Analysis of zz-menneske-no-06911894-base.sdk
Contents
Original Sudoku
level: medium
position: 25.6....9.......5.....3..6.6...43.....7.....5...21..4..7.1..4.........1.19...6..7 initial
Autosolve
position: 25.6....9.......5.....3..6.6...43.....7.6...5...21..4..7.1..4.........1.19...6..7 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # F1: 7,8 => CTR => F1: 1,4 * DIS # F3: 7,8 => CTR => F3: 1,2,4,5,9 * DIS # D8: 8,9 => CTR => D8: 3,4,7 * DIS # F3: 8,9 => CTR => F3: 1,2,4,5,7 * DIS # F8: 8,9 => CTR => F8: 2,4,7 * PRF # F3: 1,2,4,8,9 => SOL * DIS # H7: 2,3 => CTR => H7: 8,9 * CNT 7 HDP CHAINS / 43 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # F1: 7,8 => CTR => F1: 1,4 * DIS F1: 1,4 # F3: 7,8 => CTR => F3: 1,2,4,5,9 * DIS F1: 1,4 + F3: 1,2,4,5,9 # D8: 8,9 => CTR => D8: 3,4,7 * DIS F1: 1,4 + F3: 1,2,4,5,9 + D8: 3,4,7 # F8: 8,9 => CTR => F8: 2,4,7 * DIS F1: 1,4 + F3: 1,2,4,5,9 + D8: 3,4,7 + F8: 2,4,7 # H7: 2,3 => CTR => H7: 8,9 * DIS F1: 1,4 + F3: 1,2,4,5,9 + D8: 3,4,7 + F8: 2,4,7 + H7: 8,9 # G1: 7,8 => CTR => G1: 1,3 * DIS F1: 1,4 + F3: 1,2,4,5,9 + D8: 3,4,7 + F8: 2,4,7 + H7: 8,9 + G1: 1,3 # H1: 3 => CTR => H1: 7,8 * DIS F1: 1,4 + F3: 1,2,4,5,9 + D8: 3,4,7 + F8: 2,4,7 + H7: 8,9 + G1: 1,3 + H1: 7,8 # E8: 7,8 => CTR => E8: 2,5,9 * DIS F1: 1,4 + F3: 1,2,4,5,9 + D8: 3,4,7 + F8: 2,4,7 + H7: 8,9 + G1: 1,3 + H1: 7,8 + E8: 2,5,9 # E2: 2,9 => CTR => E2: 7,8 * PRF F1: 1,4 + F3: 1,2,4,5,9 + D8: 3,4,7 + F8: 2,4,7 + H7: 8,9 + G1: 1,3 + H1: 7,8 + E8: 2,5,9 + E2: 7,8 # F2: 1,4 => SOL * STA F1: 1,4 + F3: 1,2,4,5,9 + D8: 3,4,7 + F8: 2,4,7 + H7: 8,9 + G1: 1,3 + H1: 7,8 + E8: 2,5,9 + E2: 7,8 + F2: 1,4 * CNT 10 HDP CHAINS / 66 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| 25.6....9.......5.....3..6.6...43.....7.....5...21..4..7.1..4.........1.19...6..7 | initial |
| 25.6....9.......5.....3..6.6...43.....7.6...5...21..4..7.1..4.........1.19...6..7 | autosolve |
| 251684379863971254749532861615743928427869135938215746376158492582497613194326587 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (8) E1: 7,8 A5: 3,4 B6: 3,8 D4: 5,7 D5: 8,9 F5: 8,9 F6: 5,7 H5: 2,3 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) B5,G5: 1.. / B5 = 1 => 12 pairs (_) / G5 = 1 => 13 pairs (_) D8,D9: 3.. / D8 = 3 => 9 pairs (_) / D9 = 3 => 9 pairs (_) I2,I3: 4.. / I2 = 4 => 8 pairs (_) / I3 = 4 => 9 pairs (_) A5,B5: 4.. / A5 = 4 => 7 pairs (_) / B5 = 4 => 0 pairs (X) C1,F1: 4.. / C1 = 4 => 9 pairs (_) / F1 = 4 => 10 pairs (_) C9,D9: 4.. / C9 = 4 => 9 pairs (_) / D9 = 4 => 8 pairs (_) D3,F3: 5.. / D3 = 5 => 24 pairs (_) / F3 = 5 => 6 pairs (_) D4,F6: 5.. / D4 = 5 => 6 pairs (_) / F6 = 5 => 24 pairs (_) G8,G9: 5.. / G8 = 5 => 16 pairs (_) / G9 = 5 => 9 pairs (_) C4,D4: 5.. / C4 = 5 => 24 pairs (_) / D4 = 5 => 6 pairs (_) D3,D4: 5.. / D3 = 5 => 24 pairs (_) / D4 = 5 => 6 pairs (_) F3,F6: 5.. / F3 = 5 => 6 pairs (_) / F6 = 5 => 24 pairs (_) B2,C2: 6.. / B2 = 6 => 8 pairs (_) / C2 = 6 => 13 pairs (_) G6,I6: 6.. / G6 = 6 => 11 pairs (_) / I6 = 6 => 13 pairs (_) C7,I7: 6.. / C7 = 6 => 8 pairs (_) / I7 = 6 => 12 pairs (_) B2,B8: 6.. / B2 = 6 => 8 pairs (_) / B8 = 6 => 13 pairs (_) G6,G8: 6.. / G6 = 6 => 11 pairs (_) / G8 = 6 => 13 pairs (_) A2,A3: 7.. / A2 = 7 => 8 pairs (_) / A3 = 7 => 8 pairs (_) D4,F6: 7.. / D4 = 7 => 24 pairs (_) / F6 = 7 => 6 pairs (_) F6,G6: 7.. / F6 = 7 => 6 pairs (_) / G6 = 7 => 24 pairs (_) H1,H4: 7.. / H1 = 7 => 16 pairs (_) / H4 = 7 => 11 pairs (_) D5,F5: 8.. / D5 = 8 => 8 pairs (_) / F5 = 8 => 7 pairs (_) D5,F5: 9.. / D5 = 9 => 7 pairs (_) / F5 = 9 => 8 pairs (_) H7,G8: 9.. / H7 = 9 => 11 pairs (_) / G8 = 9 => 0 pairs (X) H4,H7: 9.. / H4 = 9 => 0 pairs (X) / H7 = 9 => 11 pairs (_) * DURATION: 0:00:33.043706 START: 06:53:32.690690 END: 06:54:05.734396 2017-05-01 * CP COUNT: (25) * CLUE FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A5,B6,D4,D5,E1,F5,F6,H5) * 25.6....9.......5.....3..6.6...43.....7.6...5...21..4..7.1..4.........1.19...6..7 * PAIR E1: 7,8 BLK 2 F1: 7,8,1,4 # reduction candidate for 7,8 F1: 7,8 => CTR * 254678139.6.9...5.....3..6.6...43.71.17.6..25...217.4..7.1..49..4.....1.19.4.6.87 F1: 1,4 # 9 pairs D2: 7,8,4,9 # reduction candidate for 7,8 D2: 7,8 # 11 pairs E2: 7,8,2,9 # reduction candidate for 7,8 E2: 7,8 # 13 pairs F2: 7,8,1,2,4,9 # reduction candidate for 7,8 F2: 7,8 # 12 pairs D3: 7,8,4,5,9 # reduction candidate for 7,8 D3: 7,8 # 10 pairs F3: 7,8,1,2,4,5,9 # reduction candidate for 7,8 F3: 7,8 => CTR * 25.681379763492.5...15372646.57439..4.7869135..92157463761584925.2.7.61.19..265.7 F3: 1,2,4,5,9 # 8 pairs * PAIR E1: 7,8 ROW 1 G1: 7,8,1,3 # reduction candidate for 7,8 G1: 7,8 # 16 pairs H1: 7,8,3 # reduction candidate for 7,8 H1: 7,8 # 11 pairs * PAIR E1: 7,8 COL E E8: 7,8,2,5,9 # reduction candidate for 7,8 E8: 7,8 # 11 pairs E8: 2,5,9 # 10 pairs * PAIR A5: 3,4 BLK 4 B5: 3,4,1,2 # reduction candidate for 3,4 B5: 3,4 # 22 pairs B5: 1,2 # 9 pairs * PAIR A5: 3,4 COL A A2: 3,4,7,8,9 # reduction candidate for 3,4 A2: 3,4 # 11 pairs A8: 3,4,5,8 # reduction candidate for 3,4 A8: 3,4 # 10 pairs * PAIR B6: 3,8 BLK 4 A6: 3,8,5,9 # reduction candidate for 3,8 A6: 3,8 # 21 pairs C6: 3,8,5,9 # reduction candidate for 3,8 C6: 3,8 # 19 pairs * PAIR B6: 3,8 ROW 6 G6: 3,8,6,7,9 # reduction candidate for 3,8 G6: 3,8 # 16 pairs I6: 3,8,6 # reduction candidate for 3,8 I6: 3,8 # 11 pairs * PAIR B6: 3,8 COL B B2: 3,8,1,4,6 # reduction candidate for 3,8 B2: 3,8 # 16 pairs B8: 3,8,2,4,6 # reduction candidate for 3,8 B8: 3,8 # 11 pairs * PAIR D4: 5,7 COL D D3: 5,7,4,8,9 # reduction candidate for 5,7 D3: 5,7 # 9 pairs D3: 4,8,9 # 6 pairs * PAIR D5: 8,9 COL D D2: 8,9,4,7 # reduction candidate for 8,9 D2: 8,9 # 10 pairs D3: 8,9,4,5,7 # reduction candidate for 8,9 D3: 8,9 # 9 pairs D8: 8,9,3,4,7 # reduction candidate for 8,9 D8: 8,9 => CTR * 25.6....9.......5.....3..6.6...43.....7.6...5...21..4..7.1..4.......4.1.1943.6..7 D8: 3,4,7 # 8 pairs * PAIR F5: 8,9 COL F F2: 8,9,1,2,4,7 # reduction candidate for 8,9 F2: 8,9 # 11 pairs F3: 8,9,1,2,4,5,7 # reduction candidate for 8,9 F3: 8,9 => CTR * 25.68..79.6.....5.7..539.6.6.57439....7968..5...215746.761.249.......61.19...65.7 F3: 1,2,4,5,7 # 8 pairs F7: 8,9,2 # reduction candidate for 8,9 F7: 8,9 # 9 pairs F8: 8,9,2,4,7 # reduction candidate for 8,9 F8: 8,9 => CTR * 25.68...9....2..5.....3..6.6...43.....7869..5...21..4..7.1924......7891.19..56..7 F8: 2,4,7 # 8 pairs * PAIR F6: 5,7 COL F F3: 5,7,1,2,4,8,9 # reduction candidate for 5,7 F3: 1,2,4,8,9 => SOLVED * 251684379863971254749532861615743928427869135938215746376158492582497613194326587 F3: 5,7 # 9 pairs * PAIR H5: 2,3 BLK 6 G5: 2,3,1 # reduction candidate for 2,3 G5: 1 # 13 pairs G5: 2,3 # 12 pairs * PAIR H5: 2,3 ROW 5 B5: 2,3,1,4 # reduction candidate for 2,3 B5: 2,3 # 13 pairs B5: 1,4 # 10 pairs * PAIR H5: 2,3 COL H H7: 2,3,8,9 # reduction candidate for 2,3 H7: 2,3 => CTR * 25.681379.....2.5.....35.6.6..54379...7.6...5...21764..7.1..4.......491.194.26587 H7: 8,9 # 9 pairs H9: 2,3,8 # reduction candidate for 2,3 H9: 2,3 # 13 pairs * INCONCLUSIVE * SAVE PR GRAPH zz-menneske-no-06911894-base-pr-000.dot * REASONING * DIS # F1: 7,8 => CTR => F1: 1,4 * DIS # F3: 7,8 => CTR => F3: 1,2,4,5,9 * DIS # D8: 8,9 => CTR => D8: 3,4,7 * DIS # F3: 8,9 => CTR => F3: 1,2,4,5,7 * DIS # F8: 8,9 => CTR => F8: 2,4,7 * PRF # F3: 1,2,4,8,9 => SOL * DIS # H7: 2,3 => CTR => H7: 8,9 * CNT 7 HDP CHAINS / 43 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A5,B6,D4,D5,E1,F5,F6,H5) * 25.6....9.......5.....3..6.6...43.....7.6...5...21..4..7.1..4.........1.19...6..7 * PAIR E1: 7,8 BLK 2 F1: 7,8,1,4 # reduction candidate for 7,8 F1: 7,8 => CTR * 254678139.6.9...5.....3..6.6...43.71.17.6..25...217.4..7.1..49..4.....1.19.4.6.87 D2: 7,8,4,9 # reduction candidate for 7,8 D2: 7,8 # 11 pairs E2: 7,8,2,9 # reduction candidate for 7,8 E2: 7,8 # 13 pairs F2: 7,8,1,2,4,9 # reduction candidate for 7,8 F2: 7,8 # 12 pairs D3: 7,8,4,5,9 # reduction candidate for 7,8 D3: 7,8 # 10 pairs F3: 7,8,1,2,4,5,9 # reduction candidate for 7,8 F3: 7,8 => CTR * 25.681379763492.5...15372646.57439..4.7869135..92157463761584925.2.7.61.19..265.7 * PAIR E1: 7,8 ROW 1 G1: 7,8,1,3 # reduction candidate for 7,8 G1: 7,8 # 16 pairs H1: 7,8,3 # reduction candidate for 7,8 H1: 7,8 # 11 pairs * PAIR E1: 7,8 COL E E8: 7,8,2,5,9 # reduction candidate for 7,8 E8: 7,8 # 12 pairs E8: 2,5,9 # 11 pairs * PAIR RESTART * PAIR E1: 7,8 BLK 2 D2: 7,8,4,9 # reduction candidate for 7,8 D2: 7,8 # 11 pairs E2: 7,8,2,9 # reduction candidate for 7,8 E2: 7,8 # 13 pairs F2: 7,8,1,2,4,9 # reduction candidate for 7,8 F2: 7,8 # 12 pairs D3: 7,8,4,5,9 # reduction candidate for 7,8 D3: 7,8 # 10 pairs * PAIR E1: 7,8 ROW 1 G1: 7,8,1,3 # reduction candidate for 7,8 G1: 7,8 # 16 pairs H1: 7,8,3 # reduction candidate for 7,8 H1: 7,8 # 11 pairs * PAIR E1: 7,8 COL E E8: 7,8,2,5,9 # reduction candidate for 7,8 E8: 7,8 # 12 pairs E8: 2,5,9 # 11 pairs * PAIR A5: 3,4 BLK 4 B5: 3,4,1,2 # reduction candidate for 3,4 B5: 3,4 # 22 pairs B5: 1,2 # 10 pairs * PAIR A5: 3,4 COL A A2: 3,4,7,8,9 # reduction candidate for 3,4 A2: 3,4 # 12 pairs A8: 3,4,5,8 # reduction candidate for 3,4 A8: 3,4 # 11 pairs * PAIR B6: 3,8 BLK 4 A6: 3,8,5,9 # reduction candidate for 3,8 A6: 3,8 # 22 pairs C6: 3,8,5,9 # reduction candidate for 3,8 C6: 3,8 # 20 pairs * PAIR B6: 3,8 ROW 6 G6: 3,8,6,7,9 # reduction candidate for 3,8 G6: 3,8 # 17 pairs I6: 3,8,6 # reduction candidate for 3,8 I6: 3,8 # 12 pairs * PAIR B6: 3,8 COL B B2: 3,8,1,4,6 # reduction candidate for 3,8 B2: 3,8 # 17 pairs B8: 3,8,2,4,6 # reduction candidate for 3,8 B8: 3,8 # 12 pairs * PAIR D4: 5,7 COL D D3: 5,7,4,8,9 # reduction candidate for 5,7 D3: 5,7 # 10 pairs D3: 4,8,9 # 7 pairs * PAIR D5: 8,9 COL D D2: 8,9,4,7 # reduction candidate for 8,9 D2: 8,9 # 11 pairs D3: 8,9,4,5,7 # reduction candidate for 8,9 D3: 8,9 # 10 pairs D8: 8,9,3,4,7 # reduction candidate for 8,9 D8: 8,9 => CTR * 25.6....9.......5.....3..6.6...43.....7.6...5...21..4..7.1..4.......4.1.1943.6..7 * PAIR RESTART * PAIR D5: 8,9 COL D D2: 8,9,4,7 # reduction candidate for 8,9 D2: 8,9 # 11 pairs D3: 8,9,4,5,7 # reduction candidate for 8,9 D3: 8,9 # 10 pairs * PAIR F5: 8,9 COL F F2: 8,9,1,2,4,7 # reduction candidate for 8,9 F2: 8,9 # 12 pairs F7: 8,9,2 # reduction candidate for 8,9 F7: 8,9 # 10 pairs F8: 8,9,2,4,7 # reduction candidate for 8,9 F8: 8,9 => CTR * 25.68...9....2..5.....3..6.6...43.....7869..5...21..4..7.1924......7891.19..56..7 * PAIR RESTART * PAIR F5: 8,9 COL F F2: 8,9,1,2,4,7 # reduction candidate for 8,9 F2: 8,9 # 12 pairs F7: 8,9,2 # reduction candidate for 8,9 F7: 8,9 # 10 pairs * PAIR H5: 2,3 BLK 6 G5: 2,3,1 # reduction candidate for 2,3 G5: 2,3 # 13 pairs G5: 1 # 13 pairs * PAIR H5: 2,3 ROW 5 B5: 2,3,1,4 # reduction candidate for 2,3 B5: 2,3 # 13 pairs B5: 1,4 # 11 pairs * PAIR H5: 2,3 COL H H7: 2,3,8,9 # reduction candidate for 2,3 H7: 2,3 => CTR * 25.68..79....7..5.7...35.6.6..54379...7869..5...21764..7.1984.....75491.194326587 H9: 2,3,8 # reduction candidate for 2,3 H9: 2,3 # 13 pairs * RESTART * PAIR H5: 2,3 COL H H9: 2,3,8 # reduction candidate for 2,3 H9: 8 # 18 pairs H9: 2,3 # 13 pairs * PAIR RESTART * PAIR H5: 2,3 BLK 6 G5: 2,3,1 # reduction candidate for 2,3 G5: 2,3 # 14 pairs G5: 1 # 14 pairs * PAIR H5: 2,3 ROW 5 B5: 2,3,1,4 # reduction candidate for 2,3 B5: 2,3 # 14 pairs B5: 1,4 # 12 pairs * PAIR H5: 2,3 COL H H9: 2,3,8 # reduction candidate for 2,3 H9: 8 # 18 pairs H9: 2,3 # 13 pairs * LEVEL 0 PASS 1 ROUND 2 (AUTO SOLVE) (A5,B6,D4,D5,E1,F1,F5,F6,H5,H7) * 25.6....9.......5.....3..6.6...43.....7.6...5...21..4..7.1..4.........1.19...6..7 * PAIR E1: 7,8 BLK 2 D2: 7,8,4,9 # reduction candidate for 7,8 D2: 7,8 # 12 pairs E2: 7,8,2,9 # reduction candidate for 7,8 E2: 7,8 # 14 pairs F2: 7,8,1,2,4,9 # reduction candidate for 7,8 F2: 7,8 # 13 pairs D3: 7,8,4,5,9 # reduction candidate for 7,8 D3: 7,8 # 12 pairs * PAIR E1: 7,8 ROW 1 G1: 7,8,1,3 # reduction candidate for 7,8 G1: 7,8 => CTR * 25.6...39.......5.....35.6.6..543.7...7.6..25...217.4..7.1..49....794.1.1943.6.87 H1: 7,8,3 # reduction candidate for 7,8 H1: 7,8 # 12 pairs * RESTART * PAIR E1: 7,8 ROW 1 H1: 7,8,3 # reduction candidate for 7,8 H1: 3 => CTR * 258674139.......5.....35.6.6..543.71.17.6.325...217.4..7.1..49....792.1.194356287 * PAIR E1: 7,8 COL E E8: 7,8,2,5,9 # reduction candidate for 7,8 E8: 7,8 => CTR * 25.68..79....9..5.....35.6.6..54379.4.7968.25...21764.37.15948....37491.194826537 * PAIR RESTART * PAIR E1: 7,8 BLK 2 E2: 7,8,2,9 # reduction candidate for 7,8 E2: 2,9 => CTR * 25.67..89.......5.....3..6.6...43.7...7.6...5...217.4..7.1..49....794.1.1943.6.27 * PAIR F1: 1,4 BLK 2 F2: 1,4,2 # reduction candidate for 1,4 F2: 1,4 => SOLVED * 251684379863971254749532861615743928427869135938215746376158492582497613194326587 * DURATION: 0:00:51.103410 START: 06:54:36.173042 END: 06:55:27.276452 2017-05-01 * SOLUTION FOUND * SAVE PR GRAPH zz-menneske-no-06911894-base-pr-001.dot * REASONING * DIS # F1: 7,8 => CTR => F1: 1,4 * DIS F1: 1,4 # F3: 7,8 => CTR => F3: 1,2,4,5,9 * DIS F1: 1,4 + F3: 1,2,4,5,9 # D8: 8,9 => CTR => D8: 3,4,7 * DIS F1: 1,4 + F3: 1,2,4,5,9 + D8: 3,4,7 # F8: 8,9 => CTR => F8: 2,4,7 * DIS F1: 1,4 + F3: 1,2,4,5,9 + D8: 3,4,7 + F8: 2,4,7 # H7: 2,3 => CTR => H7: 8,9 * DIS F1: 1,4 + F3: 1,2,4,5,9 + D8: 3,4,7 + F8: 2,4,7 + H7: 8,9 # G1: 7,8 => CTR => G1: 1,3 * DIS F1: 1,4 + F3: 1,2,4,5,9 + D8: 3,4,7 + F8: 2,4,7 + H7: 8,9 + G1: 1,3 # H1: 3 => CTR => H1: 7,8 * DIS F1: 1,4 + F3: 1,2,4,5,9 + D8: 3,4,7 + F8: 2,4,7 + H7: 8,9 + G1: 1,3 + H1: 7,8 # E8: 7,8 => CTR => E8: 2,5,9 * DIS F1: 1,4 + F3: 1,2,4,5,9 + D8: 3,4,7 + F8: 2,4,7 + H7: 8,9 + G1: 1,3 + H1: 7,8 + E8: 2,5,9 # E2: 2,9 => CTR => E2: 7,8 * PRF F1: 1,4 + F3: 1,2,4,5,9 + D8: 3,4,7 + F8: 2,4,7 + H7: 8,9 + G1: 1,3 + H1: 7,8 + E8: 2,5,9 + E2: 7,8 # F2: 1,4 => SOL * STA F1: 1,4 + F3: 1,2,4,5,9 + D8: 3,4,7 + F8: 2,4,7 + H7: 8,9 + G1: 1,3 + H1: 7,8 + E8: 2,5,9 + E2: 7,8 + F2: 1,4 * CNT 10 HDP CHAINS / 66 HYP OPENED
Header Info
http://www.menneske.no/sudoku/utskrift.html?number=6911894 umulig -------------------------------------------------- level: medium * PAIR REDUCTION .. * ROUND 1: 25.6....9.......5.....3..6.6...43.....7.6...5...21..4..7.1..4.........1.19...6..7 E1: 7,8 F1: 1,4,7,8 # reduction candidate for 7,8 F1: 7,8 => CTR * 254678139.6.9...5.....3..6.6...43.71.17.6..25...217.4..7.1..49..4.....1.19.4.6.87 D2: 4,7,8,9 # reduction candidate for 7,8 E2: 2,7,8,9 # reduction candidate for 7,8 F2: 1,2,4,7,8,9 # reduction candidate for 7,8 D3: 4,5,7,8,9 # reduction candidate for 7,8 F3: 1,2,4,5,7,8,9 # reduction candidate for 7,8 F3: 7,8 => CTR * 25.681379763492.5...15372646.57439..4.7869135..92157463761584925.2.7.61.19..265.7 G1: 1,3,7,8 # reduction candidate for 7,8 H1: 3,7,8 # reduction candidate for 7,8 E8: 2,5,7,8,9 # reduction candidate for 7,8 A5: 3,4 B5: 1,2,3,4 # reduction candidate for 3,4 A2: 3,4,7,8,9 # reduction candidate for 3,4 A8: 3,4,5,8 # reduction candidate for 3,4 B6: 3,8 A6: 3,5,8,9 # reduction candidate for 3,8 C6: 3,5,8,9 # reduction candidate for 3,8 G6: 3,6,7,8,9 # reduction candidate for 3,8 I6: 3,6,8 # reduction candidate for 3,8 B2: 1,3,4,6,8 # reduction candidate for 3,8 B8: 2,3,4,6,8 # reduction candidate for 3,8 D4: 5,7 D3: 4,5,7,8,9 # reduction candidate for 5,7 D5: 8,9 D2: 4,7,8,9 # reduction candidate for 8,9 D3: 4,5,7,8,9 # reduction candidate for 8,9 D8: 3,4,7,8,9 # reduction candidate for 8,9 D8: 8,9 => CTR * 25.6....9.......5.....3..6.6...43.....7.6...5...21..4..7.1..4.......4.1.1943.6..7 F5: 8,9 F2: 1,2,4,7,8,9 # reduction candidate for 8,9 F7: 2,8,9 # reduction candidate for 8,9 F8: 2,4,7,8,9 # reduction candidate for 8,9 F8: 8,9 => CTR * 25.68...9....2..5.....3..6.6...43.....7869..5...21..4..7.1924......7891.19..56..7 F6: 5,7 H5: 2,3 G5: 1,2,3 # reduction candidate for 2,3 B5: 1,2,3,4 # reduction candidate for 2,3 H7: 2,3,8,9 # reduction candidate for 2,3 H7: 2,3 => CTR * 25.68..79....7..5.7...35.6.6..54379...7869..5...21764..7.1984.....75491.194326587 H9: 2,3,8 # reduction candidate for 2,3 * ROUND 2: 25.6....9.......5.....3..6.6...43.....7.6...5...21..4..7.1..4.........1.19...6..7 E1: 7,8 D2: 4,7,8,9 # reduction candidate for 7,8 E2: 2,7,8,9 # reduction candidate for 7,8 F2: 1,2,4,7,8,9 # reduction candidate for 7,8 D3: 4,5,7,8,9 # reduction candidate for 7,8 G1: 1,3,7,8 # reduction candidate for 7,8 G1: 7,8 => CTR * 25.6...39.......5.....35.6.6..543.7...7.6..25...217.4..7.1..49....794.1.1943.6.87 H1: 3,7,8 # reduction candidate for 7,8 H1: 3 => CTR * 258674139.......5.....35.6.6..543.71.17.6.325...217.4..7.1..49....792.1.194356287 E8: 2,5,7,8,9 # reduction candidate for 7,8 E8: 7,8 => CTR * 25.68..79....9..5.....35.6.6..54379.4.7968.25...21764.37.15948....37491.194826537 F1: 1,4 F2: 1,2,4,8,9 # reduction candidate for 1,4 F2: 1,4 => SOLVED * 251684379863971254749532861615743928427869135938215746376158492582497613194326587 * SOLVED!
Solution
position: 251684379863971254749532861615743928427869135938215746376158492582497613194326587 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:
* DIS # F1: 7,8 => CTR => F1: 1,4 * INC # F1: 1,4 => UNS * INC # D2: 7,8 => UNS * INC # E2: 7,8 => UNS * INC # F2: 7,8 => UNS * INC # D3: 7,8 => UNS * DIS # F3: 7,8 => CTR => F3: 1,2,4,5,9 * INC # F3: 1,2,4,5,9 => UNS * INC # G1: 7,8 => UNS * INC # H1: 7,8 => UNS * INC # E8: 7,8 => UNS * INC # E8: 2,5,9 => UNS * INC # B5: 3,4 => UNS * INC # B5: 1,2 => UNS * INC # A2: 3,4 => UNS * INC # A8: 3,4 => UNS * INC # A6: 3,8 => UNS * INC # C6: 3,8 => UNS * INC # G6: 3,8 => UNS * INC # I6: 3,8 => UNS * INC # B2: 3,8 => UNS * INC # B8: 3,8 => UNS * INC # D3: 5,7 => UNS * INC # D3: 4,8,9 => UNS * INC # D2: 8,9 => UNS * INC # D3: 8,9 => UNS * DIS # D8: 8,9 => CTR => D8: 3,4,7 * INC # D8: 3,4,7 => UNS * INC # F2: 8,9 => UNS * DIS # F3: 8,9 => CTR => F3: 1,2,4,5,7 * INC # F3: 1,2,4,5,7 => UNS * INC # F7: 8,9 => UNS * DIS # F8: 8,9 => CTR => F8: 2,4,7 * INC # F8: 2,4,7 => UNS * INC # F3: 5,7 => UNS * PRF # F3: 1,2,4,8,9 => SOL * INC # G5: 2,3 => UNS * INC # G5: 1 => UNS * INC # B5: 2,3 => UNS * INC # B5: 1,4 => UNS * DIS # H7: 2,3 => CTR => H7: 8,9 * INC # H7: 8,9 => UNS * INC # H9: 2,3 => UNS * CNT 43 HDP CHAINS / 43 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # F1: 7,8 => CTR => F1: 1,4 * INC F1: 1,4 # D2: 7,8 => UNS * INC F1: 1,4 # E2: 7,8 => UNS * INC F1: 1,4 # F2: 7,8 => UNS * INC F1: 1,4 # D3: 7,8 => UNS * DIS F1: 1,4 # F3: 7,8 => CTR => F3: 1,2,4,5,9 * INC F1: 1,4 + F3: 1,2,4,5,9 # G1: 7,8 => UNS * INC F1: 1,4 + F3: 1,2,4,5,9 # H1: 7,8 => UNS * INC F1: 1,4 + F3: 1,2,4,5,9 # E8: 7,8 => UNS * INC F1: 1,4 + F3: 1,2,4,5,9 # E8: 2,5,9 => UNS * INC F1: 1,4 + F3: 1,2,4,5,9 # D2: 7,8 => UNS * INC F1: 1,4 + F3: 1,2,4,5,9 # E2: 7,8 => UNS * INC F1: 1,4 + F3: 1,2,4,5,9 # F2: 7,8 => UNS * INC F1: 1,4 + F3: 1,2,4,5,9 # D3: 7,8 => UNS * INC F1: 1,4 + F3: 1,2,4,5,9 # G1: 7,8 => UNS * INC F1: 1,4 + F3: 1,2,4,5,9 # H1: 7,8 => UNS * INC F1: 1,4 + F3: 1,2,4,5,9 # E8: 7,8 => UNS * INC F1: 1,4 + F3: 1,2,4,5,9 # E8: 2,5,9 => UNS * INC F1: 1,4 + F3: 1,2,4,5,9 # B5: 3,4 => UNS * INC F1: 1,4 + F3: 1,2,4,5,9 # B5: 1,2 => UNS * INC F1: 1,4 + F3: 1,2,4,5,9 # A2: 3,4 => UNS * INC F1: 1,4 + F3: 1,2,4,5,9 # A8: 3,4 => UNS * INC F1: 1,4 + F3: 1,2,4,5,9 # A6: 3,8 => UNS * INC F1: 1,4 + F3: 1,2,4,5,9 # C6: 3,8 => UNS * INC F1: 1,4 + F3: 1,2,4,5,9 # G6: 3,8 => UNS * INC F1: 1,4 + F3: 1,2,4,5,9 # I6: 3,8 => UNS * INC F1: 1,4 + F3: 1,2,4,5,9 # B2: 3,8 => UNS * INC F1: 1,4 + F3: 1,2,4,5,9 # B8: 3,8 => UNS * INC F1: 1,4 + F3: 1,2,4,5,9 # D3: 5,7 => UNS * INC F1: 1,4 + F3: 1,2,4,5,9 # D3: 4,8,9 => UNS * INC F1: 1,4 + F3: 1,2,4,5,9 # D2: 8,9 => UNS * INC F1: 1,4 + F3: 1,2,4,5,9 # D3: 8,9 => UNS * DIS F1: 1,4 + F3: 1,2,4,5,9 # D8: 8,9 => CTR => D8: 3,4,7 * INC F1: 1,4 + F3: 1,2,4,5,9 + D8: 3,4,7 # D2: 8,9 => UNS * INC F1: 1,4 + F3: 1,2,4,5,9 + D8: 3,4,7 # D3: 8,9 => UNS * INC F1: 1,4 + F3: 1,2,4,5,9 + D8: 3,4,7 # F2: 8,9 => UNS * INC F1: 1,4 + F3: 1,2,4,5,9 + D8: 3,4,7 # F7: 8,9 => UNS * DIS F1: 1,4 + F3: 1,2,4,5,9 + D8: 3,4,7 # F8: 8,9 => CTR => F8: 2,4,7 * INC F1: 1,4 + F3: 1,2,4,5,9 + D8: 3,4,7 + F8: 2,4,7 # F2: 8,9 => UNS * INC F1: 1,4 + F3: 1,2,4,5,9 + D8: 3,4,7 + F8: 2,4,7 # F7: 8,9 => UNS * INC F1: 1,4 + F3: 1,2,4,5,9 + D8: 3,4,7 + F8: 2,4,7 # G5: 2,3 => UNS * INC F1: 1,4 + F3: 1,2,4,5,9 + D8: 3,4,7 + F8: 2,4,7 # G5: 1 => UNS * INC F1: 1,4 + F3: 1,2,4,5,9 + D8: 3,4,7 + F8: 2,4,7 # B5: 2,3 => UNS * INC F1: 1,4 + F3: 1,2,4,5,9 + D8: 3,4,7 + F8: 2,4,7 # B5: 1,4 => UNS * DIS F1: 1,4 + F3: 1,2,4,5,9 + D8: 3,4,7 + F8: 2,4,7 # H7: 2,3 => CTR => H7: 8,9 * INC F1: 1,4 + F3: 1,2,4,5,9 + D8: 3,4,7 + F8: 2,4,7 + H7: 8,9 # H9: 2,3 => UNS * INC F1: 1,4 + F3: 1,2,4,5,9 + D8: 3,4,7 + F8: 2,4,7 + H7: 8,9 # H9: 2,3 => UNS * INC F1: 1,4 + F3: 1,2,4,5,9 + D8: 3,4,7 + F8: 2,4,7 + H7: 8,9 # H9: 8 => UNS * INC F1: 1,4 + F3: 1,2,4,5,9 + D8: 3,4,7 + F8: 2,4,7 + H7: 8,9 # G5: 2,3 => UNS * INC F1: 1,4 + F3: 1,2,4,5,9 + D8: 3,4,7 + F8: 2,4,7 + H7: 8,9 # G5: 1 => UNS * INC F1: 1,4 + F3: 1,2,4,5,9 + D8: 3,4,7 + F8: 2,4,7 + H7: 8,9 # B5: 2,3 => UNS * INC F1: 1,4 + F3: 1,2,4,5,9 + D8: 3,4,7 + F8: 2,4,7 + H7: 8,9 # B5: 1,4 => UNS * INC F1: 1,4 + F3: 1,2,4,5,9 + D8: 3,4,7 + F8: 2,4,7 + H7: 8,9 # H9: 2,3 => UNS * INC F1: 1,4 + F3: 1,2,4,5,9 + D8: 3,4,7 + F8: 2,4,7 + H7: 8,9 # H9: 8 => UNS * INC F1: 1,4 + F3: 1,2,4,5,9 + D8: 3,4,7 + F8: 2,4,7 + H7: 8,9 # D2: 7,8 => UNS * INC F1: 1,4 + F3: 1,2,4,5,9 + D8: 3,4,7 + F8: 2,4,7 + H7: 8,9 # E2: 7,8 => UNS * INC F1: 1,4 + F3: 1,2,4,5,9 + D8: 3,4,7 + F8: 2,4,7 + H7: 8,9 # F2: 7,8 => UNS * INC F1: 1,4 + F3: 1,2,4,5,9 + D8: 3,4,7 + F8: 2,4,7 + H7: 8,9 # D3: 7,8 => UNS * DIS F1: 1,4 + F3: 1,2,4,5,9 + D8: 3,4,7 + F8: 2,4,7 + H7: 8,9 # G1: 7,8 => CTR => G1: 1,3 * INC F1: 1,4 + F3: 1,2,4,5,9 + D8: 3,4,7 + F8: 2,4,7 + H7: 8,9 + G1: 1,3 # H1: 7,8 => UNS * INC F1: 1,4 + F3: 1,2,4,5,9 + D8: 3,4,7 + F8: 2,4,7 + H7: 8,9 + G1: 1,3 # H1: 7,8 => UNS * DIS F1: 1,4 + F3: 1,2,4,5,9 + D8: 3,4,7 + F8: 2,4,7 + H7: 8,9 + G1: 1,3 # H1: 3 => CTR => H1: 7,8 * DIS F1: 1,4 + F3: 1,2,4,5,9 + D8: 3,4,7 + F8: 2,4,7 + H7: 8,9 + G1: 1,3 + H1: 7,8 # E8: 7,8 => CTR => E8: 2,5,9 * INC F1: 1,4 + F3: 1,2,4,5,9 + D8: 3,4,7 + F8: 2,4,7 + H7: 8,9 + G1: 1,3 + H1: 7,8 + E8: 2,5,9 # E2: 7,8 => UNS * DIS F1: 1,4 + F3: 1,2,4,5,9 + D8: 3,4,7 + F8: 2,4,7 + H7: 8,9 + G1: 1,3 + H1: 7,8 + E8: 2,5,9 # E2: 2,9 => CTR => E2: 7,8 * PRF F1: 1,4 + F3: 1,2,4,5,9 + D8: 3,4,7 + F8: 2,4,7 + H7: 8,9 + G1: 1,3 + H1: 7,8 + E8: 2,5,9 + E2: 7,8 # F2: 1,4 => SOL * STA F1: 1,4 + F3: 1,2,4,5,9 + D8: 3,4,7 + F8: 2,4,7 + H7: 8,9 + G1: 1,3 + H1: 7,8 + E8: 2,5,9 + E2: 7,8 + F2: 1,4 * CNT 66 HDP CHAINS / 66 HYP OPENED