 3,4 => SOLVED * 415827639836519247297463518184295763972631485653748192568974321329156874741382956 H2: 1 # 17 pairs * PAIR B2: 3,4 COL B B6: 3,4,5 # reduction candidate for 3,4 B6: 3,4 => CTR * 5128...498..5.92..69742.5.898.2....372.69.485...7.81922689..351379156824.5.3829.. B6: 5 # 18 pairs * PAIR H1: 3,4 BLK 3 H2: 3,4,1 # reduction candidate for 3,4 H2: 3,4 => SOLVED * 415827639836519247297463518184295763972631485653748192568974321329156874741382956 H2: 1 # 17 pairs * PAIR H1: 3,4 ROW 1 A1: 3,4,2,5,6 # reduction candidate for 3,4 A1: 3,4 => SOLVED * 415827639836519247297463518184295763972631485653748192568974321329156874741382956 A1: 2,5,6 # 17 pairs C1: 3,4,2,5,6 # reduction candidate for 3,4 C1: 3,4 => CTR * 51......98..5.92..2974..5...8......3......485...7..192.689..3.1..9.56..4...3.29.. C1: 2,5,6 # 17 pairs * PAIR I2: 6,7 BLK 3 G1: 6,7,8 # reduction candidate for 6,7 G1: 8 => CTR * .1....8.98..5.9217.974.1536.8....673.2...3485...7.81922689..3.1..9856724...312968 G1: 6,7 # 14 pairs * PAIR I2: 6,7 ROW 2 E2: 6,7,1,3 # reduction candidate for 6,7 E2: 1,3 # 20 pairs E2: 6,7 # 19 pairs * PAIR I2: 6,7 COL I I9: 6,7,8 # reduction candidate for 6,7 I9: 8 => CTR * .126..8.98465392173974..5.6.8....673.2....485...7..1922689..351.39856724.7.312968 I9: 6,7 # 14 pairs * PAIR H3: 1,3 BLK 3 H2: 1,3,4 # reduction candidate for 1,3 H2: 4 => SOLVED * 415827639836519247297463518184295763972631485653748192568974321329156874741382956 H2: 1,3 # 17 pairs * PAIR H3: 1,3 ROW 3 E3: 1,3,2,6,8 # reduction candidate for 1,3 E3: 1,3 => CTR * .1......98..5.92..2974..5.6.8....673......485...7..1925689..321..9.56..4...3.29.. E3: 2,6,8 # 17 pairs F3: 1,3,8 # reduction candidate for 1,3 F3: 1,3 # 21 pairs * PAIR I3: 6,8 BLK 3 G1: 6,8,7 # reduction candidate for 6,8 G1: 7 => CTR * .1.8.37498..579216.974.1538.8....673......485...7..192.689473.1..9.56824...382967 G1: 6,8 # 18 pairs * PAIR I3: 6,8 ROW 3 E3: 6,8,1,2,3 # reduction candidate for 6,8 E3: 6,8 => SOLVED * 415827639836519247297463518184295763972631485653748192568974321329156874741382956 E3: 1,2,3 # 17 pairs * PAIR I3: 6,8 COL I I9: 6,8,7 # reduction candidate for 6,8 I9: 7 => CTR * .1.8..7.98..579216.974..538.8....673...6..485...7.8192.689473.1..9.568.4...382967 I9: 6,8 # 18 pairs * PAIR D4: 1,2 BLK 5 E4: 1,2,4,9 # reduction candidate for 1,2 E4: 1,2 # 23 pairs D5: 1,2,6 # reduction candidate for 1,2 D5: 1,2 => CTR * .1.6..8.98..5.9217.974.1536.8....673.2.1.3485...7.81922689..3.1..9856724...312968 D5: 6 # 18 pairs E5: 1,2,3,6,9 # reduction candidate for 1,2 E5: 1,2 => CTR * 41582763983.5.92.7.974..5.818.295763972613485.53748192568974321329156874741382956 E5: 3,6,9 # 17 pairs * PAIR D4: 1,2 ROW 4 A4: 1,2,4,5,9 # reduction candidate for 1,2 A4: 1,2 => SOLVED * 415827639836519247297463518184295763972631485653748192568974321329156874741382956 A4: 4,5,9 # 17 pairs C4: 1,2,4,5 # reduction candidate for 1,2 C4: 1,2 # 20 pairs * PAIR F5: 1,3 BLK 5 E5: 1,3,2,6,9 # reduction candidate for 1,3 E5: 1,3 => SOLVED * 415827639836519247297463518184295763972631485653748192568974321329156874741382956 E5: 2,6,9 # 17 pairs * PAIR F5: 1,3 ROW 5 A5: 1,3,2,6,7,9 # reduction candidate for 1,3 A5: 1,3 => CTR * 4158276398365192.7.974..5.898.2.5763172693485.53748192568974321329156874741382956 A5: 2,6,7,9 # 17 pairs C5: 1,3,2,6 # reduction candidate for 1,3 C5: 1,3 # 20 pairs * PAIR F5: 1,3 COL F F3: 1,3,8 # reduction candidate for 1,3 F3: 8 => CTR * .1......98..5.92...974.85.6.8....673......485...78.192.689..3.1..9856724...312968 F3: 1,3 # 21 pairs * PAIR G4: 6,7 COL G G1: 6,7,8 # reduction candidate for 6,7 G1: 8 => CTR * .1....8.98..5.9217.974.1536.8....673.2...3485...7.81922689..3.1..9856724...312968 G1: 6,7 # 14 pairs * PAIR H4: 6,7 COL H H9: 6,7,5 # reduction candidate for 6,7 H9: 6,7 # 23 pairs H9: 5 # 21 pairs * PAIR A7: 2,5 COL A A1: 2,5,3,4,6 # reduction candidate for 2,5 A1: 2,5 # 22 pairs A4: 2,5,1,4,9 # reduction candidate for 2,5 A4: 2,5 => CTR * .1......98..5.92...974..5...8..9...397....485...7..192.689..3.1.29.56.747..3.29.. A4: 1,4,9 # 17 pairs * PAIR E9: 1,8 COL E E3: 1,8,2,3,6 # reduction candidate for 1,8 E3: 1,8 => CTR * .1......98..5.92..2974..5.6.8....673......485...7..1925689..321..9.56..4...3.29.. E3: 2,3,6 # 17 pairs * PAIR G8: 7,8 BLK 9 I9: 7,8,6 # reduction candidate for 7,8 I9: 7,8 => CTR * 5128637498..5792166974215..98.2..67372..9.485...7.81922689..351..9.56.24...382967 I9: 6 # 14 pairs * PAIR G8: 7,8 COL G G1: 7,8,6 # reduction candidate for 7,8 G1: 7,8 => CTR * 5128637498..5792166974215..98.2..67372..9.485...7.81922689..351..9.56.24...382967 G1: 6 # 14 pairs * PAIR H8: 2,7 ROW 8 A8: 2,7,1,3 # reduction candidate for 2,7 A8: 2,7 => CTR * .128..64984.5.92.7.9742.5.8.8.2.576372.69.485.5.7.8192.689.43.1239156874.753829.6 A8: 1,3 # 18 pairs B8: 2,7,3 # reduction candidate for 2,7 B8: 2,7 # 17 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060827-absurd-base-pr-000.dot * REASONING * PRF # A1: 3,4 => SOL * DIS # C1: 3,4 => CTR => C1: 2,5,6 * PRF # H2: 3,4 => SOL * DIS # B6: 3,4 => CTR => B6: 5 * PRF # H2: 3,4 => SOL * PRF # A1: 3,4 => SOL * DIS # C1: 3,4 => CTR => C1: 2,5,6 * DIS # G1: 8 => CTR => G1: 6,7 * DIS # I9: 8 => CTR => I9: 6,7 * PRF # H2: 4 => SOL * DIS # E3: 1,3 => CTR => E3: 2,6,8 * DIS # G1: 7 => CTR => G1: 6,8 * PRF # E3: 6,8 => SOL * DIS # I9: 7 => CTR => I9: 6,8 * DIS # D5: 1,2 => CTR => D5: 6 * DIS # E5: 1,2 => CTR => E5: 3,6,9 * PRF # A4: 1,2 => SOL * PRF # E5: 1,3 => SOL * DIS # A5: 1,3 => CTR => A5: 2,6,7,9 * DIS # F3: 8 => CTR => F3: 1,3 * DIS # G1: 8 => CTR => G1: 6,7 * DIS # A4: 2,5 => CTR => A4: 1,4,9 * DIS # E3: 1,8 => CTR => E3: 2,3,6 * DIS # I9: 7,8 => CTR => I9: 6 * DIS # G1: 7,8 => CTR => G1: 6 * DIS # A8: 2,7 => CTR => A8: 1,3 * CNT 26 HDP CHAINS / 63 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A7,B2,D4,D8,E7,E9,F5,F7,G4,G8,H1,H3,H4,H7,H8,I2,I3) * .1......98..5.92...974..5...8......3......485...7..192.689..3.1..9.56..4...3.29.. * PAIR B2: 3,4 BLK 1 A1: 3,4,2,5,6 # reduction candidate for 3,4 A1: 3,4 => SOLVED * 415827639836519247297463518184295763972631485653748192568974321329156874741382956 * DURATION: 0:00:02.012626 START: 02:08:42.617932 END: 02:08:44.630558 2019-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060827-absurd-base-pr-001.dot * REASONING * PRF # A1: 3,4 => SOL * STA A1: 3,4 * CNT 1 HDP CHAINS / 1 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Aug&YEAR=2006, 20060827, absurd
Solution
position: 415827639836519247297463518184295763972631485653748192568974321329156874741382956 solved
See section Pair Reduction for the HDP chains leading to this result.
Appendix: Full HDP Chains
A1. Pair Reduction Analysis
Full list of HDP chains traversed:
* PRF # A1: 3,4 => SOL * INC # A1: 2,5,6 => UNS * DIS # C1: 3,4 => CTR => C1: 2,5,6 * INC # C1: 2,5,6 => UNS * INC # C2: 3,4 => UNS * PRF # H2: 3,4 => SOL * INC # H2: 1 => UNS * DIS # B6: 3,4 => CTR => B6: 5 * INC # B6: 5 => UNS * PRF # H2: 3,4 => SOL * INC # H2: 1 => UNS * PRF # A1: 3,4 => SOL * INC # A1: 2,5,6 => UNS * DIS # C1: 3,4 => CTR => C1: 2,5,6 * INC # C1: 2,5,6 => UNS * INC # G1: 6,7 => UNS * DIS # G1: 8 => CTR => G1: 6,7 * INC # E2: 6,7 => UNS * INC # E2: 1,3 => UNS * INC # I9: 6,7 => UNS * DIS # I9: 8 => CTR => I9: 6,7 * INC # H2: 1,3 => UNS * PRF # H2: 4 => SOL * DIS # E3: 1,3 => CTR => E3: 2,6,8 * INC # E3: 2,6,8 => UNS * INC # F3: 1,3 => UNS * INC # G1: 6,8 => UNS * DIS # G1: 7 => CTR => G1: 6,8 * PRF # E3: 6,8 => SOL * INC # E3: 1,2,3 => UNS * INC # I9: 6,8 => UNS * DIS # I9: 7 => CTR => I9: 6,8 * INC # E4: 1,2 => UNS * DIS # D5: 1,2 => CTR => D5: 6 * INC # D5: 6 => UNS * DIS # E5: 1,2 => CTR => E5: 3,6,9 * INC # E5: 3,6,9 => UNS * PRF # A4: 1,2 => SOL * INC # A4: 4,5,9 => UNS * INC # C4: 1,2 => UNS * PRF # E5: 1,3 => SOL * INC # E5: 2,6,9 => UNS * DIS # A5: 1,3 => CTR => A5: 2,6,7,9 * INC # A5: 2,6,7,9 => UNS * INC # C5: 1,3 => UNS * INC # F3: 1,3 => UNS * DIS # F3: 8 => CTR => F3: 1,3 * INC # G1: 6,7 => UNS * DIS # G1: 8 => CTR => G1: 6,7 * INC # H9: 6,7 => UNS * INC # H9: 5 => UNS * INC # A1: 2,5 => UNS * DIS # A4: 2,5 => CTR => A4: 1,4,9 * INC # A4: 1,4,9 => UNS * DIS # E3: 1,8 => CTR => E3: 2,3,6 * INC # E3: 2,3,6 => UNS * DIS # I9: 7,8 => CTR => I9: 6 * INC # I9: 6 => UNS * DIS # G1: 7,8 => CTR => G1: 6 * INC # G1: 6 => UNS * DIS # A8: 2,7 => CTR => A8: 1,3 * INC # A8: 1,3 => UNS * INC # B8: 2,7 => UNS * CNT 63 HDP CHAINS / 63 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* PRF # A1: 3,4 => SOL * STA A1: 3,4 * CNT 1 HDP CHAINS / 1 HYP OPENED