Analysis of xx-top95-076-base.sdk
Contents
Original Sudoku
level: medium
position: ....1.78.5....9..........4..2..........6....3.74.8.........3..2.8..4..1.6..5..... initial
Autosolve
position: 2.9.1.78.5487.9...7.18.2.4..26..7..889562..73.74.8....457193862983246517612578..4 autosolve
Pair Reduction Variants
Pair Reduction Analysis
The following important HDP chains were detected:
* DIS # E3: 3,6 => CTR => E3: 5 * PRF # E3: 5 => SOL * PRF # G3: 3,6 => SOL * DIS # G3: 9 => CTR => G3: 3,6 * PRF # D4: 3,4 => SOL * DIS # D4: 9 => CTR => D4: 3,4 * DIS # E3: 3,6 => CTR => E3: 5 * PRF # E3: 5 => SOL * DIS # G2: 3,6 => CTR => G2: 1,2 * DIS # I3: 5,6 => CTR => I3: 9 * PRF # I3: 9 => SOL * DIS # G2: 1,6 => CTR => G2: 2,3 * DIS # G2: 1,6 => CTR => G2: 2,3 * PRF # I6: 1,6 => SOL * DIS # I6: 9 => CTR => I6: 1,6 * DIS # E3: 6 => CTR => E3: 3,5 * DIS # D4: 3,9 => CTR => D4: 4 * PRF # D4: 4 => SOL * DIS # H6: 5,9 => CTR => H6: 2 * PRF # H6: 2 => SOL * PRF # G4: 9 => SOL * PRF # G3: 6 => SOL * CNT 22 HDP CHAINS / 28 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Pair Reduction
The following important HDP chains were detected:
* DIS # E3: 3,6 => CTR => E3: 5 * PRF E3: 5 => SOL * STA E3: 5 * CNT 2 HDP CHAINS / 1 HYP OPENED
See Appendix: Full HDP Chains for full list of HDP chains.
Details
Positions
| ....1.78.5....9..........4..2..........6....3.74.8.........3..2.8..4..1.6..5..... | initial |
| 2.9.1.78.5487.9...7.18.2.4..26..7..889562..73.74.8....457193862983246517612578..4 | autosolve |
| 269314785548769231731852649126437958895621473374985126457193862983246517612578394 | solved |
Classification
level: medium
Pairing Analysis
-------------------------------------------------- * PAIRS (18) B1: 3,6 B3: 3,6 D1: 3,4 F1: 4,5 E2: 3,6 I1: 5,6 H2: 2,3 I2: 1,6 A4: 1,3 A6: 1,3 E4: 3,5 F5: 1,4 D6: 3,9 F6: 1,5 H4: 5,9 G5: 1,4 G9: 3,9 H9: 3,9 -------------------------------------------------- * CONSTRAINT PAIRS (AUTO SOLVE) G2,I2: 1.. / G2 = 1 => 0 pairs (X) / I2 = 1 => 18 pairs (_) A4,A6: 1.. / A4 = 1 => 0 pairs (*) / A6 = 1 => 0 pairs (X) F5,F6: 1.. / F5 = 1 => 0 pairs (*) / F6 = 1 => 0 pairs (X) A4,G4: 1.. / A4 = 1 => 0 pairs (*) / G4 = 1 => 0 pairs (X) F5,G5: 1.. / F5 = 1 => 0 pairs (*) / G5 = 1 => 0 pairs (X) I2,I6: 1.. / I2 = 1 => 18 pairs (_) / I6 = 1 => 0 pairs (X) G2,H2: 2.. / G2 = 2 => 0 pairs (*) / H2 = 2 => 0 pairs (X) G6,H6: 2.. / G6 = 2 => 0 pairs (X) / H6 = 2 => 0 pairs (_) G2,G6: 2.. / G2 = 2 => 0 pairs (*) / G6 = 2 => 0 pairs (X) H2,H6: 2.. / H2 = 2 => 0 pairs (X) / H6 = 2 => 0 pairs (_) B1,B3: 3.. / B1 = 3 => 0 pairs (X) / B3 = 3 => 0 pairs (_) A4,A6: 3.. / A4 = 3 => 0 pairs (X) / A6 = 3 => 0 pairs (_) G9,H9: 3.. / G9 = 3 => 0 pairs (*) / H9 = 3 => 0 pairs (X) B1,D1: 3.. / B1 = 3 => 0 pairs (X) / D1 = 3 => 0 pairs (_) A6,D6: 3.. / A6 = 3 => 0 pairs (*) / D6 = 3 => 0 pairs (X) H2,H9: 3.. / H2 = 3 => 0 pairs (*) / H9 = 3 => 0 pairs (X) D1,F1: 4.. / D1 = 4 => 0 pairs (X) / F1 = 4 => 0 pairs (_) D4,F5: 4.. / D4 = 4 => 0 pairs (*) / F5 = 4 => 0 pairs (X) G4,G5: 4.. / G4 = 4 => 0 pairs (X) / G5 = 4 => 0 pairs (_) D4,G4: 4.. / D4 = 4 => 0 pairs (*) / G4 = 4 => 0 pairs (X) F5,G5: 4.. / F5 = 4 => 0 pairs (X) / G5 = 4 => 0 pairs (_) D1,D4: 4.. / D1 = 4 => 0 pairs (X) / D4 = 4 => 0 pairs (_) F1,F5: 4.. / F1 = 4 => 0 pairs (*) / F5 = 4 => 0 pairs (X) F1,E3: 5.. / F1 = 5 => 0 pairs (X) / E3 = 5 => 0 pairs (_) I1,I3: 5.. / I1 = 5 => 0 pairs (*) / I3 = 5 => 0 pairs (X) E4,F6: 5.. / E4 = 5 => 0 pairs (X) / F6 = 5 => 0 pairs (_) H4,H6: 5.. / H4 = 5 => 0 pairs (*) / H6 = 5 => 0 pairs (X) F1,I1: 5.. / F1 = 5 => 0 pairs (X) / I1 = 5 => 0 pairs (_) E3,I3: 5.. / E3 = 5 => 0 pairs (*) / I3 = 5 => 0 pairs (X) E4,H4: 5.. / E4 = 5 => 0 pairs (X) / H4 = 5 => 0 pairs (_) F6,H6: 5.. / F6 = 5 => 0 pairs (*) / H6 = 5 => 0 pairs (X) E3,E4: 5.. / E3 = 5 => 0 pairs (*) / E4 = 5 => 0 pairs (X) F1,F6: 5.. / F1 = 5 => 0 pairs (X) / F6 = 5 => 0 pairs (_) B1,B3: 6.. / B1 = 6 => 0 pairs (*) / B3 = 6 => 0 pairs (X) E2,E3: 6.. / E2 = 6 => 20 pairs (_) / E3 = 6 => 0 pairs (X) G6,I6: 6.. / G6 = 6 => 0 pairs (X) / I6 = 6 => 0 pairs (_) B1,I1: 6.. / B1 = 6 => 0 pairs (*) / I1 = 6 => 0 pairs (X) G3,I3: 9.. / G3 = 9 => 0 pairs (X) / I3 = 9 => 0 pairs (_) D4,D6: 9.. / D4 = 9 => 0 pairs (X) / D6 = 9 => 0 pairs (_) G9,H9: 9.. / G9 = 9 => 0 pairs (X) / H9 = 9 => 0 pairs (_) I3,I6: 9.. / I3 = 9 => 0 pairs (*) / I6 = 9 => 0 pairs (X) * DURATION: 0:01:52.369644 START: 00:39:44.520192 END: 00:41:36.889836 2017-05-04 * CP COUNT: (41) * SOLUTION FOUND -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,A6,B1,B3,D1,D6,E2,E4,F1,F5,F6,G5,G9,H2,H4,H9,I1,I2) * 2.9.1.78.5487.9...7.18.2.4..26..7..889562..73.74.8....457193862983246517612578..4 * PAIR B3: 3,6 ROW 3 E3: 3,6,5 # reduction candidate for 3,6 E3: 3,6 => CTR * 2.9.15786548769..1761832945.26.57.9889562..73.74.8....457193862983246517612578..4 E3: 5 => SOLVED * 269314785548769231731852649126437958895621473374985126457193862983246517612578394 G3: 3,6,9 # reduction candidate for 3,6 G3: 3,6 => SOLVED * 269314785548769231731852649126437958895621473374985126457193862983246517612578394 G3: 9 => CTR * 2.9.1.78.5487.9.317.18.294..269.7458895624173.7438...9457193862983246517612578394 * PAIR D1: 3,4 COL D D4: 3,4,9 # reduction candidate for 3,4 D4: 3,4 => SOLVED * 269314785548769231731852649126437958895621473374985126457193862983246517612578394 D4: 9 => CTR * 2.9415786548769..17618329453269.7..889562..73.74.8....457193862983246517612578..4 * PAIR E2: 3,6 BLK 2 E3: 3,6,5 # reduction candidate for 3,6 E3: 3,6 => CTR * 2.9.15786548769..1761832945.26.57.9889562..73.74.8....457193862983246517612578..4 E3: 5 => SOLVED * 269314785548769231731852649126437958895621473374985126457193862983246517612578394 * PAIR E2: 3,6 ROW 2 G2: 3,6,1,2 # reduction candidate for 3,6 G2: 3,6 => CTR * 269314785548769321731852649.26437.58895621473.74.8.2.6457193862983246517612578.34 G2: 1,2 # 19 pairs * PAIR I1: 5,6 BLK 3 I3: 5,6,9 # reduction candidate for 5,6 I3: 5,6 => CTR * 2.9.1.78.5487.9.317.18.294..269.7458895624173.7438...9457193862983246517612578394 I3: 9 => SOLVED * 269314785548769231731852649126437958895621473374985126457193862983246517612578394 * PAIR H2: 2,3 BLK 3 G2: 2,3,1,6 # reduction candidate for 2,3 G2: 1,6 => CTR * 2.9.1.78.5487.9.2.7.18.2349.26..7..889562..73.74.8.2.6457193862983246517612578934 G2: 2,3 # 20 pairs * PAIR I2: 1,6 BLK 3 G2: 1,6,2,3 # reduction candidate for 1,6 G2: 1,6 => CTR * 2.9.1.78.5487.9.2.7.18.2349.26..7..889562..73.74.8.2.6457193862983246517612578934 G2: 2,3 # 20 pairs * PAIR I2: 1,6 COL I I6: 1,6,9 # reduction candidate for 1,6 I6: 1,6 => SOLVED * 269314785548769231731852649126437958895621473374985126457193862983246517612578394 I6: 9 => CTR * 2.9.1.78.5487692317.18.294..269.7458895624173.7438.629457193862983246517612578.94 * PAIR E4: 3,5 COL E E3: 3,5,6 # reduction candidate for 3,5 E3: 6 => CTR * 2.9.15786548769...7.18.2.4..26..7..889562..73.74.8....457193862983246517612578..4 E3: 3,5 # 20 pairs * PAIR D6: 3,9 BLK 5 D4: 3,9,4 # reduction candidate for 3,9 D4: 3,9 => CTR * 2.9415786548769..1761832945.26.5749889562..73.74.8....457193862983246517612578..4 D4: 4 => SOLVED * 269314785548769231731852649126437958895621473374985126457193862983246517612578394 * PAIR H4: 5,9 BLK 6 H6: 5,9,2 # reduction candidate for 5,9 H6: 5,9 => CTR * 269314785548769321731852649.26437.58895621473.74.8.2.6457193862983246517612578.34 H6: 2 => SOLVED * 269314785548769231731852649126437958895621473374985126457193862983246517612578394 * PAIR G5: 1,4 BLK 6 G4: 1,4,9 # reduction candidate for 1,4 G4: 9 => SOLVED * 269314785548769231731852649126437958895621473374985126457193862983246517612578394 G4: 1,4 # 19 pairs * PAIR G9: 3,9 COL G G3: 3,9,6 # reduction candidate for 3,9 G3: 6 => SOLVED * 269314785548769231731852649126437958895621473374985126457193862983246517612578394 G3: 3,9 # 22 pairs * INCONCLUSIVE * SAVE PR GRAPH xx-top95-076-base-pr-000.dot * REASONING * DIS # E3: 3,6 => CTR => E3: 5 * PRF # E3: 5 => SOL * PRF # G3: 3,6 => SOL * DIS # G3: 9 => CTR => G3: 3,6 * PRF # D4: 3,4 => SOL * DIS # D4: 9 => CTR => D4: 3,4 * DIS # E3: 3,6 => CTR => E3: 5 * PRF # E3: 5 => SOL * DIS # G2: 3,6 => CTR => G2: 1,2 * DIS # I3: 5,6 => CTR => I3: 9 * PRF # I3: 9 => SOL * DIS # G2: 1,6 => CTR => G2: 2,3 * DIS # G2: 1,6 => CTR => G2: 2,3 * PRF # I6: 1,6 => SOL * DIS # I6: 9 => CTR => I6: 1,6 * DIS # E3: 6 => CTR => E3: 3,5 * DIS # D4: 3,9 => CTR => D4: 4 * PRF # D4: 4 => SOL * DIS # H6: 5,9 => CTR => H6: 2 * PRF # H6: 2 => SOL * PRF # G4: 9 => SOL * PRF # G3: 6 => SOL * CNT 22 HDP CHAINS / 28 HYP OPENED -------------------------------------------------- * PREPARE PR GRAPH * PAIR REDUCTION .. * LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (A4,A6,B1,B3,D1,D6,E2,E4,F1,F5,F6,G5,G9,H2,H4,H9,I1,I2) * 2.9.1.78.5487.9...7.18.2.4..26..7..889562..73.74.8....457193862983246517612578..4 * PAIR B3: 3,6 ROW 3 E3: 3,6,5 # reduction candidate for 3,6 E3: 3,6 => CTR * 2.9.15786548769..1761832945.26.57.9889562..73.74.8....457193862983246517612578..4 E3: 5 => SOLVED * 269314785548769231731852649126437958895621473374985126457193862983246517612578394 * DURATION: 0:00:02.346315 START: 00:42:28.082482 END: 00:42:30.428797 2017-05-04 * SOLUTION FOUND * SAVE PR GRAPH xx-top95-076-base-pr-001.dot * REASONING * DIS # E3: 3,6 => CTR => E3: 5 * PRF E3: 5 => SOL * STA E3: 5 * CNT 2 HDP CHAINS / 1 HYP OPENED
Header Info
Top 95 Sudokus 076 [sudoku:top95] “95 Hard Puzzles”, http://magictour.free.fr/top95, or http://norvig.com/top95.txt
Solution
position: 269314785548769231731852649126437958895621473374985126457193862983246517612578394 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 # E3: 3,6 => CTR => E3: 5 * PRF # E3: 5 => SOL * PRF # G3: 3,6 => SOL * DIS # G3: 9 => CTR => G3: 3,6 * PRF # D4: 3,4 => SOL * DIS # D4: 9 => CTR => D4: 3,4 * DIS # E3: 3,6 => CTR => E3: 5 * PRF # E3: 5 => SOL * DIS # G2: 3,6 => CTR => G2: 1,2 * INC # G2: 1,2 => UNS * DIS # I3: 5,6 => CTR => I3: 9 * PRF # I3: 9 => SOL * INC # G2: 2,3 => UNS * DIS # G2: 1,6 => CTR => G2: 2,3 * DIS # G2: 1,6 => CTR => G2: 2,3 * INC # G2: 2,3 => UNS * PRF # I6: 1,6 => SOL * DIS # I6: 9 => CTR => I6: 1,6 * INC # E3: 3,5 => UNS * DIS # E3: 6 => CTR => E3: 3,5 * DIS # D4: 3,9 => CTR => D4: 4 * PRF # D4: 4 => SOL * DIS # H6: 5,9 => CTR => H6: 2 * PRF # H6: 2 => SOL * INC # G4: 1,4 => UNS * PRF # G4: 9 => SOL * INC # G3: 3,9 => UNS * PRF # G3: 6 => SOL * CNT 28 HDP CHAINS / 28 HYP OPENED
A2. Pair Reduction
Full list of HDP chains traversed:
* DIS # E3: 3,6 => CTR => E3: 5 * PRF E3: 5 => SOL * STA E3: 5 * CNT 2 HDP CHAINS / 1 HYP OPENED