Analysis of zz-www.sudokuwiki.org-0152-base.sdk

Contents

Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=152

level: medium

Sudoku from http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=152

position: ..7...2...9..4..5.6..8........3....4..562.1..7....1...9....4..1.1..5..3...3...7.. initial

Autosolve

position: ..75..2...9..4..5.65.8........3.5..4..562.1..7..4.1..597.2345.1.1..5..3.5.3...7.. autosolve
Autosolve

Pair Reduction Variants

Pair Reduction Analysis

Pair Reduction Analysis

The following important HDP chains were detected:

* DIS # E4: 8,9 => CTR => E4: 7
* DIS # G6: 8,9 => CTR => G6: 3,6
* DIS # C8: 6,8 => CTR => C8: 2,4
* DIS # H9: 6,8 => CTR => H9: 4,9
* DIS # I9: 6,8 => CTR => I9: 2,9
* DIS # G8: 6,8 => CTR => G8: 4,9
* DIS # H9: 6,8 => CTR => H9: 4,9
* DIS # I9: 6,8 => CTR => I9: 2,9
* DIS # H1: 6,8 => CTR => H1: 1,4,9
* CNT   9 HDP CHAINS /  32 HYP OPENED

See Appendix: Full HDP Chains for full list of HDP chains.

Pair Reduction

Pair Reduction

The following important HDP chains were detected:

* DIS # E4: 8,9 => CTR => E4: 7
* DIS E4: 7 # G6: 8,9 => CTR => G6: 3,6
* DIS E4: 7 + G6: 3,6 # C8: 6,8 => CTR => C8: 2,4
* DIS E4: 7 + G6: 3,6 + C8: 2,4 # H9: 6,8 => CTR => H9: 4,9
* DIS E4: 7 + G6: 3,6 + C8: 2,4 + H9: 4,9 # I9: 6,8 => CTR => I9: 2,9
* DIS E4: 7 + G6: 3,6 + C8: 2,4 + H9: 4,9 + I9: 2,9 # G8: 6,8 => CTR => G8: 4,9
* DIS E4: 7 + G6: 3,6 + C8: 2,4 + H9: 4,9 + I9: 2,9 + G8: 4,9 # H1: 6,8 => CTR => H1: 1,4,9
* DIS E4: 7 + G6: 3,6 + C8: 2,4 + H9: 4,9 + I9: 2,9 + G8: 4,9 + H1: 1,4,9 # H6: 6,8 => CTR => H6: 2,9
* PRF E4: 7 + G6: 3,6 + C8: 2,4 + H9: 4,9 + I9: 2,9 + G8: 4,9 + H1: 1,4,9 + H6: 2,9 # H4: 2,9 => SOL
* STA E4: 7 + G6: 3,6 + C8: 2,4 + H9: 4,9 + I9: 2,9 + G8: 4,9 + H1: 1,4,9 + H6: 2,9 + H4: 2,9
* CNT   9 HDP CHAINS /  31 HYP OPENED

See Appendix: Full HDP Chains for full list of HDP chains.

Details

Positions

..7...2...9..4..5.6..8........3....4..562.1..7....1...9....4..1.1..5..3...3...7.. initial
..75..2...9..4..5.65.8........3.5..4..562.1..7..4.1..597.2345.1.1..5..3.5.3...7.. autosolve
847563219392147856651892473189375624435629187726481395978234561214756938563918742 solved

Classification

level: medium

Pairing Analysis

--------------------------------------------------
* PAIRS (7)
D2: 1,7
E6: 8,9
C7: 6,8
D8: 7,9
D9: 1,9
F9: 6,8
H7: 6,8

--------------------------------------------------
* CONSTRAINT PAIRS (AUTO SOLVE)
H1,H3: 1.. / H1 = 1  => 11 pairs (_) / H3 = 1  => 12 pairs (_)
A4,C4: 1.. / A4 = 1  =>  7 pairs (_) / C4 = 1  => 14 pairs (_)
D9,E9: 1.. / D9 = 1  => 11 pairs (_) / E9 = 1  =>  9 pairs (_)
D2,D9: 1.. / D2 = 1  =>  9 pairs (_) / D9 = 1  => 11 pairs (_)
F2,F3: 2.. / F2 = 2  =>  9 pairs (_) / F3 = 2  =>  9 pairs (_)
H4,H6: 2.. / H4 = 2  => 11 pairs (_) / H6 = 2  =>  7 pairs (_)
I8,I9: 2.. / I8 = 2  => 16 pairs (_) / I9 = 2  =>  8 pairs (_)
C3,F3: 2.. / C3 = 2  =>  9 pairs (_) / F3 = 2  =>  9 pairs (_)
B9,I9: 2.. / B9 = 2  => 16 pairs (_) / I9 = 2  =>  8 pairs (_)
I5,G6: 3.. / I5 = 3  =>  0 pairs (X) / G6 = 3  => 11 pairs (_)
B6,G6: 3.. / B6 = 3  =>  0 pairs (X) / G6 = 3  => 11 pairs (_)
A5,B5: 4.. / A5 = 4  => 10 pairs (_) / B5 = 4  => 11 pairs (_)
G8,H9: 4.. / G8 = 4  =>  0 pairs (X) / H9 = 4  =>  9 pairs (_)
B9,H9: 4.. / B9 = 4  =>  0 pairs (X) / H9 = 4  =>  9 pairs (_)
C3,C8: 4.. / C3 = 4  =>  0 pairs (X) / C8 = 4  =>  9 pairs (_)
G3,G8: 4.. / G3 = 4  =>  9 pairs (_) / G8 = 4  =>  0 pairs (X)
C7,H7: 6.. / C7 = 6  =>  6 pairs (_) / H7 = 6  =>  8 pairs (_)
E1,E9: 6.. / E1 = 6  =>  9 pairs (_) / E9 = 6  => 12 pairs (_)
E4,F5: 7.. / E4 = 7  =>  9 pairs (_) / F5 = 7  =>  0 pairs (X)
D8,F8: 7.. / D8 = 7  =>  9 pairs (_) / F8 = 7  => 11 pairs (_)
E4,H4: 7.. / E4 = 7  =>  9 pairs (_) / H4 = 7  =>  0 pairs (X)
D2,D8: 7.. / D2 = 7  => 11 pairs (_) / D8 = 7  =>  9 pairs (_)
E3,E4: 7.. / E3 = 7  =>  0 pairs (X) / E4 = 7  =>  9 pairs (_)
C7,H7: 8.. / C7 = 8  =>  8 pairs (_) / H7 = 8  =>  6 pairs (_)
C4,C6: 9.. / C4 = 9  =>  9 pairs (_) / C6 = 9  => 11 pairs (_)
D8,D9: 9.. / D8 = 9  => 11 pairs (_) / D9 = 9  =>  9 pairs (_)
* DURATION: 0:00:33.795908  START: 06:17:56.304723  END: 06:18:30.100631 2017-05-01
* CP COUNT: (26)
* CLUE FOUND

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (C7,D2,D8,D9,E6,F9,H7)
* ..75..2...9..4..5.65.8........3.5..4..562.1..7..4.1..597.2345.1.1..5..3.5.3...7..
* PAIR D2: 1,7 BLK 2
E3: 1,7,9                                # reduction candidate for 1,7
E3: 9                                    # 12 pairs
E3: 1,7                                  #  9 pairs
* PAIR E6: 8,9 BLK 5
E4: 8,9,7                                # reduction candidate for 8,9
E4: 8,9 => CTR
* ..756.2...9.14.65765.87.......3.5.74..56271..7..4.1.2597.2345.1.1.75..3.5.391.7..
E4: 7                                    #  9 pairs
F5: 8,9,7                                # reduction candidate for 8,9
F5: 8,9                                  #  9 pairs
* PAIR E6: 8,9 ROW 6
C6: 8,9,2,6                              # reduction candidate for 8,9
C6: 8,9                                  # 10 pairs
G6: 8,9,3,6                              # reduction candidate for 8,9
G6: 8,9 => CTR
* 3475..2...9..423566528.34.7129375..4485629173736481925978234561214.5..3.5.3...74.
G6: 3,6                                  #  8 pairs
H6: 8,9,2,6                              # reduction candidate for 8,9
H6: 8,9                                  # 17 pairs
* PAIR C7: 6,8 BLK 7
C8: 6,8,2,4                              # reduction candidate for 6,8
C8: 6,8 => CTR
* .875..246.92.468576548729138213956744356271..76948132597.2345.121..5.43.543...7.2
C8: 2,4                                  #  8 pairs
B9: 6,8,2,4                              # reduction candidate for 6,8
B9: 6,8                                  # 13 pairs
* PAIR C7: 6,8 COL C
C4: 6,8,1,2,9                            # reduction candidate for 6,8
C4: 6,8                                  # 14 pairs
C6: 6,8,2,9                              # reduction candidate for 6,8
C6: 6,8                                  # 12 pairs
* PAIR F9: 6,8 BLK 8
F8: 6,8,7                                # reduction candidate for 6,8
F8: 6,8                                  #  9 pairs
E9: 6,8,1                                # reduction candidate for 6,8
E9: 6,8                                  # 11 pairs
* PAIR F9: 6,8 ROW 9
B9: 6,8,2,4                              # reduction candidate for 6,8
B9: 6,8                                  # 13 pairs
H9: 6,8,4,9                              # reduction candidate for 6,8
H9: 6,8 => CTR
* ..756.24..9.14..566548.2.17..1375..44.562.17.7.9481..597.2345.1.1.75.43954391.7.2
H9: 4,9                                  #  8 pairs
I9: 6,8,2,9                              # reduction candidate for 6,8
I9: 6,8 => CTR
* ..756.2...9.14.65.65.8..4.....3.58.4.8562.1..7..4813.5976234581814756932523918746
I9: 2,9                                  #  8 pairs
* PAIR H7: 6,8 BLK 9
G8: 6,8,4,9                              # reduction candidate for 6,8
G8: 6,8 => CTR
* ..75.62...9.742.566528.34.72.1375964..5629178769481325976234581814957632523168749
G8: 4,9                                  #  8 pairs
I8: 6,8,2,9                              # reduction candidate for 6,8
I8: 6,8                                  # 11 pairs
H9: 6,8,4,9                              # reduction candidate for 6,8
H9: 6,8 => CTR
* ..756.24..9.14..566548.2.17..1375..44.562.17.7.9481..597.2345.1.1.75.43954391.7.2
H9: 4,9                                  #  8 pairs
I9: 6,8,2,9                              # reduction candidate for 6,8
I9: 6,8 => CTR
* ..756.2...9.14.65.65.8..4.....3.58.4.8562.1..7..4813.5976234581814756932523918746
I9: 2,9                                  #  8 pairs
* PAIR H7: 6,8 COL H
H1: 6,8,1,4,9                            # reduction candidate for 6,8
H1: 6,8 => CTR
* 1.75..28..9..42.5.6528..41....3.5..4..562.1..7..4.1..5978234561214.56938563918742
H1: 1,4,9                                #  7 pairs
H4: 6,8,2,7,9                            # reduction candidate for 6,8
H4: 6,8                                  # 12 pairs
H6: 6,8,2,9                              # reduction candidate for 6,8
H6: 6,8                                  # 14 pairs
* INCONCLUSIVE
* SAVE PR GRAPH zz-www.sudokuwiki.org-0152-base-pr-000.dot
* REASONING
* DIS # E4: 8,9 => CTR => E4: 7
* DIS # G6: 8,9 => CTR => G6: 3,6
* DIS # C8: 6,8 => CTR => C8: 2,4
* DIS # H9: 6,8 => CTR => H9: 4,9
* DIS # I9: 6,8 => CTR => I9: 2,9
* DIS # G8: 6,8 => CTR => G8: 4,9
* DIS # H9: 6,8 => CTR => H9: 4,9
* DIS # I9: 6,8 => CTR => I9: 2,9
* DIS # H1: 6,8 => CTR => H1: 1,4,9
* CNT   9 HDP CHAINS /  32 HYP OPENED

--------------------------------------------------
* PREPARE PR GRAPH
* PAIR REDUCTION ..
* LEVEL 0 PASS 1 ROUND 1 (AUTO SOLVE) (C7,D2,D8,D9,E6,F9,H7)
* ..75..2...9..4..5.65.8........3.5..4..562.1..7..4.1..597.2345.1.1..5..3.5.3...7..
* PAIR D2: 1,7 BLK 2
E3: 1,7,9                                # reduction candidate for 1,7
E3: 9                                    # 12 pairs
E3: 1,7                                  #  9 pairs
* PAIR E6: 8,9 BLK 5
E4: 8,9,7                                # reduction candidate for 8,9
E4: 8,9 => CTR
* ..756.2...9.14.65765.87.......3.5.74..56271..7..4.1.2597.2345.1.1.75..3.5.391.7..
* RESTART
* PAIR E6: 8,9 ROW 6
C6: 8,9,2,6                              # reduction candidate for 8,9
C6: 8,9                                  # 12 pairs
G6: 8,9,3,6                              # reduction candidate for 8,9
G6: 8,9 => CTR
* 3475.62.8.9..423566528.34.7129375..4485629173736481925978234561.14.5..3.5.3...74.
H6: 8,9,2,6                              # reduction candidate for 8,9
H6: 8,9                                  # 17 pairs
* PAIR RESTART
* PAIR E6: 8,9 ROW 6
C6: 8,9,2,6                              # reduction candidate for 8,9
C6: 8,9                                  # 12 pairs
H6: 8,9,2,6                              # reduction candidate for 8,9
H6: 8,9                                  # 17 pairs
* PAIR C7: 6,8 BLK 7
C8: 6,8,2,4                              # reduction candidate for 6,8
C8: 6,8 => CTR
* ..75..24..92.4..5.654892317..13759.44.56291737394.1..597.2345.121..5.43.543...7.2
B9: 6,8,2,4                              # reduction candidate for 6,8
B9: 6,8                                  # 19 pairs
* RESTART
* PAIR C7: 6,8 BLK 7
B9: 6,8,2,4                              # reduction candidate for 6,8
B9: 6,8                                  # 19 pairs
B9: 2,4                                  # 14 pairs
* PAIR C7: 6,8 COL C
C4: 6,8,1,2,9                            # reduction candidate for 6,8
C4: 6,8                                  # 15 pairs
C6: 6,8,2,9                              # reduction candidate for 6,8
C6: 6,8                                  # 16 pairs
* PAIR F9: 6,8 BLK 8
F8: 6,8,7                                # reduction candidate for 6,8
F8: 6,8                                  # 18 pairs
E9: 6,8,1                                # reduction candidate for 6,8
E9: 6,8                                  # 30 pairs
* PAIR F9: 6,8 ROW 9
B9: 6,8,2,4                              # reduction candidate for 6,8
B9: 6,8                                  # 19 pairs
H9: 6,8,4,9                              # reduction candidate for 6,8
H9: 6,8 => CTR
* ..756.24.29.147.56654892......375..44.562.1..7..4.1..5976234581812.5.439543918762
I9: 6,8,2,9                              # reduction candidate for 6,8
I9: 6,8 => CTR
* ..756.2...9.14.65.65.89.4.....3758.4.856291737..4.1..5976234581814.5.932523918746
* RESTART
* PAIR F9: 6,8 ROW 9
B9: 6,8,2,4                              # reduction candidate for 6,8
B9: 2,4                                  # 30 pairs
B9: 6,8                                  # 19 pairs
* PAIR RESTART
* PAIR F9: 6,8 BLK 8
F8: 6,8,7                                # reduction candidate for 6,8
F8: 6,8                                  # 19 pairs
E9: 6,8,1                                # reduction candidate for 6,8
E9: 6,8                                  # 30 pairs
* PAIR F9: 6,8 ROW 9
B9: 6,8,2,4                              # reduction candidate for 6,8
B9: 2,4                                  # 30 pairs
B9: 6,8                                  # 19 pairs
* PAIR H7: 6,8 BLK 9
G8: 6,8,4,9                              # reduction candidate for 6,8
G8: 6,8 => CTR
* .875.62.33917428566528.34.7...3759.4..56291787.94813.5976234581814957632523168749
* RESTART
* PAIR H7: 6,8 COL H
H1: 6,8,1,4,9                            # reduction candidate for 6,8
H1: 6,8 => CTR
* 14756328939814265765.89.41....375..4..562917.7..481..597.2345.1.14.5.93.5.391.742
H4: 6,8,2,9                              # reduction candidate for 6,8
H4: 6,8                                  # 17 pairs
H6: 6,8,2,9                              # reduction candidate for 6,8
H6: 6,8 => CTR
* .8756.21.291.4..5.65.81....169375824..56281..728491365976234581812.57436543186792
* RESTART
* PAIR H7: 6,8 COL H
H4: 6,8,2,9                              # reduction candidate for 6,8
H4: 2,9 => SOLVED
* 847563219392147856651892473189375624435629187726481395978234561214756938563918742
* DURATION: 0:00:30.110523  START: 06:18:53.473895  END: 06:19:23.584418 2017-05-01
* SOLUTION FOUND
* SAVE PR GRAPH zz-www.sudokuwiki.org-0152-base-pr-001.dot
* REASONING
* DIS # E4: 8,9 => CTR => E4: 7
* DIS E4: 7 # G6: 8,9 => CTR => G6: 3,6
* DIS E4: 7 + G6: 3,6 # C8: 6,8 => CTR => C8: 2,4
* DIS E4: 7 + G6: 3,6 + C8: 2,4 # H9: 6,8 => CTR => H9: 4,9
* DIS E4: 7 + G6: 3,6 + C8: 2,4 + H9: 4,9 # I9: 6,8 => CTR => I9: 2,9
* DIS E4: 7 + G6: 3,6 + C8: 2,4 + H9: 4,9 + I9: 2,9 # G8: 6,8 => CTR => G8: 4,9
* DIS E4: 7 + G6: 3,6 + C8: 2,4 + H9: 4,9 + I9: 2,9 + G8: 4,9 # H1: 6,8 => CTR => H1: 1,4,9
* DIS E4: 7 + G6: 3,6 + C8: 2,4 + H9: 4,9 + I9: 2,9 + G8: 4,9 + H1: 1,4,9 # H6: 6,8 => CTR => H6: 2,9
* PRF E4: 7 + G6: 3,6 + C8: 2,4 + H9: 4,9 + I9: 2,9 + G8: 4,9 + H1: 1,4,9 + H6: 2,9 # H4: 2,9 => SOL
* STA E4: 7 + G6: 3,6 + C8: 2,4 + H9: 4,9 + I9: 2,9 + G8: 4,9 + H1: 1,4,9 + H6: 2,9 + H4: 2,9
* CNT   9 HDP CHAINS /  31 HYP OPENED

Header Info

http://www.sudokuwiki.org/Print_Weekly_Sudoku.asp?unsolvable=152

Solution

position: 847563219392147856651892473189375624435629187726481395978234561214756938563918742 solved
Solution

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 # E3: 1,7 => UNS
* INC # E3: 9 => UNS
* DIS # E4: 8,9 => CTR => E4: 7
* INC # E4: 7 => UNS
* INC # F5: 8,9 => UNS
* INC # C6: 8,9 => UNS
* DIS # G6: 8,9 => CTR => G6: 3,6
* INC # G6: 3,6 => UNS
* INC # H6: 8,9 => UNS
* DIS # C8: 6,8 => CTR => C8: 2,4
* INC # C8: 2,4 => UNS
* INC # B9: 6,8 => UNS
* INC # C4: 6,8 => UNS
* INC # C6: 6,8 => UNS
* INC # F8: 6,8 => UNS
* INC # E9: 6,8 => UNS
* INC # B9: 6,8 => UNS
* DIS # H9: 6,8 => CTR => H9: 4,9
* INC # H9: 4,9 => UNS
* DIS # I9: 6,8 => CTR => I9: 2,9
* INC # I9: 2,9 => UNS
* DIS # G8: 6,8 => CTR => G8: 4,9
* INC # G8: 4,9 => UNS
* INC # I8: 6,8 => UNS
* DIS # H9: 6,8 => CTR => H9: 4,9
* INC # H9: 4,9 => UNS
* DIS # I9: 6,8 => CTR => I9: 2,9
* INC # I9: 2,9 => UNS
* DIS # H1: 6,8 => CTR => H1: 1,4,9
* INC # H1: 1,4,9 => UNS
* INC # H4: 6,8 => UNS
* INC # H6: 6,8 => UNS
* CNT  32 HDP CHAINS /  32 HYP OPENED

A2. Pair Reduction

Full list of HDP chains traversed:

* INC # E3: 1,7 => UNS
* INC # E3: 9 => UNS
* DIS # E4: 8,9 => CTR => E4: 7
* INC E4: 7 # C6: 8,9 => UNS
* DIS E4: 7 # G6: 8,9 => CTR => G6: 3,6
* INC E4: 7 + G6: 3,6 # H6: 8,9 => UNS
* INC E4: 7 + G6: 3,6 # C6: 8,9 => UNS
* INC E4: 7 + G6: 3,6 # H6: 8,9 => UNS
* DIS E4: 7 + G6: 3,6 # C8: 6,8 => CTR => C8: 2,4
* INC E4: 7 + G6: 3,6 + C8: 2,4 # B9: 6,8 => UNS
* INC E4: 7 + G6: 3,6 + C8: 2,4 # B9: 6,8 => UNS
* INC E4: 7 + G6: 3,6 + C8: 2,4 # B9: 2,4 => UNS
* INC E4: 7 + G6: 3,6 + C8: 2,4 # C4: 6,8 => UNS
* INC E4: 7 + G6: 3,6 + C8: 2,4 # C6: 6,8 => UNS
* INC E4: 7 + G6: 3,6 + C8: 2,4 # F8: 6,8 => UNS
* INC E4: 7 + G6: 3,6 + C8: 2,4 # E9: 6,8 => UNS
* INC E4: 7 + G6: 3,6 + C8: 2,4 # B9: 6,8 => UNS
* DIS E4: 7 + G6: 3,6 + C8: 2,4 # H9: 6,8 => CTR => H9: 4,9
* DIS E4: 7 + G6: 3,6 + C8: 2,4 + H9: 4,9 # I9: 6,8 => CTR => I9: 2,9
* INC E4: 7 + G6: 3,6 + C8: 2,4 + H9: 4,9 + I9: 2,9 # B9: 6,8 => UNS
* INC E4: 7 + G6: 3,6 + C8: 2,4 + H9: 4,9 + I9: 2,9 # B9: 2,4 => UNS
* INC E4: 7 + G6: 3,6 + C8: 2,4 + H9: 4,9 + I9: 2,9 # F8: 6,8 => UNS
* INC E4: 7 + G6: 3,6 + C8: 2,4 + H9: 4,9 + I9: 2,9 # E9: 6,8 => UNS
* INC E4: 7 + G6: 3,6 + C8: 2,4 + H9: 4,9 + I9: 2,9 # B9: 6,8 => UNS
* INC E4: 7 + G6: 3,6 + C8: 2,4 + H9: 4,9 + I9: 2,9 # B9: 2,4 => UNS
* DIS E4: 7 + G6: 3,6 + C8: 2,4 + H9: 4,9 + I9: 2,9 # G8: 6,8 => CTR => G8: 4,9
* DIS E4: 7 + G6: 3,6 + C8: 2,4 + H9: 4,9 + I9: 2,9 + G8: 4,9 # H1: 6,8 => CTR => H1: 1,4,9
* INC E4: 7 + G6: 3,6 + C8: 2,4 + H9: 4,9 + I9: 2,9 + G8: 4,9 + H1: 1,4,9 # H4: 6,8 => UNS
* DIS E4: 7 + G6: 3,6 + C8: 2,4 + H9: 4,9 + I9: 2,9 + G8: 4,9 + H1: 1,4,9 # H6: 6,8 => CTR => H6: 2,9
* INC E4: 7 + G6: 3,6 + C8: 2,4 + H9: 4,9 + I9: 2,9 + G8: 4,9 + H1: 1,4,9 + H6: 2,9 # H4: 6,8 => UNS
* PRF E4: 7 + G6: 3,6 + C8: 2,4 + H9: 4,9 + I9: 2,9 + G8: 4,9 + H1: 1,4,9 + H6: 2,9 # H4: 2,9 => SOL
* STA E4: 7 + G6: 3,6 + C8: 2,4 + H9: 4,9 + I9: 2,9 + G8: 4,9 + H1: 1,4,9 + H6: 2,9 + H4: 2,9
* CNT  31 HDP CHAINS /  31 HYP OPENED