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A new candidate for "toughest puzzle"?

 
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humble_programmer

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

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PostPosted: Sun Dec 31, 2006 11:49 pm    Post subject: A new candidate for "toughest puzzle"? Reply with quote

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 brain-damaged 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

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Thunderwave

Joined: 03 Jun 2007
Posts: 6
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PostPosted: Sun Jun 03, 2007 11:41 pm    Post subject: First Puzzle Reply with quote

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 (non-intersecting) 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 (non-intersecting) 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 5-link 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 X-Wing 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 4-link 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 5-link 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 5-link 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 5-link 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 (non-intersecting) 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 6-link 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 6-link 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 X-Wing
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
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PostPosted: Sun Jun 03, 2007 11:43 pm    Post subject: Reply with quote

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: 243
:

Items
PostPosted: Tue Sep 11, 2007 12:23 pm    Post subject: 9.1 and 10.5 Reply with quote

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.


      [ 22 clues ]
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..


      [ 23 clues ]
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 X-Wing
    3 Hidden Pair
    1 Unique Rectangle type 2
    1 BUG type 1
    1 Bidirectional Y-Cycle
    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
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Location: Sandwich, Kent, England

Items
PostPosted: Sun Dec 23, 2007 10:39 pm    Post subject: The most difficult . . . Reply with quote

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