Analysis of zz-www.sudokuoftheday.co.uk-20060609-absurd-base.sdk
Contents
Sudoku from http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Jun&YEAR=2006
level: medium
position: ....7....5.8...14..76..1.....7....2..5..674.18..4..3..7...1..32.....69....4..9... initial
Autosolve
position: ....7....5.86..147.76.41.....71...2..5..674.18..4..37.7...14.32...7.69.4..4..97.. autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # F1: 2,3 => CTR => F1: 5,8 * DIS # D9: 5,8 => CTR => D9: 2,3 * CNT 2 HDP CHAINS / 25 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # F1: 2,3 => CTR => F1: 5,8 * DIS F1: 5,8 # D9: 5,8 => CTR => D9: 2,3 * DIS F1: 5,8 + D9: 2,3 # H1: 5,8 => CTR => H1: 6,9 * PRF F1: 5,8 + D9: 2,3 + H1: 6,9 # G7: 5,8 => SOL * STA F1: 5,8 + D9: 2,3 + H1: 6,9 + G7: 5,8 * CNT 4 HDP CHAINS / 61 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ....7....5.8...14..76..1.....7....2..5..674.18..4..3..7...1..32.....69....4..9... | initial |
| ....7....5.86..147.76.41.....71...2..5..674.18..4..37.7...14.32...7.69.4..4..97.. | autosolve |
| 413275698528693147976841253647138529352967481891452376769514832235786914184329765 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (5) F2: 2,3 F6: 2,5 H5: 8,9 C7: 5,9 D7: 5,8 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) B6,C6: 1.. / B6 = 1 => 11 pairs (_) / C6 = 1 => 7 pairs (_) H8,H9: 1.. / H8 = 1 => 9 pairs (_) / H9 = 1 => 6 pairs (_) G1,G3: 2.. / G1 = 2 => 6 pairs (_) / G3 = 2 => 6 pairs (_) I1,I3: 3.. / I1 = 3 => 5 pairs (_) / I3 = 3 => 6 pairs (_) A1,B1: 4.. / A1 = 4 => 5 pairs (_) / B1 = 4 => 8 pairs (_) A4,B4: 4.. / A4 = 4 => 8 pairs (_) / B4 = 4 => 5 pairs (_) A1,A4: 4.. / A1 = 4 => 5 pairs (_) / A4 = 4 => 8 pairs (_) B1,B4: 4.. / B1 = 4 => 8 pairs (_) / B4 = 4 => 5 pairs (_) C7,C8: 5.. / C7 = 5 => 0 pairs (X) / C8 = 5 => 8 pairs (_) B6,I6: 6.. / B6 = 6 => 11 pairs (_) / I6 = 6 => 10 pairs (_) B7,G7: 6.. / B7 = 6 => 12 pairs (_) / G7 = 6 => 8 pairs (_) A4,A9: 6.. / A4 = 6 => 8 pairs (_) / A9 = 6 => 8 pairs (_) H1,H9: 6.. / H1 = 6 => 5 pairs (_) / H9 = 6 => 12 pairs (_) D5,H5: 8.. / D5 = 8 => 0 pairs (X) / H5 = 8 => 7 pairs (_) F1,F4: 8.. / F1 = 8 => 12 pairs (_) / F4 = 8 => 19 pairs (_) B7,C7: 9.. / B7 = 9 => 0 pairs (X) / C7 = 9 => 8 pairs (_) B2,E2: 9.. / B2 = 9 => 18 pairs (_) / E2 = 9 => 15 pairs (_) * DURATION: 0:00:14.923903 START: 23:43:38.885814 END: 23:43:53.809717 2019-04-30 * CP COUNT: (17) * CLUE FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (C7,D7,F2,F6,H5) * ....7....5.86..147.76.41.....71...2..5..674.18..4..37.7...14.32...7.69.4..4..97.. * PAIR F2: 2,3 BLK 2 D1: 2,3,5,8,9 # reduction candidate for 2,3 D1: 2,3 # 19 pairs F1: 2,3,5,8 # reduction candidate for 2,3 F1: 2,3 => CTR * ....7....5.86..147.76.41.....71.8.2..5..674818..4.537.7...14.32...7.69.4..4..97.. F1: 5,8 # 6 pairs E2: 2,3,9 # reduction candidate for 2,3 E2: 2,3 # 18 pairs D3: 2,3,5,8,9 # reduction candidate for 2,3 D3: 2,3 # 22 pairs * PAIR F2: 2,3 ROW 2 B2: 2,3,9 # reduction candidate for 2,3 B2: 9 # 18 pairs B2: 2,3 # 15 pairs * PAIR F6: 2,5 BLK 5 E6: 2,5,9 # reduction candidate for 2,5 E6: 9 # 19 pairs E6: 2,5 # 9 pairs * PAIR F6: 2,5 COL F F1: 2,5,3,8 # reduction candidate for 2,5 F1: 2,5 # 19 pairs F1: 3,8 # 12 pairs * PAIR H5: 8,9 BLK 6 I4: 8,9,5,6 # reduction candidate for 8,9 I4: 8,9 # 8 pairs I4: 5,6 # 6 pairs * PAIR H5: 8,9 ROW 5 D5: 8,9,2,3 # reduction candidate for 8,9 D5: 2,3 # 18 pairs D5: 8,9 # 9 pairs * PAIR H5: 8,9 COL H H1: 8,9,5,6 # reduction candidate for 8,9 H1: 8,9 # 13 pairs H3: 8,9,5 # reduction candidate for 8,9 H3: 8,9 # 8 pairs * PAIR D7: 5,8 BLK 8 E8: 5,8,2,3 # reduction candidate for 5,8 E8: 5,8 # 11 pairs D9: 5,8,2,3 # reduction candidate for 5,8 D9: 5,8 => CTR * ....75...528693147.76.41.....71...2..5.9674818..45237.7...14.32...7.69.4..4..97.. D9: 2,3 # 6 pairs E9: 5,8,2,3 # reduction candidate for 5,8 E9: 5,8 # 8 pairs * PAIR D7: 5,8 ROW 7 G7: 5,8,6 # reduction candidate for 5,8 G7: 5,8 # 12 pairs G7: 6 # 8 pairs * PAIR D7: 5,8 COL D D1: 5,8,2,3,9 # reduction candidate for 5,8 D1: 5,8 # 13 pairs D3: 5,8,2,3,9 # reduction candidate for 5,8 D3: 5,8 # 10 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060609-absurd-base-pr-000.dot * REASONING * DIS # F1: 2,3 => CTR => F1: 5,8 * DIS # D9: 5,8 => CTR => D9: 2,3 * CNT 2 HDP CHAINS / 25 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (C7,D7,F2,F6,H5) * ....7....5.86..147.76.41.....71...2..5..674.18..4..37.7...14.32...7.69.4..4..97.. * PAIR F2: 2,3 BLK 2 D1: 2,3,5,8,9 # reduction candidate for 2,3 D1: 2,3 # 19 pairs F1: 2,3,5,8 # reduction candidate for 2,3 F1: 2,3 => CTR * ....7....5.86..147.76.41.....71.8.2..5..674818..4.537.7...14.32...7.69.4..4..97.. E2: 2,3,9 # reduction candidate for 2,3 E2: 2,3 # 18 pairs D3: 2,3,5,8,9 # reduction candidate for 2,3 D3: 2,3 # 22 pairs * PAIR F2: 2,3 ROW 2 B2: 2,3,9 # reduction candidate for 2,3 B2: 9 # 18 pairs B2: 2,3 # 16 pairs * PAIR RESTART * PAIR F2: 2,3 BLK 2 D1: 2,3,5,8,9 # reduction candidate for 2,3 D1: 2,3 # 19 pairs E2: 2,3,9 # reduction candidate for 2,3 E2: 2,3 # 18 pairs D3: 2,3,5,8,9 # reduction candidate for 2,3 D3: 2,3 # 22 pairs * PAIR F2: 2,3 ROW 2 B2: 2,3,9 # reduction candidate for 2,3 B2: 9 # 18 pairs B2: 2,3 # 16 pairs * PAIR F6: 2,5 BLK 5 E6: 2,5,9 # reduction candidate for 2,5 E6: 9 # 19 pairs E6: 2,5 # 10 pairs * PAIR H5: 8,9 BLK 6 I4: 8,9,5,6 # reduction candidate for 8,9 I4: 8,9 # 9 pairs I4: 5,6 # 7 pairs * PAIR H5: 8,9 ROW 5 D5: 8,9,2,3 # reduction candidate for 8,9 D5: 2,3 # 18 pairs D5: 8,9 # 10 pairs * PAIR H5: 8,9 COL H H1: 8,9,5,6 # reduction candidate for 8,9 H1: 8,9 # 14 pairs H3: 8,9,5 # reduction candidate for 8,9 H3: 8,9 # 9 pairs * PAIR D7: 5,8 BLK 8 E8: 5,8,2,3 # reduction candidate for 5,8 E8: 5,8 # 12 pairs D9: 5,8,2,3 # reduction candidate for 5,8 D9: 5,8 => CTR * ....75...528693147.76.41.....71...2..5.9674818..45237.7...14.32...7.69.4..4..97.. E9: 5,8,2,3 # reduction candidate for 5,8 E9: 5,8 # 9 pairs * PAIR D7: 5,8 ROW 7 G7: 5,8,6 # reduction candidate for 5,8 G7: 5,8 # 14 pairs G7: 6 # 10 pairs * PAIR D7: 5,8 COL D D1: 5,8,2,3,9 # reduction candidate for 5,8 D1: 5,8 # 13 pairs D3: 5,8,2,3,9 # reduction candidate for 5,8 D3: 5,8 # 10 pairs * PAIR RESTART * PAIR D7: 5,8 BLK 8 E8: 5,8,2,3 # reduction candidate for 5,8 E8: 5,8 # 12 pairs E9: 5,8,2,3 # reduction candidate for 5,8 E9: 5,8 # 9 pairs * PAIR D7: 5,8 ROW 7 G7: 5,8,6 # reduction candidate for 5,8 G7: 5,8 # 14 pairs G7: 6 # 10 pairs * PAIR D7: 5,8 COL D D1: 5,8,2,3,9 # reduction candidate for 5,8 D1: 5,8 # 13 pairs D3: 5,8,2,3,9 # reduction candidate for 5,8 D3: 5,8 # 10 pairs * LEVEL 0 PASS 1 ROUND 2 (AUTO SOLVE) (C7,D7,D9,F1,F2,F6,H5) * ....7....5.86..147.76.41.....71...2..5..674.18..4..37.7...14.32...7.69.4..4..97.. * PAIR F1: 5,8 BLK 2 D1: 5,8,2,3,9 # reduction candidate for 5,8 D1: 5,8 # 13 pairs D3: 5,8,2,3,9 # reduction candidate for 5,8 D3: 5,8 # 10 pairs * PAIR F1: 5,8 ROW 1 G1: 5,8,2,6 # reduction candidate for 5,8 G1: 5,8 # 14 pairs H1: 5,8,6,9 # reduction candidate for 5,8 H1: 5,8 => CTR * 4...7865.5.86..147.765412..6471...2..5..674818..4..376769.14832..57.69141.4..9765 I1: 5,8,3,6,9 # reduction candidate for 5,8 I1: 5,8 # 14 pairs * PAIR F1: 5,8 COL F F4: 5,8,3 # reduction candidate for 5,8 F4: 3 # 16 pairs F4: 5,8 # 11 pairs * PAIR RESTART * PAIR F1: 5,8 BLK 2 D1: 5,8,2,3,9 # reduction candidate for 5,8 D1: 5,8 # 13 pairs D3: 5,8,2,3,9 # reduction candidate for 5,8 D3: 5,8 # 11 pairs * PAIR F1: 5,8 ROW 1 G1: 5,8,2,6 # reduction candidate for 5,8 G1: 5,8 # 14 pairs I1: 5,8,3,6,9 # reduction candidate for 5,8 I1: 5,8 # 14 pairs * PAIR F1: 5,8 COL F F4: 5,8,3 # reduction candidate for 5,8 F4: 3 # 16 pairs F4: 5,8 # 11 pairs * PAIR F2: 2,3 BLK 2 D1: 2,3,5,8,9 # reduction candidate for 2,3 D1: 2,3 # 20 pairs E2: 2,3,9 # reduction candidate for 2,3 E2: 2,3 # 19 pairs D3: 2,3,5,8,9 # reduction candidate for 2,3 D3: 2,3 # 22 pairs * PAIR F2: 2,3 ROW 2 B2: 2,3,9 # reduction candidate for 2,3 B2: 9 # 19 pairs B2: 2,3 # 18 pairs * PAIR F6: 2,5 BLK 5 E6: 2,5,9 # reduction candidate for 2,5 E6: 9 # 20 pairs E6: 2,5 # 12 pairs * PAIR H5: 8,9 BLK 6 I4: 8,9,5,6 # reduction candidate for 8,9 I4: 8,9 # 11 pairs I4: 5,6 # 9 pairs * PAIR H5: 8,9 ROW 5 D5: 8,9,2,3 # reduction candidate for 8,9 D5: 2,3 # 19 pairs D5: 8,9 # 12 pairs * PAIR H5: 8,9 COL H H3: 8,9,5 # reduction candidate for 8,9 H3: 8,9 # 12 pairs H3: 5 # 10 pairs * PAIR D7: 5,8 BLK 8 E8: 5,8,2,3 # reduction candidate for 5,8 E8: 5,8 # 13 pairs E9: 5,8,2,3 # reduction candidate for 5,8 E9: 5,8 # 10 pairs * PAIR D7: 5,8 ROW 7 G7: 5,8,6 # reduction candidate for 5,8 G7: 5,8 => SOLVED * 413275698528693147976841253647138529352967481891452376769514832235786914184329765 * DURATION: 0:00:33.269013 START: 23:44:06.557434 END: 23:44:39.826447 2019-04-30 * SOLUTION FOUND * SAVE PR GRAPH zz-www.sudokuoftheday.co.uk-20060609-absurd-base-pr-001.dot * REASONING * DIS # F1: 2,3 => CTR => F1: 5,8 * DIS F1: 5,8 # D9: 5,8 => CTR => D9: 2,3 * DIS F1: 5,8 + D9: 2,3 # H1: 5,8 => CTR => H1: 6,9 * PRF F1: 5,8 + D9: 2,3 + H1: 6,9 # G7: 5,8 => SOL * STA F1: 5,8 + D9: 2,3 + H1: 6,9 + G7: 5,8 * CNT 4 HDP CHAINS / 61 HYP OPENED
Header Info
http://www.sudokuoftheday.co.uk/cgi-bin/sudoku1280.cgi?ACTION=archive2&USER=&MONTH=Jun&YEAR=2006, 20060609, absurd
Solution
position: 413275698528693147976841253647138529352967481891452376769514832235786914184329765 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 # D1: 2,3 => UNS * DIS # F1: 2,3 => CTR => F1: 5,8 * INC # F1: 5,8 => UNS * INC # E2: 2,3 => UNS * INC # D3: 2,3 => UNS * INC # B2: 2,3 => UNS * INC # B2: 9 => UNS * INC # E6: 2,5 => UNS * INC # E6: 9 => UNS * INC # F1: 2,5 => UNS * INC # F1: 3,8 => UNS * INC # I4: 8,9 => UNS * INC # I4: 5,6 => UNS * INC # D5: 8,9 => UNS * INC # D5: 2,3 => UNS * INC # H1: 8,9 => UNS * INC # H3: 8,9 => UNS * INC # E8: 5,8 => UNS * DIS # D9: 5,8 => CTR => D9: 2,3 * INC # D9: 2,3 => UNS * INC # E9: 5,8 => UNS * INC # G7: 5,8 => UNS * INC # G7: 6 => UNS * INC # D1: 5,8 => UNS * INC # D3: 5,8 => UNS * CNT 25 HDP CHAINS / 25 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* INC # D1: 2,3 => UNS * DIS # F1: 2,3 => CTR => F1: 5,8 * INC F1: 5,8 # E2: 2,3 => UNS * INC F1: 5,8 # D3: 2,3 => UNS * INC F1: 5,8 # B2: 2,3 => UNS * INC F1: 5,8 # B2: 9 => UNS * INC F1: 5,8 # D1: 2,3 => UNS * INC F1: 5,8 # E2: 2,3 => UNS * INC F1: 5,8 # D3: 2,3 => UNS * INC F1: 5,8 # B2: 2,3 => UNS * INC F1: 5,8 # B2: 9 => UNS * INC F1: 5,8 # E6: 2,5 => UNS * INC F1: 5,8 # E6: 9 => UNS * INC F1: 5,8 # I4: 8,9 => UNS * INC F1: 5,8 # I4: 5,6 => UNS * INC F1: 5,8 # D5: 8,9 => UNS * INC F1: 5,8 # D5: 2,3 => UNS * INC F1: 5,8 # H1: 8,9 => UNS * INC F1: 5,8 # H3: 8,9 => UNS * INC F1: 5,8 # E8: 5,8 => UNS * DIS F1: 5,8 # D9: 5,8 => CTR => D9: 2,3 * INC F1: 5,8 + D9: 2,3 # E9: 5,8 => UNS * INC F1: 5,8 + D9: 2,3 # G7: 5,8 => UNS * INC F1: 5,8 + D9: 2,3 # G7: 6 => UNS * INC F1: 5,8 + D9: 2,3 # D1: 5,8 => UNS * INC F1: 5,8 + D9: 2,3 # D3: 5,8 => UNS * INC F1: 5,8 + D9: 2,3 # E8: 5,8 => UNS * INC F1: 5,8 + D9: 2,3 # E9: 5,8 => UNS * INC F1: 5,8 + D9: 2,3 # G7: 5,8 => UNS * INC F1: 5,8 + D9: 2,3 # G7: 6 => UNS * INC F1: 5,8 + D9: 2,3 # D1: 5,8 => UNS * INC F1: 5,8 + D9: 2,3 # D3: 5,8 => UNS * INC F1: 5,8 + D9: 2,3 # D1: 5,8 => UNS * INC F1: 5,8 + D9: 2,3 # D3: 5,8 => UNS * INC F1: 5,8 + D9: 2,3 # G1: 5,8 => UNS * DIS F1: 5,8 + D9: 2,3 # H1: 5,8 => CTR => H1: 6,9 * INC F1: 5,8 + D9: 2,3 + H1: 6,9 # I1: 5,8 => UNS * INC F1: 5,8 + D9: 2,3 + H1: 6,9 # F4: 5,8 => UNS * INC F1: 5,8 + D9: 2,3 + H1: 6,9 # F4: 3 => UNS * INC F1: 5,8 + D9: 2,3 + H1: 6,9 # D1: 5,8 => UNS * INC F1: 5,8 + D9: 2,3 + H1: 6,9 # D3: 5,8 => UNS * INC F1: 5,8 + D9: 2,3 + H1: 6,9 # G1: 5,8 => UNS * INC F1: 5,8 + D9: 2,3 + H1: 6,9 # I1: 5,8 => UNS * INC F1: 5,8 + D9: 2,3 + H1: 6,9 # F4: 5,8 => UNS * INC F1: 5,8 + D9: 2,3 + H1: 6,9 # F4: 3 => UNS * INC F1: 5,8 + D9: 2,3 + H1: 6,9 # D1: 2,3 => UNS * INC F1: 5,8 + D9: 2,3 + H1: 6,9 # E2: 2,3 => UNS * INC F1: 5,8 + D9: 2,3 + H1: 6,9 # D3: 2,3 => UNS * INC F1: 5,8 + D9: 2,3 + H1: 6,9 # B2: 2,3 => UNS * INC F1: 5,8 + D9: 2,3 + H1: 6,9 # B2: 9 => UNS * INC F1: 5,8 + D9: 2,3 + H1: 6,9 # E6: 2,5 => UNS * INC F1: 5,8 + D9: 2,3 + H1: 6,9 # E6: 9 => UNS * INC F1: 5,8 + D9: 2,3 + H1: 6,9 # I4: 8,9 => UNS * INC F1: 5,8 + D9: 2,3 + H1: 6,9 # I4: 5,6 => UNS * INC F1: 5,8 + D9: 2,3 + H1: 6,9 # D5: 8,9 => UNS * INC F1: 5,8 + D9: 2,3 + H1: 6,9 # D5: 2,3 => UNS * INC F1: 5,8 + D9: 2,3 + H1: 6,9 # H3: 8,9 => UNS * INC F1: 5,8 + D9: 2,3 + H1: 6,9 # H3: 5 => UNS * INC F1: 5,8 + D9: 2,3 + H1: 6,9 # E8: 5,8 => UNS * INC F1: 5,8 + D9: 2,3 + H1: 6,9 # E9: 5,8 => UNS * PRF F1: 5,8 + D9: 2,3 + H1: 6,9 # G7: 5,8 => SOL * STA F1: 5,8 + D9: 2,3 + H1: 6,9 + G7: 5,8 * CNT 61 HDP CHAINS / 61 HYP OPENED