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Free Press February 24, 2012

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keith

Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA

Posted: Sat Feb 25, 2012 2:59 pm Post subject: Free Press February 24, 2012

Not yet completed.

Code:

Puzzle: FP022412
+-------+-------+-------+
| 4 . . | . . 5 | . . 9 |
| . 1 . | . 6 . | . . . |
| . . . | 9 . . | . 1 2 |
+-------+-------+-------+
| . 2 . | . 3 . | 9 6 . |
| . . . | . . . | . . . |
| . 6 5 | . 4 . | 3 2 . |
+-------+-------+-------+
| 1 7 . | . . 9 | . . . |
| . . 3 | . 7 . | . . . |
| 2 . . | 4 . . | . . 6 |
+-------+-------+-------+

Play this puzzle online at the Daily Sudoku site

Keith

tlanglet

Joined: 17 Oct 2007
Posts: 2468
Location: Northern California Foothills

Posted: Sat Feb 25, 2012 3:34 pm Post subject:

A finned x-wing(4)r47c39 or skyscraper(4)r48c9 does the deed. Ted

Marty R.

Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA

Posted: Sat Feb 25, 2012 5:54 pm Post subject:

This grid was looking fairly hopeless until I spotted the Finned X-Wing, after which I looked no more.

keith

Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA

Posted: Sat Feb 25, 2012 6:02 pm Post subject:

Marty R. wrote:

This grid was looking fairly hopeless until I spotted the Finned X-Wing, after which I looked no more.

Sudoku Susser does not do skyscrapers. It required 13 chains!

Quote:

10 x Comprehensive Forcing Chains
3 x Simple Forcing Chains
1 x Simple X-Wing
3 x Intersection Removal
2 x Simple Hidden Sets
1 x Simple Naked Sets
9 x Pinned Squares

More steps than Marty! Razz

Keith

Marty R.

Joined: 12 Feb 2006
Posts: 5770
Location: Rochester, NY, USA

Posted: Sat Feb 25, 2012 6:15 pm Post subject:

Quote:

More steps than Marty!

Well, you don't get to see the solutions to 95% of my puzzles, which is just as well, as it could be highly embarrassing. Embarassed

daj95376

Joined: 23 Aug 2008
Posts: 3854

Posted: Sat Feb 25, 2012 8:23 pm Post subject:

keith wrote:

Sudoku Susser does not do skyscrapers. It required 13 chains!

Code:

10 x Comprehensive Forcing Chains
3 x Simple Forcing Chains
1 x Simple X-Wing
3 x Intersection Removal
2 x Simple Hidden Sets
1 x Simple Naked Sets
9 x Pinned Squares

Apparently, Sudoku Susser doesn't optimize its chain search. Otherwise, it would have found these two chains at the start.

Code:

after basics
+-----------------------------------------------------------------------+
| 4 38 2 | 37 1 5 | 6 378 9 |
| 3578 1 9 | 237 6 2347 | 4578 34578 34578 |
| 3567 35 67 | 9 8 347 | 457 1 2 |
|-----------------------+-----------------------+-----------------------|
| 78 2 147 | 5 3 178 | 9 6 1478 |
| 378 348 147 | 26 9 26 | 14578 4578 14578 |
| 9 6 5 | 178 4 178 | 3 2 178 |
|-----------------------+-----------------------+-----------------------|
| 1 7 46 | 368 2 9 | 458 3458 3458 |
| 56 45 3 | 168 7 168 | 2 9 148 |
| 2 9 8 | 4 5 13 | 17 37 6 |
+-----------------------------------------------------------------------+
# 87 eliminations remain

Skyscraper: (4)r4c3 = r4c9 - r8c9 = (4)r8c2 => r5c2,r7c3<>4 -or-
2-String Kite: (4)r8c2 = r7c3 - r4c3 = (4)r4c9 => r8c9<>4

keith

Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA

Posted: Sat Feb 25, 2012 10:01 pm Post subject:

SS finds XY chains and what it calls "Comprehensive Chains". Here is its solution:

Quote:

Deduction pass 1; 25 squares solved; 56 remaining.

* The following immediate observations can be made:

R3C5 must be <8>.

Deduction pass 2; 26 squares solved; 55 remaining.

* R6C1 is the only square in row 6 that can be <9>. It is thus pinned to that value.

Deduction pass 3; 27 squares solved; 54 remaining.

* R2C3 is the only square in row 2 that can be <9>. It is thus pinned to that value.

From this deduction, the following moves are immediately forced:

R9C3 must be <8>.

Deduction pass 4; 29 squares solved; 52 remaining.

* R5C5 is the only square in row 5 that can be <9>. It is thus pinned to that value.

Deduction pass 5; 30 squares solved; 51 remaining.

* R1C3 is the only square in column 3 that can be <2>. It is thus pinned to that value.

From this deduction, the following moves are immediately forced:

R1C5 must be <1>.
R9C5 must be <5>.
R9C2 must be <9>.
R7C5 must be <2>.

Deduction pass 6; 35 squares solved; 46 remaining.

* R1C7 is the only square in row 1 that can be <6>. It is thus pinned to that value.

Deduction pass 7; 36 squares solved; 45 remaining.

* R8C7 is the only square in row 8 that can be <2>. It is thus pinned to that value.

Deduction pass 8; 37 squares solved; 44 remaining.

* R8C8 is the only square in row 8 that can be <9>. It is thus pinned to that value.

Deduction pass 9; 38 squares solved; 43 remaining.

* Squares R4C6, R6C4 and R6C6 in block 5 form a simple naked triplet. These 3 squares all contain the 3 possibilities <178>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.

R4C4 - removing <178> from <1578> leaving <5>.
R5C4 - removing <178> from <125678> leaving <256>.
R5C6 - removing <178> from <12678> leaving <26>.

Deduction pass 10; 39 squares solved; 42 remaining.

* Intersection of row 7 with block 9. The value <5> only appears in one or more of squares R7C7, R7C8 and R7C9 of row 7. These squares are the ones that intersect with block 9. Thus, the other (non-intersecting) squares of block 9 cannot contain this value.

R8C9 - removing <5> from <1458> leaving <148>.

Deduction pass 11; 39 squares solved; 42 remaining.

* Found a 4-link Comprehensive Chain. If we assume that square R3C1 is <3> then we can make the following chain of conclusions:

R8C1 must be <6> (C1 pin), which means that
R8C2 must be <5> (R8 pin), which means that
R3C2 must be <3> (force), which means that
R3C1 can't be <3> (buddy contradiction).

Since this is logically inconsistent, R3C1 cannot be <3>.

(5 links were considered before finding this chain)

Deduction pass 12; 39 squares solved; 42 remaining.

* Found a 5-link Comprehensive Chain. If we assume that square R1C4 is <3> then we can make the following chain of conclusions:

R1C8 must be <7> (R1 pin), which means that
R9C8 must be <3> (force), which means that
R9C6 must be <1> (force), which means that
R7C4 must be <3> (B8 pin), which means that
R1C4 can't be <3> (buddy contradiction).

Since this is logically inconsistent, R1C4 cannot be <3>.

(5 links were considered before finding this chain)

Deduction pass 13; 40 squares solved; 41 remaining.

* Squares R2C4 and R7C4 in column 4 and R2C9 and R7C9 in column 9 form a Simple X-Wing pattern on possibility <3>. All other instances of this possibility in rows 2 and 7 can be removed.

R2C1 - removing <3> from <3578> leaving <578>.
R2C6 - removing <3> from <234> leaving <24>.
R2C8 - removing <3> from <34578> leaving <4578>.
R7C8 - removing <3> from <3458> leaving <458>.

Deduction pass 14; 40 squares solved; 41 remaining.

* R5C1 is the only square in column 1 that can be <3>. It is thus pinned to that value.

Deduction pass 15; 41 squares solved; 40 remaining.

* Found a 4-link Comprehensive Chain. If we assume that square R4C9 is <7> then we can make the following chain of conclusions:

R4C3 must be <4> (R4 pin), which means that
R5C2 must be <8> (force), which means that
R4C1 must be <7> (force), which means that
R4C9 can't be <7> (buddy contradiction).

Since this is logically inconsistent, R4C9 cannot be <7>.

(9 links were considered before finding this chain)

Deduction pass 16; 41 squares solved; 40 remaining.

* Found a 6-link Comprehensive Chain. If we assume that square R2C9 is <4> then we can make the following chain of conclusions:

R2C4 must be <3> (R2 pin), which means that
R3C6 must be <4> (force), which means that
R3C2 must be <3> (R3 pin), which means that
R8C2 must be <5> (C2 pin), which means that
R8C9 must be <4> (R8 pin), which means that
R2C9 can't be <4> (buddy contradiction).

Since this is logically inconsistent, R2C9 cannot be <4>.

(28 links were considered before finding this chain)

Deduction pass 17; 41 squares solved; 40 remaining.

* Found a 6-link Comprehensive Chain. If we assume that square R5C7 is <4> then we can make the following chain of conclusions:

R5C2 must be <8> (force), which means that
R1C2 must be <3> (force), which means that
R3C2 must be <5> (force), which means that
R3C6 must be <3> (R3 pin), which means that
R3C7 must be <4> (R3 pin), which means that
R5C7 can't be <4> (buddy contradiction).

Since this is logically inconsistent, R5C7 cannot be <4>.

(28 links were considered before finding this chain)

Deduction pass 18; 41 squares solved; 40 remaining.

* Found a 6-link Comprehensive Chain. If we assume that square R7C7 is <4> then we can make the following chain of conclusions:

R7C3 must be <6> (force), which means that
R8C2 must be <4> (B7 pin), which means that
R3C2 must be <5> (C2 pin), which means that
R3C6 must be <3> (R3 pin), which means that
R3C7 must be <4> (R3 pin), which means that
R7C7 can't be <4> (buddy contradiction).

Since this is logically inconsistent, R7C7 cannot be <4>.

(28 links were considered before finding this chain)

Deduction pass 19; 41 squares solved; 40 remaining.

* Intersection of column 7 with block 3. The value <4> only appears in one or more of squares R1C7, R2C7 and R3C7 of column 7. These squares are the ones that intersect with block 3. Thus, the other (non-intersecting) squares of block 3 cannot contain this value.

R2C8 - removing <4> from <4578> leaving <578>.

Deduction pass 20; 41 squares solved; 40 remaining.

* Found a 5-link Comprehensive Chain. If we assume that square R2C7 is <7> then we can make the following chain of conclusions:

R2C6 must be <4> (R2 pin), which means that
R3C6 must be <3> (force), which means that
R9C6 must be <1> (force), which means that
R9C7 must be <7> (force), which means that
R2C7 can't be <7> (buddy contradiction).

Since this is logically inconsistent, R2C7 cannot be <7>.

(15 links were considered before finding this chain)

Deduction pass 21; 41 squares solved; 40 remaining.

* Found a 5-link Comprehensive Chain. If we assume that square R2C7 is <8> then we can make the following chain of conclusions:

R2C6 must be <4> (R2 pin), which means that
R2C4 must be <2> (R2 pin), which means that
R2C9 must be <3> (R2 pin), which means that
R1C8 must be <8> (force), which means that
R2C7 can't be <8> (buddy contradiction).

Since this is logically inconsistent, R2C7 cannot be <8>.

(15 links were considered before finding this chain)

Deduction pass 22; 41 squares solved; 40 remaining.

* Found a 5-link Comprehensive Chain. If we assume that square R5C8 is <8> then we can make the following chain of conclusions:

R7C8 must be <4> (C8 pin), which means that
R7C3 must be <6> (force), which means that
R8C2 must be <4> (B7 pin), which means that
R5C2 must be <8> (force), which means that
R5C8 can't be <8> (buddy contradiction).

Since this is logically inconsistent, R5C8 cannot be <8>.

(15 links were considered before finding this chain)

Deduction pass 23; 41 squares solved; 40 remaining.

* Found a 5-link Comprehensive Chain. If we assume that square R7C8 is <8> then we can make the following chain of conclusions:

R5C8 must be <4> (C8 pin), which means that
R5C2 must be <8> (force), which means that
R1C2 must be <3> (force), which means that
R1C8 must be <8> (force), which means that
R7C8 can't be <8> (buddy contradiction).

Since this is logically inconsistent, R7C8 cannot be <8>.

(15 links were considered before finding this chain)

Deduction pass 24; 41 squares solved; 40 remaining.

* Intersection of column 8 with block 3. The value <8> only appears in one or more of squares R1C8, R2C8 and R3C8 of column 8. 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 <8> from <3578> leaving <357>.

Deduction pass 25; 41 squares solved; 40 remaining.

* Found a 7-link Simple Forcing Chain. If we assume that square R5C7 is <8> then we can make the following chain of conclusions:

R5C2 must be <4>, which means that
R8C2 must be <5>, which means that
R8C1 must be <6>, which means that
R7C3 must be <4>, which means that
R7C8 must be <5>, which means that
R7C7 must be <8>, which means that
R5C7 can't be <8>.

Since this is logically inconsistent, R5C7 cannot be <8>.

(7 links were considered before finding this chain)

Deduction pass 26; 41 squares solved; 40 remaining.

* R7C7 is the only square in column 7 that can be <8>. It is thus pinned to that value.

Deduction pass 27; 42 squares solved; 39 remaining.

* A set of 2 squares form a simple hidden pair. R6C4 and R8C4 all contain the 2 possibilities <18>. No other squares in column 4 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.

R8C4 - removing <6> from <168> leaving <18>.

Deduction pass 28; 42 squares solved; 39 remaining.

* Found a 7-link Simple Forcing Chain. If we assume that square R2C8 is <5> then we can make the following chain of conclusions:

R2C7 must be <4>, which means that
R2C6 must be <2>, which means that
R2C4 must be <3>, which means that
R7C4 must be <6>, which means that
R7C3 must be <4>, which means that
R7C8 must be <5>, which means that
R2C8 can't be <5>.

Since this is logically inconsistent, R2C8 cannot be <5>.

(22 links were considered before finding this chain)

Deduction pass 29; 42 squares solved; 39 remaining.

* A set of 2 squares form a simple hidden pair. R5C8 and R7C8 all contain the 2 possibilities <45>. No other squares in column 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.

R5C8 - removing <7> from <457> leaving <45>.

Deduction pass 30; 42 squares solved; 39 remaining.

* Found a 6-link Simple Forcing Chain. If we assume that square R5C2 is <4> then we can make the following chain of conclusions:

R5C8 must be <5>, which means that
R7C8 must be <4>, which means that
R7C3 must be <6>, which means that
R8C1 must be <5>, which means that
R8C2 must be <4>, which means that
R5C2 can't be <4>.

Since this is logically inconsistent, R5C2 cannot be <4>.

(18 links were considered before finding this chain)

From this deduction, the following moves are immediately forced:

R1C2 must be <3>.
R4C1 must be <7>.
R1C8 must be <8>.
R3C2 must be <5>.
R2C8 must be <7>.
R9C8 must be <3>.
R3C7 must be <4>.
R8C2 must be <4>.
R2C1 must be <8>.
R3C6 must be <3>.
R2C7 must be <5>.
R3C1 must be <6>.
R8C9 must be <1>.
R7C3 must be <6>.
R8C4 must be <8>.
R9C7 must be <7>.
R9C6 must be <1>.
R2C9 must be <3>.
R5C7 must be <1>.
R2C4 must be <2>.
R3C3 must be <7>.
R8C1 must be <5>.
R5C3 must be <4>.
R7C4 must be <3>.
R8C6 must be <6>.
R6C4 must be <1>.
R5C6 must be <2>.
R4C6 must be <8>.
R2C6 must be <4>.
R5C4 must be <6>.
R4C9 must be <4>.
R6C6 must be <7>.
R4C3 must be <1>

Keith

daj95376

Joined: 23 Aug 2008
Posts: 3854

Posted: Sat Feb 25, 2012 11:43 pm Post subject:

keith wrote:

SS finds XY chains and what it calls "Comprehensive Chains". Here is its solution: <snip>

Hmmm!!! Interesting!!! None of the Sudoku Susser chains ever use the same digit twice in succession. If this is an actual shortcoming in the solver, then it will never find turbot patterns. _ Shocked

_

Is there any chance that Sudoku Susser allows for X-Chains ... and they aren't enabled?

keith

Joined: 19 Sep 2005
Posts: 3355
Location: near Detroit, Michigan, USA

Posted: Sun Feb 26, 2012 1:46 am Post subject:

daj95376 wrote:

keith wrote:

SS finds XY chains and what it calls "Comprehensive Chains". Here is its solution: <snip>

Hmmm!!! Interesting!!! None of the Sudoku Susser chains ever use the same digit twice in succession. If this is an actual shortcoming in the solver, then it will never find turbot patterns. _ Shocked

_

Is there any chance that Sudoku Susser allows for X-Chains ... and they aren't enabled?

Right. It does XY chains and what it calls comprehensive chains. The charm of SS is its user interface and its wonderful explanations of basic and the simpler advanced techniques. It does not do X-chains or coloring.

Right, it does not find Turbots as such.

Keith

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