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 humble_programmer
 Joined: 27 Jun 2006  Posts: 69  :  Location: Colorado Springs, USA  Items 

Posted: Sun Dec 31, 2006 11:49 pm Post subject: A new candidate for "toughest puzzle"? 


This user submission to the "Scanraid Sudoku Solver" web site has a single unique solution, but other than a single hidden pair doesn't seem to have fall to any known solving techniques. It also gives SudoCue and my own slightly braindamaged solver fits. Anyone else want to have a go at it?
Code:  .8..1..7.4....3.....6...2....5..9.8.3.......4.7.6..1....2...6.....5....9.1..8..5.
289416573451273896736895241165349782328157964974628135592734618847561329613982457

This one stops dead after a "Finned Swordfish":
Code:  1....7.9..3..2...8..96..5....53..9...1..8...26....4...3......1..4......7..7...3..
162857493534129678789643521475312986913586742628794135356478219241935867897261354 
_________________ Cheers!
Humble Programmer
,,,^..^,,,
www.humbleprogrammer.com 

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 Thunderwave
 Joined: 03 Jun 2007  Posts: 6  :   Items 

Posted: Sun Jun 03, 2007 11:41 pm Post subject: First Puzzle 


Quote:  Deduction pass 1; 22 squares solved; 59 remaining.
* A set of 2 squares form a simple hidden pair. R2C3 and R3C1 all contain the 2 possibilities <17>. No other squares in block 1 have those possibilities. Since the 2 squares are the only possible locations for 2 possible values, any additional possibilities these squares have (if any) can be eliminated. These squares now become a simple naked pair.
R2C3  removing <9> from <179> leaving <17>.
R3C1  removing <59> from <1579> leaving <17>.
Deduction pass 2; 22 squares solved; 59 remaining.
* Made progress using Trebor's Tables to find inferences about the puzzle. A total of 18475 implications about the puzzle were generated and examined in order to find these inferences  you'd run through several pencils working them out by hand!
The following verities were found (only first verity proving the assertion is shown):
R1C1<>9 (Implied by all valid values of R1C1)
R7C9<>3 (Implied by all valid values of R1C1)
R2C7<>5 (Implied by all valid values of R1C1)
R8C8<>4 (Implied by all valid values of R1C1)
R1C7<>4 (Implied by all valid values of R1C1)
R7C8<>4 (Implied by all valid values of R1C1)
R3C8=4 (Implied by all valid values of R1C1)
R3C8<>1 (Implied by all valid values of R1C1)
R3C8<>3 (Implied by all valid values of R1C1)
R3C8<>9 (Implied by all valid values of R1C1)
R3C4<>4 (Implied by all valid values of R1C1)
R3C5<>4 (Implied by all valid values of R1C1)
R3C6<>4 (Implied by all valid values of R1C1)
R5C7<>7 (Implied by all valid values of R1C1)
R2C9<>8 (Implied by all valid values of R2C4)
R7C9<>7 (Implied by all valid values of R2C8)
R3C9<>5 (Implied by all valid values of R2C9)
R7C1<>7 (Implied by all valid values of R3C2)
R7C1<>9 (Implied by all valid values of R3C2)
R4C1<>2 (Implied by all valid values of R3C2)
R4C4<>4 (Implied by all valid values of R4C4)
R1C6<>5 (Implied by all valid values of R6C9)
R5C3<>9 (Implied by all valid values of R7C1)
R5C8<>2 (Implied by all valid values of R7C9)
R6C9<>3 (Implied by all valid values of R8C5)
R1C7<>3 (Implied by all valid values of R8C5)
R6C1<>2 (Implied by all valid values of R8C5)
R7C1<>8 (Implied by all valid values of R8C5)
R7C9=8 (Implied by all valid values of R8C5)
R7C9<>1 (Implied by all valid values of R8C5)
R3C9<>8 (Implied by all valid values of R8C5)
R8C7<>8 (Implied by all valid values of R8C5)
R2C7=8 (Implied by all valid values of R8C5)
R2C7<>9 (Implied by all valid values of R8C5)
R2C4<>8 (Implied by all valid values of R8C5)
R7C2<>5 (Implied by all valid values of R8C5)
R1C1<>5 (Implied by all valid values of R8C5)
R1C4<>2 (Implied by all valid values of R8C5)
R1C6<>2 (Implied by all valid values of R8C5)
R2C2<>2 (Implied by all valid values of R8C5)
R1C1=2 (Implied by all valid values of R8C5)
R7C1=5 (Implied by all valid values of R8C5)
R8C6<>4 (Implied by all valid values of R8C6)
R8C6<>6 (Implied by all valid values of R8C6)
R2C8<>1 (Implied by all valid values of R9C1)
R8C3<>3 (Implied by all valid values of R9C6)
R9C9<>3 (Implied by all valid values of R9C7)
The following veracities were found (may duplicate verities, above):
R1C1=2 (Implied by at least 2 R8<>1 squares)
R1C1<>5 (Implied by at least 2 R8<>1 squares)
R1C1<>9 (Implied by all R1=2 squares)
R1C4<>2 (Implied by at least 2 R8<>1 squares)
R1C6<>2 (Implied by at least 2 R8<>1 squares)
R1C6<>5 (Implied by all R7=1 squares)
R1C7<>3 (Implied by at least 2 R8<>1 squares)
R1C7<>4 (Implied by all R1=2 squares)
R2C2<>2 (Implied by at least 2 R8<>1 squares)
R2C4<>8 (Implied by at least 2 R8<>1 squares)
R2C7=8 (Implied by at least 2 R8<>1 squares)
R2C7<>5 (Implied by all R1=2 squares)
R2C7<>9 (Implied by at least 2 R8<>1 squares)
R2C8<>1 (Implied by all R9=6 squares)
R2C9<>8 (Implied by all R2=1 squares)
R3C4<>4 (Implied by all R1=2 squares)
R3C5<>4 (Implied by all R1=2 squares)
R3C6<>4 (Implied by all R1=2 squares)
R3C8=4 (Implied by all R1=2 squares)
R3C8<>1 (Implied by all R1=2 squares)
R3C8<>3 (Implied by all R1=2 squares)
R3C8<>9 (Implied by all R1=2 squares)
R3C9<>5 (Implied by all R2=5 squares)
R3C9<>8 (Implied by at least 2 R8<>1 squares)
R4C1<>2 (Implied by at least 2 R3<>1 squares)
R4C4<>4 (Implied by at least 2 R4<>1 squares)
R4C4<>7 (Implied by all R5=7 squares)
R4C5<>7 (Implied by all R5=7 squares)
R5C2<>9 (Implied by all C1=9 squares)
R5C3<>9 (Implied by all R7=1 squares)
R5C7<>7 (Implied by all R1=2 squares)
R5C8<>2 (Implied by all R7=1 squares)
R6C1<>2 (Implied by at least 2 R8<>1 squares)
R6C8<>9 (Implied by all C1=9 squares)
R6C9<>3 (Implied by at least 2 R8<>1 squares)
R7C1=5 (Implied by at least 2 R8<>1 squares)
R7C1<>7 (Implied by at least 2 R3<>1 squares)
R7C1<>8 (Implied by at least 2 R8<>1 squares)
R7C1<>9 (Implied by at least 2 R3<>1 squares)
R7C2<>5 (Implied by at least 2 R8<>1 squares)
R7C8<>4 (Implied by all R1=2 squares)
R7C9=8 (Implied by at least 2 R8<>1 squares)
R7C9<>1 (Implied by at least 2 R8<>1 squares)
R7C9<>3 (Implied by all R1=2 squares)
R7C9<>7 (Implied by all R2=1 squares)
R8C3<>3 (Implied by all R9=2 squares)
R8C5<>7 (Implied by all R7=7 squares)
R8C6<>4 (Implied by all R8=1 squares)
R8C6<>6 (Implied by all R8=1 squares)
R8C6<>7 (Implied by all R7=7 squares)
R8C7<>8 (Implied by at least 2 R8<>1 squares)
R8C8<>4 (Implied by all R1=2 squares)
R9C4<>7 (Implied by all R7=7 squares)
R9C6<>7 (Implied by all R7=7 squares)
R9C9<>3 (Implied by all R9=3 squares)
The following squares can have possibilities eliminated:
R1C4: remove <2> from <249> leaving <49>.
R1C6: remove <25> from <2456> leaving <46>.
R1C7: remove <34> from <3459> leaving <59>.
R2C2: remove <2> from <259> leaving <59>.
R2C4: remove <8> from <2789> leaving <279>.
R2C8: remove <1> from <169> leaving <69>.
R2C9: remove <8> from <1568> leaving <156>.
R3C4: remove <4> from <4789> leaving <789>.
R3C5: remove <4> from <4579> leaving <579>.
R3C6: remove <4> from <4578> leaving <578>.
R3C9: remove <58> from <1358> leaving <13>.
R4C1: remove <2> from <126> leaving <16>.
R4C4: remove <47> from <12347> leaving <123>.
R4C5: remove <7> from <2347> leaving <234>.
R5C2: remove <9> from <269> leaving <26>.
R5C3: remove <9> from <189> leaving <18>.
R5C7: remove <7> from <579> leaving <59>.
R5C8: remove <2> from <269> leaving <69>.
R6C1: remove <2> from <289> leaving <89>.
R6C8: remove <9> from <239> leaving <23>.
R6C9: remove <3> from <235> leaving <25>.
R7C2: remove <5> from <3459> leaving <349>.
R7C8: remove <4> from <134> leaving <13>.
R8C3: remove <3> from <3478> leaving <478>.
R8C5: remove <7> from <23467> leaving <2346>.
R8C6: remove <467> from <12467> leaving <12>.
R8C7: remove <8> from <3478> leaving <347>.
R8C8: remove <4> from <1234> leaving <123>.
R9C4: remove <7> from <23479> leaving <2349>.
R9C6: remove <7> from <2467> leaving <246>.
R9C9: remove <3> from <237> leaving <27>.
The following squares can be solved:
R1C1 = 2
R2C7 = 8
R3C8 = 4
R7C1 = 5
R7C9 = 8
Tabling was terminated after 5 reductions or solves were found...
Deduction pass 3; 27 squares solved; 54 remaining.
* Intersection of row 1 with block 3. The value <5> only appears in one or more of squares R1C7, R1C8 and R1C9 of row 1. These squares are the ones that intersect with block 3. Thus, the other (nonintersecting) squares of block 3 cannot contain this value.
R2C9  removing <5> from <156> leaving <16>.
Deduction pass 4; 27 squares solved; 54 remaining.
* Intersection of block 3 with column 9. The values <13> only appears in one or more of squares R1C9, R2C9 and R3C9 of block 3. These squares are the ones that intersect with column 9. Thus, the other (nonintersecting) squares of column 9 cannot contain these values.
R4C9  removing <3> from <2367> leaving <267>.
Deduction pass 5; 27 squares solved; 54 remaining.
* Found a 5link Simple Forcing Chain. If we assume that square R4C9 is <6> then we can make the following chain of conclusions:
R4C1 must be <1>, which means that
R3C1 must be <7>, which means that
R2C3 must be <1>, which means that
R2C9 must be <6>, which means that
R4C9 can't be <6>.
Since this is logically inconsistent, R4C9 cannot be <6>.
(5 links were considered before finding this chain)
Deduction pass 6; 27 squares solved; 54 remaining.
* R5C8 is the only square in block 6 that can be <6>. It is thus pinned to that value.
From this deduction, the following moves are immediately forced:
R5C2 must be <2>.
R2C8 must be <9>.
R2C2 must be <5>.
R1C7 must be <5>.
R5C7 must be <9>.
Deduction pass 7; 33 squares solved; 48 remaining.
* R6C9 is the only square in column 9 that can be <5>. It is thus pinned to that value.
Deduction pass 8; 34 squares solved; 47 remaining.
* Squares R3C2 and R7C2 in column 2 and R3C5 and R7C5 in column 5 form a Simple XWing pattern on possibility <9>. All other instances of this possibility in rows 3 and 7 can be removed.
R3C4  removing <9> from <789> leaving <78>.
R7C4  removing <9> from <13479> leaving <1347>.
Deduction pass 9; 34 squares solved; 47 remaining.
* Found a 4link Comprehensive Chain. If we assume that square R8C1 is <6> then we can make the following chain of conclusions:
R8C3 must be <8> (R8 pin), which means that
R5C3 must be <1> (force), which means that
R4C1 must be <6> (force), which means that
R8C1 can't be <6> (buddy contradiction).
Since this is logically inconsistent, R8C1 cannot be <6>.
(8 links were considered before finding this chain)
Deduction pass 10; 34 squares solved; 47 remaining.
* Found a 5link Comprehensive Chain. If we assume that square R9C3 is <7> then we can make the following chain of conclusions:
R1C3 must be <3> (C3 pin), which means that
R1C9 must be <6> (force), which means that
R2C9 must be <1> (force), which means that
R2C3 must be <7> (force), which means that
R9C3 can't be <7> (buddy contradiction).
Since this is logically inconsistent, R9C3 cannot be <7>.
(15 links were considered before finding this chain)
Deduction pass 11; 34 squares solved; 47 remaining.
* Found a 5link Comprehensive Chain. If we assume that square R9C4 is <2> then we can make the following chain of conclusions:
R1C4 must be <9> (C4 pin), which means that
R1C6 must be <4> (R1 pin), which means that
R2C5 must be <6> (B2 pin), which means that
R2C4 must be <2> (R2 pin), which means that
R9C4 can't be <2> (buddy contradiction).
Since this is logically inconsistent, R9C4 cannot be <2>.
(15 links were considered before finding this chain)
Deduction pass 12; 34 squares solved; 47 remaining.
* Found a 5link Comprehensive Chain. If we assume that square R6C6 is <2> then we can make the following chain of conclusions:
R6C8 must be <3> (force), which means that
R8C8 must be <2> (C8 pin), which means that
R9C9 must be <7> (force), which means that
R9C6 must be <2> (R9 pin), which means that
R6C6 can't be <2> (buddy contradiction).
Since this is logically inconsistent, R6C6 cannot be <2>.
(24 links were considered before finding this chain)
Deduction pass 13; 34 squares solved; 47 remaining.
* A set of 2 squares form a simple hidden pair. R6C5 and R6C8 all contain the 2 possibilities <23>. No other squares in row 6 have those possibilities. Since the 2 squares are the only possible locations for 2 possible values, any additional possibilities these squares have (if any) can be eliminated. These squares now become a simple naked pair.
R6C5  removing <4> from <234> leaving <23>.
Deduction pass 14; 34 squares solved; 47 remaining.
* Intersection of column 6 with block 8. The value <2> only appears in one or more of squares R7C6, R8C6 and R9C6 of column 6. These squares are the ones that intersect with block 8. Thus, the other (nonintersecting) squares of block 8 cannot contain this value.
R8C5  removing <2> from <2346> leaving <346>.
Deduction pass 15; 34 squares solved; 47 remaining.
* A set of 2 squares form a simple hidden pair. R8C6 and R8C8 all contain the 2 possibilities <12>. No other squares in row 8 have those possibilities. Since the 2 squares are the only possible locations for 2 possible values, any additional possibilities these squares have (if any) can be eliminated. These squares now become a simple naked pair.
R8C8  removing <3> from <123> leaving <12>.
Deduction pass 16; 34 squares solved; 47 remaining.
* Found a 6link Simple Forcing Chain. If we assume that square R6C3 is <9> then we can make the following chain of conclusions:
R6C1 must be <8>, which means that
R6C6 must be <4>, which means that
R1C6 must be <6>, which means that
R1C9 must be <3>, which means that
R1C3 must be <9>, which means that
R6C3 can't be <9>.
Since this is logically inconsistent, R6C3 cannot be <9>.
(7 links were considered before finding this chain)
Deduction pass 17; 34 squares solved; 47 remaining.
* R6C1 is the only square in row 6 that can be <9>. It is thus pinned to that value.
Deduction pass 18; 35 squares solved; 46 remaining.
* R8C1 is the only square in column 1 that can be <8>. It is thus pinned to that value.
Deduction pass 19; 36 squares solved; 45 remaining.
* A set of 2 squares form a simple hidden pair. R1C3 and R9C3 all contain the 2 possibilities <39>. No other squares in column 3 have those possibilities. Since the 2 squares are the only possible locations for 2 possible values, any additional possibilities these squares have (if any) can be eliminated. These squares now become a simple naked pair.
R9C3  removing <4> from <349> leaving <39>.
Deduction pass 20; 36 squares solved; 45 remaining.
* Found a 6link Simple Forcing Chain. If we assume that square R9C6 is <6> then we can make the following chain of conclusions:
R9C1 must be <7>, which means that
R8C3 must be <4>, which means that
R6C3 must be <8>, which means that
R6C6 must be <4>, which means that
R1C6 must be <6>, which means that
R9C6 can't be <6>.
Since this is logically inconsistent, R9C6 cannot be <6>.
(14 links were considered before finding this chain)
Deduction pass 21; 36 squares solved; 45 remaining.
* R9C1 is the only square in row 9 that can be <6>. It is thus pinned to that value.
From this deduction, the following moves are immediately forced:
R4C1 must be <1>.
R3C1 must be <7>.
R5C3 must be <8>.
R6C3 must be <4>.
R6C6 must be <8>.
R8C3 must be <7>.
R4C2 must be <6>.
R2C3 must be <1>.
R2C9 must be <6>.
R1C9 must be <3>.
R3C4 must be <8>.
R3C6 must be <5>.
R3C5 must be <9>.
R1C3 must be <9>.
R3C9 must be <1>.
R3C2 must be <3>.
R1C4 must be <4>.
R9C3 must be <3>.
R1C6 must be <6>.
R8C2 must be <4>.
R8C7 must be <3>.
R7C2 must be <9>.
R8C5 must be <6>.
R4C7 must be <7>.
R7C8 must be <1>.
R9C4 must be <9>.
R4C9 must be <2>.
R9C7 must be <4>.
R4C4 must be <3>.
R9C9 must be <7>.
R6C8 must be <3>.
R6C5 must be <2>.
R8C8 must be <2>.
R8C6 must be <1>.
R9C6 must be <2>.
R4C5 must be <4>.
R7C4 must be <7>.
R2C5 must be <7>.
R7C5 must be <3>.
R7C6 must be <4>.
R2C4 must be <2>.
R5C4 must be <1>.
R5C6 must be <7>.
R5C5 must be <5>.
Deduction pass 22; 81 squares solved; 0 remaining.
Solution found!
Heuristics used:
1 x Trebor's Tables
4 x Comprehensive Forcing Chains
3 x Simple Forcing Chains
1 x Simple XWing
3 x Intersection Removal
4 x Simple Hidden Sets
5 x Pinned Squares
Deduction completed... 
Solved with Sudoku Susser. 

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 Thunderwave
 Joined: 03 Jun 2007  Posts: 6  :   Items 

Posted: Sun Jun 03, 2007 11:43 pm Post subject: 


Second Puzzle
Quote:  Deduction pass 1; 23 squares solved; 58 remaining.
* R8C3 is the only square in column 3 that can be <1>. It is thus pinned to that value.
Deduction pass 2; 24 squares solved; 57 remaining.
* Found a Nishio contradiction. After 4 cycles, it became clear that R7C6 could not be a <9>.
R7C6  removing <9> from <25689> leaving <2568>.
Here is a trace of the Nishio matrix as it was simplified.
# = Squares that must be <9>.
O = squares that can be <9>.
X = the current square (also an "O").
. = squares that cannot be <9>.
 = squares that were invalidated in the previous cycle.
P = the square that invalidated them (also a "#").
@ = the invalid group that cannot contain a <9>.
Nishio cycle 1 on <9> at R7C6
. . . . . . . # .
. . . O . O . . .
. . # . . . . . .
. . . . . . # . .
O . . O . O . . .
. O . O O . . . .
. O . O O X . . O
O . . O O O . . .
O O . O O O . . O
Nishio cycle 2 on <9> at R9C9
. . . . .  . # .
. . . O .  . . .
. . # . .  . . .
. . . . .  # . .
O . . O .  . . .
. O . O O  . . .
     P   
O . .    . . .
O O .    . . X
Nishio cycle 3 on <9> at R8C1
. . . . . . . # 
. . . O . . . . 
. . # . . . . . 
. . . . . . # . 
O . . O . . . . 
. O . O O . . . 
. . . . . #   
X . . . . .   
        P
Nishio cycle 4 on <9> at R6C2
 . . . . . . # .
 . . O . . . . .
 . # . . . . . .
 . . . . . # . .
 . . O . . . . .
 X . O O . . . .
   . . # . . .
P        
   . . . . . #
Final State:
.  . . @ . . # .
.  . O @ . . . .
.  # . @ . . . .
   . @ . # . .
   O @ . . . .
 P   @    
.  . . @ # . . .
#  . . @ . . . .
.  . . @ . . . #
Deduction pass 3; 24 squares solved; 57 remaining.
* Found a Nishio contradiction. After 4 cycles, it became clear that R7C4 could not be a <9>.
R7C4  removing <9> from <245789> leaving <24578>.
Here is a trace of the Nishio matrix as it was simplified.
# = Squares that must be <9>.
O = squares that can be <9>.
X = the current square (also an "O").
. = squares that cannot be <9>.
 = squares that were invalidated in the previous cycle.
P = the square that invalidated them (also a "#").
@ = the invalid group that cannot contain a <9>.
Nishio cycle 1 on <9> at R7C4
. . . . . . . # .
. . . O . O . . .
. . # . . . . . .
. . . . . . # . .
O . . O . O . . .
. O . O O . . . .
. O . X O . . . O
O . . O O O . . .
O O . O O O . . O
Nishio cycle 2 on <9> at R9C9
. . .  . . . # .
. . .  . O . . .
. . #  . . . . .
. . .  . . # . .
O . .  . O . . .
. O .  O . . . .
   P     
O . .    . . .
O O .    . . X
Nishio cycle 3 on <9> at R8C1
. . . . . . . # 
. . . . . O . . 
. . # . . . . . 
. . . . . . # . 
O . . . . O . . 
. O . . O . . . 
. . . # . .   
X . . . . .   
        P
Nishio cycle 4 on <9> at R6C2
 . . . . . . # .
 . . . . O . . .
 . # . . . . . .
 . . . . . # . .
 . . . . O . . .
 X . . O . . . .
   # . . . . .
P        
   . . . . . #
Final State:
.  . . @ . . # .
.  . . @ O . . .
.  # . @ . . . .
   . @ . # . .
   . @ O . . .
 P   @    
.  . # @ . . . .
#  . . @ . . . .
.  . . @ . . . #
Deduction pass 4; 24 squares solved; 57 remaining.
* Found a Nishio contradiction. After 4 cycles, it became clear that R9C4 could not be a <9>.
R9C4  removing <9> from <124589> leaving <12458>.
Here is a trace of the Nishio matrix as it was simplified.
# = Squares that must be <9>.
O = squares that can be <9>.
X = the current square (also an "O").
. = squares that cannot be <9>.
 = squares that were invalidated in the previous cycle.
P = the square that invalidated them (also a "#").
@ = the invalid group that cannot contain a <9>.
Nishio cycle 1 on <9> at R9C4
. . . . . . . # .
. . . O . O . . .
. . # . . . . . .
. . . . . . # . .
O . . O . O . . .
. O . O O . . . .
. O . . O . . . O
O . . O O O . . .
O O . X O O . . O
Nishio cycle 2 on <9> at R7C9
. . .  . . . # .
. . .  . O . . .
. . #  . . . . .
. . .  . . # . .
O . .  . O . . .
. O .  O . . . .
. O .    . . X
O . .    . . .
   P     
Nishio cycle 3 on <9> at R8C1
. . . . . . . # 
. . . . . O . . 
. . # . . . . . 
. . . . . . # . 
O . . . . O . . 
. O . . O . . . 
        P
X . . . . .   
. . . # . .   
Nishio cycle 4 on <9> at R6C2
 . . . . . . # .
 . . . . O . . .
 . # . . . . . .
 . . . . . # . .
 . . . . O . . .
 X . . O . . . .
   . . . . . #
P        
   # . . . . .
Final State:
.  . . @ . . # .
.  . . @ O . . .
.  # . @ . . . .
   . @ . # . .
   . @ O . . .
 P   @    
.  . . @ . . . #
#  . . @ . . . .
.  . # @ . . . .
Deduction pass 5; 24 squares solved; 57 remaining.
* Found a Nishio contradiction. After 4 cycles, it became clear that R9C6 could not be a <9>.
R9C6  removing <9> from <125689> leaving <12568>.
Here is a trace of the Nishio matrix as it was simplified.
# = Squares that must be <9>.
O = squares that can be <9>.
X = the current square (also an "O").
. = squares that cannot be <9>.
 = squares that were invalidated in the previous cycle.
P = the square that invalidated them (also a "#").
@ = the invalid group that cannot contain a <9>.
Nishio cycle 1 on <9> at R9C6
. . . . . . . # .
. . . O . O . . .
. . # . . . . . .
. . . . . . # . .
O . . O . O . . .
. O . O O . . . .
. O . . O . . . O
O . . O O O . . .
O O . . O X . . O
Nishio cycle 2 on <9> at R7C9
. . . . .  . # .
. . . O .  . . .
. . # . .  . . .
. . . . .  # . .
O . . O .  . . .
. O . O O  . . .
. O .    . . X
O . .    . . .
     P   
Nishio cycle 3 on <9> at R8C1
. . . . . . . # 
. . . O . . . . 
. . # . . . . . 
. . . . . . # . 
O . . O . . . . 
. O . O O . . . 
        P
X . . . . .   
. . . . . #   
Nishio cycle 4 on <9> at R6C2
 . . . . . . # .
 . . O . . . . .
 . # . . . . . .
 . . . . . # . .
 . . O . . . . .
 X . O O . . . .
   . . . . . #
P        
   . . # . . .
Final State:
.  . . @ . . # .
.  . O @ . . . .
.  # . @ . . . .
   . @ . # . .
   O @ . . . .
 P   @    
.  . . @ . . . #
#  . . @ . . . .
.  . . @ # . . .
Deduction pass 6; 24 squares solved; 57 remaining.
Heuristics used:
4 x Nishio
1 x Pinned Squares
Deduction completed... 


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 Pat
 Joined: 06 Sep 2006  Posts: 128  :   Items 

Posted: Tue Sep 11, 2007 12:23 pm Post subject: 9.1 and 10.5 


Sudoku Explainer wrote: 
humble_programmer wrote: 
Code: 
.8..1..7.4....3.....6...2....5..9.8.3.......4.7.6..1....2...6.....5....9.1..8..5.

Code: 
. 8 .  . 1 .  . 7 .
4 . .  . . 3  . . .
. . 6  . . .  2 . .
++
. . 5  . . 9  . 8 .
3 . .  . . .  . . 4
. 7 .  6 . .  1 . .
++
. . 2  . . .  6 . .
. . .  5 . .  . . 9
. 1 .  . 8 .  . 5 .


Difficulty: 9.1
57 x Hidden Single
2 x Naked Single
5 x Pointing
2 x Claiming
2 x Naked Pair
4 x Hidden Pair
1 x Turbot Fish
2 x Bidirectional Cycle
8 x Forcing Chain
1 x Nishio Forcing Chains
13 x Region Forcing Chains
5 x Cell Forcing Chains
3 x Dynamic Cell Forcing Chains
6 x Dynamic Contradiction Forcing Chains
4 x Dynamic Region Forcing Chains
humble_programmer wrote: 
Code: 
1....7.9..3..2...8..96..5....53..9...1..8...26....4...3......1..4......7..7...3..

Code: 
1 . .  . . 7  . 9 .
. 3 .  . 2 .  . . 8
. . 9  6 . .  5 . .
++
. . 5  3 . .  9 . .
. 1 .  . 8 .  . . 2
6 . .  . . 4  . . .
++
3 . .  . . .  . 1 .
. 4 .  . . .  . . 7
. . 7  . . .  3 . .


Difficulty: 10.5
54 Hidden Single
2 Direct Hidden Pair
1 Naked Single
6 Pointing
4 Claiming
2 XWing
3 Hidden Pair
1 Unique Rectangle type 2
1 BUG type 1
1 Bidirectional YCycle
3 Forcing Chain
5 Nishio Forcing Chains
6 Region Forcing Chains
21 Dynamic Contradiction Forcing Chains
4 Dynamic Region Forcing Chains
1 Dynamic Double Forcing Chains
8 Dynamic Contradiction Forcing Chains (+)
1 Dynamic Region Forcing Chains (+)
1 Dynamic Region Forcing Chains (+ Forcing Chains)
5 Dynamic Contradiction Forcing Chains (+ Forcing Chains) 


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 onecell
 Joined: 23 Nov 2007  Posts: 1  :  Location: Sandwich, Kent, England  Items 

Posted: Sun Dec 23, 2007 10:39 pm Post subject: The most difficult . . . 


Onecell's bingo call for this one is a 3 in H7. 

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