Analysis of zz-www.sudokuoftheday.co.uk-20060405-absurd-base.sdk
Contents
Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Apr&YEAR=2006
level: medium
position: 2..5.....9..73...6..7..4.....3.5.........9.1..6....2.3..2.....5.38....4..5....72. initial
Autosolve
position: 2.65.....9.5732.863.7..4..2..3.5......43.9.1..6....2.3..2.....5.38..5.4..5...372. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # D3: 1,8 => CTR => D3: 6,9 * DIS # E1: 1,8 => CTR => E1: 9 * DIS # D3: 1,8 => CTR => D3: 6,9 * PRF # F4: 1,8 => SOL * DIS # F7: 1,8 => CTR => F7: 6,7 * DIS # G1: 1,4 => CTR => G1: 3,9 * PRF # I1: 1,4 => SOL * DIS # G3: 1 => CTR => G3: 5,9 * DIS # H6: 7 => CTR => H6: 5,9 * DIS # B4: 9 => CTR => B4: 2,7 * DIS # E5: 2,7 => CTR => E5: 6,8 * PRF # E5: 6,8 => SOL * DIS # I4: 7,8 => CTR => I4: 4,9 * DIS # A5: 7,8 => CTR => A5: 5 * DIS # E5: 7,8 => CTR => E5: 2,6 * DIS # B4: 2 => CTR => B4: 7,9 * PRF # D9: 1,9 => SOL * DIS # E9: 1,9 => CTR => E9: 4,6,8 * DIS # I9: 1,9 => CTR => I9: 8 * PRF # I9: 8 => SOL * PRF # G7: 1,9 => SOL * DIS # G8: 1,9 => CTR => G8: 6 * PRF # G8: 6 => SOL * DIS # I9: 1,9 => CTR => I9: 8 * PRF # I9: 8 => SOL * PRF # D8: 1,9 => SOL * DIS # E8: 1,9 => CTR => E8: 2,6,7 * PRF # I1: 1,9 => SOL * CNT 28 HDP CHAINS / 59 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # D3: 1,8 => CTR => D3: 6,9 * DIS D3: 6,9 # E3: 6,9 => CTR => E3: 1,8 * PRF D3: 6,9 + E3: 1,8 # F4: 1,8 => SOL * STA D3: 6,9 + E3: 1,8 + F4: 1,8 * CNT 3 HDP CHAINS / 13 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 2..5.....9..73...6..7..4.....3.5.........9.1..6....2.3..2.....5.38....4..5....72. | initial |
| 2.65.....9.5732.863.7..4..2..3.5......43.9.1..6....2.3..2.....5.38..5.4..5...372. | autosolve |
| 246598371915732486387614592873251964524369817169487253492876135738125649651943728 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (11) B2: 1,4 B3: 1,8 F1: 1,8 G2: 1,4 H3: 5,9 B5: 2,7 C6: 1,9 I5: 7,8 B7: 7,9 C9: 1,9 I8: 1,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) B2,G2: 1.. / B2 = 1 => 8 pairs (_) / G2 = 1 => 15 pairs (_) C6,C9: 1.. / C6 = 1 => 0 pairs (X) / C9 = 1 => 16 pairs (_) B4,B5: 2.. / B4 = 2 => 0 pairs (X) / B5 = 2 => 15 pairs (_) D4,E5: 2.. / D4 = 2 => 15 pairs (_) / E5 = 2 => 0 pairs (X) D8,E8: 2.. / D8 = 2 => 0 pairs (X) / E8 = 2 => 15 pairs (_) B4,D4: 2.. / B4 = 2 => 0 pairs (X) / D4 = 2 => 15 pairs (_) B5,E5: 2.. / B5 = 2 => 15 pairs (_) / E5 = 2 => 0 pairs (X) D4,D8: 2.. / D4 = 2 => 15 pairs (_) / D8 = 2 => 0 pairs (X) E5,E8: 2.. / E5 = 2 => 0 pairs (X) / E8 = 2 => 15 pairs (_) G1,H1: 3.. / G1 = 3 => 0 pairs (*) / H1 = 3 => 0 pairs (X) G7,H7: 3.. / G7 = 3 => 0 pairs (X) / H7 = 3 => 0 pairs (_) G1,G7: 3.. / G1 = 3 => 0 pairs (*) / G7 = 3 => 0 pairs (X) H1,H7: 3.. / H1 = 3 => 0 pairs (X) / H7 = 3 => 0 pairs (_) B1,B2: 4.. / B1 = 4 => 8 pairs (_) / B2 = 4 => 15 pairs (_) D6,E6: 4.. / D6 = 4 => 11 pairs (_) / E6 = 4 => 12 pairs (_) G4,I4: 4.. / G4 = 4 => 0 pairs (X) / I4 = 4 => 11 pairs (_) A7,A9: 4.. / A7 = 4 => 12 pairs (_) / A9 = 4 => 0 pairs (X) B2,G2: 4.. / B2 = 4 => 15 pairs (_) / G2 = 4 => 8 pairs (_) I1,I4: 4.. / I1 = 4 => 0 pairs (X) / I4 = 4 => 11 pairs (_) G3,H3: 5.. / G3 = 5 => 20 pairs (_) / H3 = 5 => 0 pairs (X) A5,A6: 5.. / A5 = 5 => 20 pairs (_) / A6 = 5 => 0 pairs (X) G5,H6: 5.. / G5 = 5 => 0 pairs (X) / H6 = 5 => 20 pairs (_) A5,G5: 5.. / A5 = 5 => 20 pairs (_) / G5 = 5 => 0 pairs (X) A6,H6: 5.. / A6 = 5 => 0 pairs (X) / H6 = 5 => 20 pairs (_) G3,G5: 5.. / G3 = 5 => 20 pairs (_) / G5 = 5 => 0 pairs (X) H3,H6: 5.. / H3 = 5 => 0 pairs (X) / H6 = 5 => 20 pairs (_) D3,E3: 6.. / D3 = 6 => 11 pairs (_) / E3 = 6 => 0 pairs (X) E5,G5: 6.. / E5 = 6 => 0 pairs (*) / G5 = 6 => 0 pairs (X) F4,F7: 6.. / F4 = 6 => 0 pairs (X) / F7 = 6 => 0 pairs (_) H4,H7: 6.. / H4 = 6 => 0 pairs (*) / H7 = 6 => 0 pairs (X) H1,I1: 7.. / H1 = 7 => 0 pairs (*) / I1 = 7 => 0 pairs (X) A8,E8: 7.. / A8 = 7 => 16 pairs (_) / E8 = 7 => 0 pairs (X) B1,B3: 8.. / B1 = 8 => 15 pairs (_) / B3 = 8 => 11 pairs (_) G7,I9: 8.. / G7 = 8 => 0 pairs (X) / I9 = 8 => 0 pairs (_) B4,C6: 9.. / B4 = 9 => 0 pairs (X) / C6 = 9 => 16 pairs (_) B7,C9: 9.. / B7 = 9 => 16 pairs (_) / C9 = 9 => 0 pairs (X) C6,H6: 9.. / C6 = 9 => 16 pairs (_) / H6 = 9 => 0 pairs (X) B4,B7: 9.. / B4 = 9 => 0 pairs (X) / B7 = 9 => 16 pairs (_) C6,C9: 9.. / C6 = 9 => 16 pairs (_) / C9 = 9 => 0 pairs (X) * DURATION: 0:00:38.619131 START: 22:09:48.713253 END: 22:10:27.332384 2019-04-30 * CP COUNT: (39) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B2,B3,B5,B7,C6,C9,F1,G2,H3,I5,I8) * 2.65.....9.5732.863.7..4..2..3.5......43.9.1..6....2.3..2.....5.38..5.4..5...372. * PAIR B2: 1,4 BLK 1 B1: 1,4,8 # reduction candidate for 1,4 B1: 8 # 15 pairs B1: 1,4 # 11 pairs * PAIR B3: 1,8 BLK 1 B1: 1,8,4 # reduction candidate for 1,8 B1: 1,8 # 15 pairs B1: 4 # 8 pairs * PAIR B3: 1,8 ROW 3 D3: 1,8,6,9 # reduction candidate for 1,8 D3: 1,8 => CTR * 2.659..379.5732.863.7.64592..3.56.745.43.9618.69...253.92....65.38..5.4..5...372. D3: 6,9 # 12 pairs E3: 1,8,6,9 # reduction candidate for 1,8 E3: 1,8 # 14 pairs * PAIR F1: 1,8 BLK 2 E1: 1,8,9 # reduction candidate for 1,8 E1: 1,8 => CTR * 2465.....915732486387694152173258964.2436951.56....2.34.2.76..5738.2564.651..372. E1: 9 # 13 pairs D3: 1,8,6,9 # reduction candidate for 1,8 D3: 1,8 => CTR * 2.659..379.5732.863.7.64592..3.56.745.43.9618.69...253.92....65.38..5.4..5...372. D3: 6,9 # 12 pairs E3: 1,8,6,9 # reduction candidate for 1,8 E3: 1,8 # 14 pairs * PAIR F1: 1,8 ROW 1 B1: 1,8,4 # reduction candidate for 1,8 B1: 1,8 # 15 pairs B1: 4 # 8 pairs * PAIR F1: 1,8 COL F F4: 1,8,6,7 # reduction candidate for 1,8 F4: 1,8 => SOLVED * 246598371915732486387614592873251964524369817169487253492876135738125649651943728 F4: 6,7 # 12 pairs F6: 1,8,7 # reduction candidate for 1,8 F6: 1,8 # 14 pairs F7: 1,8,6,7 # reduction candidate for 1,8 F7: 1,8 => CTR * 2.65...379.5732.863.7..4592..3.56.74574329618.69..7253.92....65.38..5.4..5...372. F7: 6,7 # 12 pairs * PAIR G2: 1,4 BLK 3 G1: 1,4,3,9 # reduction candidate for 1,4 G1: 1,4 => CTR * 2.65...379.5732.863.7..4..2..3.5...4..43.9.18.6....2.3..2.....5.38..5.4..5...372. G1: 3,9 # 12 pairs I1: 1,4,7,9 # reduction candidate for 1,4 I1: 1,4 => SOLVED * 246598371915732486387614592873251964524369817169487253492876135738125649651943728 I1: 7,9 # 13 pairs * PAIR H3: 5,9 BLK 3 G3: 5,9,1 # reduction candidate for 5,9 G3: 1 => CTR * 2465.....915732486387694152173258964.2436951.56....2.34.2.76..5738.2564.651..372. G3: 5,9 # 13 pairs * PAIR H3: 5,9 COL H H6: 5,9,7 # reduction candidate for 5,9 H6: 7 => CTR * 2.65....79.5732.863.7..4.521.3.5...48.43.951.569...273.92.....5.38..5.4..51..372. H6: 5,9 # 15 pairs * PAIR B5: 2,7 BLK 4 B4: 2,7,9 # reduction candidate for 2,7 B4: 9 => CTR * 2.65.....9.5732.863.7..4..2.9325.....243.9.1..61...293.72.....5.38..5.4..5...372. B4: 2,7 # 16 pairs * PAIR B5: 2,7 ROW 5 E5: 2,7,6,8 # reduction candidate for 2,7 E5: 2,7 => CTR * 2.65...379.5732.863.7..4592..3.56.745.43.9618.69...253.92....65.38..5.4..5...372. E5: 6,8 => SOLVED * 246598371915732486387614592873251964524369817169487253492876135738125649651943728 * PAIR I5: 7,8 BLK 6 I4: 7,8,4,9 # reduction candidate for 7,8 I4: 7,8 => CTR * 2.659.3749457321863.76.4952.9325.46..2436951.561...293472..6.35.38.2564.659..372. I4: 4,9 # 12 pairs * PAIR I5: 7,8 ROW 5 A5: 7,8,5 # reduction candidate for 7,8 A5: 7,8 => CTR * 2.65.....9.5732.863.76.4.52173258.6.82436951.56....2.34.2.76..5738.2564.651..372. A5: 5 # 20 pairs E5: 7,8,2,6 # reduction candidate for 7,8 E5: 7,8 => CTR * 2.65...379.5732.863.7..45921.3256.74524379618.6....253..2....65.38.25.4..5...372. E5: 2,6 # 12 pairs * PAIR B7: 7,9 ROW 7 E7: 7,9,1,4,6,8 # reduction candidate for 7,9 E7: 7,9 # 13 pairs E7: 1,4,6,8 # 11 pairs * PAIR B7: 7,9 COL B B4: 7,9,2 # reduction candidate for 7,9 B4: 2 => CTR * 2.65.....9.5732.863.7..4..2.23.5.....74329618.69...253.92...8.5.38..5.4..5...372. B4: 7,9 # 15 pairs * PAIR C9: 1,9 ROW 9 D9: 1,9,4,6,8 # reduction candidate for 1,9 D9: 1,9 => SOLVED * 246598371915732486387614592873251964524369817169487253492876135738125649651943728 D9: 4,6,8 # 11 pairs E9: 1,9,4,6,8 # reduction candidate for 1,9 E9: 1,9 => CTR * 2.65..37.9.5732.863.76.4..2.7325..6..24369.17.69.47253492.76135738.2564.65.4.3728 E9: 4,6,8 # 11 pairs I9: 1,9,8 # reduction candidate for 1,9 I9: 1,9 => CTR * 2.65..3..9.5732.863.76.4.5217325896..2436951.56....2.34.2.76835738.2564.651..3729 I9: 8 => SOLVED * 246598371915732486387614592873251964524369817169487253492876135738125649651943728 * PAIR I8: 1,9 BLK 9 G7: 1,9,3,6,8 # reduction candidate for 1,9 G7: 1,9 => SOLVED * 246598371915732486387614592873251964524369817169487253492876135738125649651943728 G7: 3,6,8 # 11 pairs G8: 1,9,6 # reduction candidate for 1,9 G8: 1,9 => CTR * 2.65...379.5732.863.7..4592..3.56.745.43.9618.69...253.92....65.38..5.4..5...372. G8: 6 => SOLVED * 246598371915732486387614592873251964524369817169487253492876135738125649651943728 I9: 1,9,8 # reduction candidate for 1,9 I9: 1,9 => CTR * 2.65..3..9.5732.863.76.4.5217325896..2436951.56....2.34.2.76835738.2564.651..3729 I9: 8 => SOLVED * 246598371915732486387614592873251964524369817169487253492876135738125649651943728 * PAIR I8: 1,9 ROW 8 D8: 1,9,2,6 # reduction candidate for 1,9 D8: 1,9 => SOLVED * 246598371915732486387614592873251964524369817169487253492876135738125649651943728 D8: 2,6 # 12 pairs E8: 1,9,2,6,7 # reduction candidate for 1,9 E8: 1,9 => CTR * 2.65.....9.5732.863.7..4..2..3.5......432961..6....253..2....65738..5.4..5...372. E8: 2,6,7 # 11 pairs * PAIR I8: 1,9 COL I I1: 1,9,4,7 # reduction candidate for 1,9 I1: 1,9 => SOLVED * 246598371915732486387614592873251964524369817169487253492876135738125649651943728 I1: 4,7 # 13 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060405-absurd-base-pr-000.dot * REASONING * DIS # D3: 1,8 => CTR => D3: 6,9 * DIS # E1: 1,8 => CTR => E1: 9 * DIS # D3: 1,8 => CTR => D3: 6,9 * PRF # F4: 1,8 => SOL * DIS # F7: 1,8 => CTR => F7: 6,7 * DIS # G1: 1,4 => CTR => G1: 3,9 * PRF # I1: 1,4 => SOL * DIS # G3: 1 => CTR => G3: 5,9 * DIS # H6: 7 => CTR => H6: 5,9 * DIS # B4: 9 => CTR => B4: 2,7 * DIS # E5: 2,7 => CTR => E5: 6,8 * PRF # E5: 6,8 => SOL * DIS # I4: 7,8 => CTR => I4: 4,9 * DIS # A5: 7,8 => CTR => A5: 5 * DIS # E5: 7,8 => CTR => E5: 2,6 * DIS # B4: 2 => CTR => B4: 7,9 * PRF # D9: 1,9 => SOL * DIS # E9: 1,9 => CTR => E9: 4,6,8 * DIS # I9: 1,9 => CTR => I9: 8 * PRF # I9: 8 => SOL * PRF # G7: 1,9 => SOL * DIS # G8: 1,9 => CTR => G8: 6 * PRF # G8: 6 => SOL * DIS # I9: 1,9 => CTR => I9: 8 * PRF # I9: 8 => SOL * PRF # D8: 1,9 => SOL * DIS # E8: 1,9 => CTR => E8: 2,6,7 * PRF # I1: 1,9 => SOL * CNT 28 HDP CHAINS / 59 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (B2,B3,B5,B7,C6,C9,F1,G2,H3,I5,I8) * 2.65.....9.5732.863.7..4..2..3.5......43.9.1..6....2.3..2.....5.38..5.4..5...372. * PAIR B2: 1,4 BLK 1 B1: 1,4,8 # reduction candidate for 1,4 B1: 8 # 15 pairs B1: 1,4 # 11 pairs * PAIR B3: 1,8 BLK 1 B1: 1,8,4 # reduction candidate for 1,8 B1: 1,8 # 15 pairs B1: 4 # 8 pairs * PAIR B3: 1,8 ROW 3 D3: 1,8,6,9 # reduction candidate for 1,8 D3: 1,8 => CTR * 2.659..379.5732.863.7.64592..3.56.745.43.9618.69...253.92....65.38..5.4..5...372. E3: 1,8,6,9 # reduction candidate for 1,8 E3: 1,8 # 14 pairs * RESTART * PAIR B3: 1,8 ROW 3 E3: 1,8,6,9 # reduction candidate for 1,8 E3: 6,9 => CTR * 2465.....915732486387694152173258964.2436951.56....2.34.2.76..5738.2564.651..372. * PAIR RESTART * PAIR B3: 1,8 BLK 1 B1: 1,8,4 # reduction candidate for 1,8 B1: 1,8 # 16 pairs B1: 4 # 14 pairs * PAIR F1: 1,8 ROW 1 B1: 1,8,4 # reduction candidate for 1,8 B1: 1,8 # 16 pairs B1: 4 # 14 pairs * PAIR F1: 1,8 COL F F4: 1,8,6,7 # reduction candidate for 1,8 F4: 1,8 => SOLVED * 246598371915732486387614592873251964524369817169487253492876135738125649651943728 * DURATION: 0:00:07.959901 START: 22:11:01.318050 END: 22:11:09.277951 2019-04-30 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060405-absurd-base-pr-001.dot * REASONING * DIS # D3: 1,8 => CTR => D3: 6,9 * DIS D3: 6,9 # E3: 6,9 => CTR => E3: 1,8 * PRF D3: 6,9 + E3: 1,8 # F4: 1,8 => SOL * STA D3: 6,9 + E3: 1,8 + F4: 1,8 * CNT 3 HDP CHAINS / 13 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Apr&YEAR=2006, 20060405, absurd
Solution
position: 246598371915732486387614592873251964524369817169487253492876135738125649651943728 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:
* INC # B1: 1,4 => UNS * INC # B1: 8 => UNS * INC # B1: 1,8 => UNS * INC # B1: 4 => UNS * DIS # D3: 1,8 => CTR => D3: 6,9 * INC # D3: 6,9 => UNS * INC # E3: 1,8 => UNS * DIS # E1: 1,8 => CTR => E1: 9 * INC # E1: 9 => UNS * DIS # D3: 1,8 => CTR => D3: 6,9 * INC # D3: 6,9 => UNS * INC # E3: 1,8 => UNS * INC # B1: 1,8 => UNS * INC # B1: 4 => UNS * PRF # F4: 1,8 => SOL * INC # F4: 6,7 => UNS * INC # F6: 1,8 => UNS * DIS # F7: 1,8 => CTR => F7: 6,7 * INC # F7: 6,7 => UNS * DIS # G1: 1,4 => CTR => G1: 3,9 * INC # G1: 3,9 => UNS * PRF # I1: 1,4 => SOL * INC # I1: 7,9 => UNS * INC # G3: 5,9 => UNS * DIS # G3: 1 => CTR => G3: 5,9 * INC # H6: 5,9 => UNS * DIS # H6: 7 => CTR => H6: 5,9 * INC # B4: 2,7 => UNS * DIS # B4: 9 => CTR => B4: 2,7 * DIS # E5: 2,7 => CTR => E5: 6,8 * PRF # E5: 6,8 => SOL * DIS # I4: 7,8 => CTR => I4: 4,9 * INC # I4: 4,9 => UNS * DIS # A5: 7,8 => CTR => A5: 5 * INC # A5: 5 => UNS * DIS # E5: 7,8 => CTR => E5: 2,6 * INC # E5: 2,6 => UNS * INC # E7: 7,9 => UNS * INC # E7: 1,4,6,8 => UNS * INC # B4: 7,9 => UNS * DIS # B4: 2 => CTR => B4: 7,9 * PRF # D9: 1,9 => SOL * INC # D9: 4,6,8 => UNS * DIS # E9: 1,9 => CTR => E9: 4,6,8 * INC # E9: 4,6,8 => UNS * DIS # I9: 1,9 => CTR => I9: 8 * PRF # I9: 8 => SOL * PRF # G7: 1,9 => SOL * INC # G7: 3,6,8 => UNS * DIS # G8: 1,9 => CTR => G8: 6 * PRF # G8: 6 => SOL * DIS # I9: 1,9 => CTR => I9: 8 * PRF # I9: 8 => SOL * PRF # D8: 1,9 => SOL * INC # D8: 2,6 => UNS * DIS # E8: 1,9 => CTR => E8: 2,6,7 * INC # E8: 2,6,7 => UNS * PRF # I1: 1,9 => SOL * INC # I1: 4,7 => UNS * CNT 59 HDP CHAINS / 59 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # B1: 1,4 => UNS * INC # B1: 8 => UNS * INC # B1: 1,8 => UNS * INC # B1: 4 => UNS * DIS # D3: 1,8 => CTR => D3: 6,9 * INC D3: 6,9 # E3: 1,8 => UNS * INC D3: 6,9 # E3: 1,8 => UNS * DIS D3: 6,9 # E3: 6,9 => CTR => E3: 1,8 * INC D3: 6,9 + E3: 1,8 # B1: 1,8 => UNS * INC D3: 6,9 + E3: 1,8 # B1: 4 => UNS * INC D3: 6,9 + E3: 1,8 # B1: 1,8 => UNS * INC D3: 6,9 + E3: 1,8 # B1: 4 => UNS * PRF D3: 6,9 + E3: 1,8 # F4: 1,8 => SOL * STA D3: 6,9 + E3: 1,8 + F4: 1,8 * CNT 13 HDP CHAINS / 13 HYP OPENED