## CHAINS, not required. Good puzzles.

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Daj95376 wrote:Carcul, my understanding of AUP is extremely limited, and I believe that you wrote all of the primary information on the topic, but it seems to me that the <9> in [r2c5] prevents you from making an AUP claim based on the contents of [r6c6] alone. (Yes, I understand that [r2c5]<>9 in the solution, but we don't know that at this point in your argument.)

Rep'nA wrote:Is there a shorter way to see it, Carcul?

Look again at the grid: if r6c6 is not "4,9" then the emergent naked pair in cells r68c6 makes r1c6=9 which eliminates "9" from r2c5.

Daj95376 wrote:My concern is that only half of the and condition was used in Carcul's argument.

Yes, because I thought the other half would be so obvious (a naked pair).

Carcul
Carcul

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BUG, xy x, in some order.

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`..94...71..16....267...1...52.7..3.............8..6.45...2...342....49..43...75..`
wapati
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x, xy, xyz and BUG2.

That is the best I find with patterns. Kinda fun

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`. . 6 | 9 . . | . . 35 . 9 | 3 . . | 4 . .. . . | . 7 6 | . 8 .---------------------2 . . | . 3 . | 9 . .. . . | . 6 2 | 1 . .. . . | . . . | . 4 2---------------------. . 1 | . . . | . 7 47 5 . | . . . | . . .4 6 . | . . 7 | . 1 .`
wapati
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Joined: 13 September 2006

Carcul wrote:
Daj95376 wrote:Carcul, my understanding of AUP is extremely limited, and I believe that you wrote all of the primary information on the topic, but it seems to me that the <9> in [r2c5] prevents you from making an AUP claim based on the contents of [r6c6] alone. (Yes, I understand that [r2c5]<>9 in the solution, but we don't know that at this point in your argument.)

Rep'nA wrote:Is there a shorter way to see it, Carcul?

Look again at the grid: if r6c6 is not "4,9" then the emergent naked pair in cells r68c6 makes r1c6=9 which eliminates "9" from r2c5.

Daj95376 wrote:My concern is that only half of the and condition was used in Carcul's argument.

Yes, because I thought the other half would be so obvious (a naked pair).

Carcul

I'm reminded of an old story about a mathematics professor at Stanford University who told a class that some statement was obvious. A student asked if it really was so obvious. The professor turned around, scribbled on the blackboard for fifteen minutes, turned back around and informed the class that, "yes, it is obvious."

On topic, I'm sorry I wasn't explicit enough in my post Daj95376. My chain (which is now obviously not the best way to see the elimination) started from Carcul's first assumption (that r6c6<>9) and concluded the missing assumption (that r2c5<>9). Maybe Carcul should have made this more explicit originally, although, what would be the fun in him giving everything away?
re'born

Posts: 551
Joined: 31 May 2007

wapati
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This one has snarls. 6 patterns, at least.

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`. . . | 8 . . | 1 . .. . 5 | 4 7 1 | . . .. 7 . | . . . | . . 9---------------------8 5 . | . 6 9 | . 4 .. 3 . | 1 . 4 | . 9 .. 4 . | 7 8 . | . 6 1---------------------4 . . | . . . | . 5 .. . . | 5 1 8 | 6 . .. . 8 | . . 7 | . . .`
wapati
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Posts: 527
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wapati wrote:In some order:

Jellyfish, required for pattern solving, I think.

BUG1 required, I think.

One of ER, grouped-x or Turbots, should do it!

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`7 9 . | 8 . 2 | 3 . .8 . . | . . . | . . .. . . | 5 . 7 | . . .---------------------2 . 7 | . . . | . 3 .. . . | . . . | 1 5 .5 . 1 | . . . | . 2 4---------------------4 . . | . 3 . | 2 . .. . . | 1 2 6 | . 8 3. . . | . . 4 | . 1 7`

Singles and Locked Candidates take you to:

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`   *--------------------------------------------------* | 7    9    46   | 8    1    2    | 3    46   5    | | 8    5    2    | 36   4    39   | 69   7    1    | | 1    36-  346  | 5    69(*)7    | 8    469  2    | |----------------+----------------+----------------| | 2    68(*)7    | 4    5    1    | 69   3    689  | | 36   4    9    | 2    7    38   | 1    5    68   | | 5    38*  1    | 36*  69*  389  | 7    2    4    | |----------------+----------------+----------------| | 4    1    8    | 7    3    5    | 2    69   69   | | 9    7    5    | 1    2    6    | 4    8    3    | | 36   2    36   | 9    8    4    | 5    1    7    | *--------------------------------------------------*`

Now, an xy-chain from r3c5 to r4c2 eliminates the 6 from r3c2 and this reduces the puzzle to singles.

If you know that a puzzle finishes with a BUG+1 reduction, there is almost always an xy-chain that will do the same job. Moreover, it often occurs before the BUG+1 position. This may not help you during your first run through of a puzzle, but if you are one of those types who enjoys doing a post mortem after finding a solution, this may be useful.
re'born

Posts: 551
Joined: 31 May 2007

This one has twists and turns galor! Many x-wings, Ers or grouped-x, Turbot, xyz, a couple xy and a finned swordfish.

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`. 4 . | 7 . . | . 3 25 3 . | . . 2 | . . 6. . 9 | . . . | 4 . .---------------------9 . . | . 7 1 | . 4 .. . . | 5 . 4 | . . .. 5 . | 2 9 . | . . 7---------------------. . 4 | . . . | 8 . .2 . . | 4 . . | . 7 91 7 . | . . 9 | . 6 .`
wapati
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wapati wrote:This one has twists and turns galor! Many x-wings, Ers or grouped-x, Turbot, xyz, a couple xy and a finned swordfish.

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`. 4 . | 7 . . | . 3 25 3 . | . . 2 | . . 6. . 9 | . . . | 4 . .---------------------9 . . | . 7 1 | . 4 .. . . | 5 . 4 | . . .. 5 . | 2 9 . | . . 7---------------------. . 4 | . . . | 8 . .2 . . | 4 . . | . 7 91 7 . | . . 9 | . 6 .`

Well, I don't have a nice step that solves the puzzle (I'll leave that for Carcul), but I do have one that it fairly easy to spot and definitely decreases the complexity of the rest of the solution (at least for me as I don't generally spot finned swordfish).

Singles and 1 x-wing (to remove two 1's in column 5) bring us to:

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`  *--------------------------------------------------------------------* | 68     4      168a   | 7      158    58     | 9      3      2      | | 5      3      18     | 9      4      2      | 7      18a    6      | | 7      2      9      | 1368a  368    368    | 4      5      18     | |----------------------+----------------------+----------------------| | 9      68     2      | 368    7      1      | 356    4      358    | | 368    1      7      | 5      368    4      | 2      9      38     | | 4      5      368    | 2      9      368    | 136a   18     7      | |----------------------+----------------------+----------------------| | 36     9      4      | 136    356    7      | 8      2      135a   | | 2      68     3568*  | 4      13568a 3568   | 135*   7      9      | | 1      7      358*   | 38     2      9      | 35*    6      4      | *--------------------------------------------------------------------*`

Notice the potential for a deadly pattern in ([89],[37])<35>. Moreover, note that the cells marked 'a' are either all 1's or all not 1's. We now have the easy deduction:

(7,9)1 [ >(8,7)!1 ] [ > (1,3)1 > (2,3)8 > ([89],3)!8] [ > (6,7)1 > (4,7)6 > (4,2)8 > (8,2)6 > (8,3)!6 ]

Therefore, the cells marked with 'a' are all not 1.

More singles take you to:

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`  *-----------------------------------------------------------* | 68    4     68    | 7     1     5     | 9     3     2     | | 5     3     1     | 9     4     2     | 7     8     6     | | 7     2     9     | 368   368   368   | 4     5     1     | |-------------------+-------------------+-------------------| | 9     68(%) 2     | 368   7     1     | 356-  4     358   | | 368   1     7     | 5     368   4     | 2     9     38    | | 4     5     368-  | 2     9     368   | 36(%) 1     7     | |-------------------+-------------------+-------------------| | 36    9     4     | 1     356   7     | 8     2     35    | | 2     68(*) 3568  | 4     3568- 368-  | 1     7     9     | | 1     7     358-  | 38(*) 2     9     | 35    6     4     | *-----------------------------------------------------------*`

An xy-chain from (9,4) to (8,2) will eliminate the 8's in (9,3) and (8,[56]). After spotting this xy-chain, one might be compelled to write down the related xy-chain from (4,2) to (6,7) that eliminates the 6's in (4,7) and (6,3). From here singles, an x-wing and an xy-wing will solve the puzzle.
re'born

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rep'nA wrote:If you know that a puzzle finishes with a BUG+1 reduction, there is almost always an xy-chain that will do the same job. Moreover, it often occurs before the BUG+1 position.

Thanks, I'll watch for that!

Here is another with a swordfish, finned I think. I quite like sword patterns, and this puzzle is close to "the braid" in appearance.

Finned sword, xyz and two grouped x-wings.

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`. . . | . . . | . 4 3. . . | . 6 . | 2 . 8. . . | 1 . 7 | 6 5 .---------------------. . 7 | 4 5 . | 8 . .. 6 . | 8 . 1 | . 7 .. . 2 | . 7 3 | 4 . .---------------------. 7 9 | 5 . 8 | . . .2 . 6 | . 1 . | . . .8 5 . | . . . | . . .`
wapati
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This one has a sword, but other patterns overlap so you don't need it, may not find it.

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`. . 2 | . 7 . | 4 . .. . 1 | 3 . . | . . .9 5 . | . . 6 | . . 8---------------------. 7 . | . 3 . | 5 . .5 . . | 1 . 9 | . . 7. . 3 | . 6 . | . 4 .---------------------7 . . | 6 . . | . 2 5. . . | . . 5 | 7 . .. . 5 | . 4 . | 9 . .`
wapati
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Posts: 527
Joined: 13 September 2006

A grouped x-wing, xyz and lesser stuff.

Code: Select all
`. 9 3 | . . . | . 5 .7 . 5 | . 4 . | . . 22 6 . | 8 . . | . . .---------------------. . 6 | 9 3 . | . . .. 4 . | 6 . 7 | . 8 .. . . | . 2 8 | 9 . .---------------------. . . | . . 6 | . 4 56 . . | . 9 . | 7 . 8. 2 . | . . . | 1 9 .`
wapati
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Posts: 527
Joined: 13 September 2006

Wapati wrote:This one has twists and turns galor! Many x-wings, Ers or grouped-x, Turbot, xyz, a couple xy and a finned swordfish.

Code: Select all
` *-------------------------------------------------------------* | 68     4      168  | 7      158    58   | 9      3      2   | | 5      3      18   | 9      4      2    | 7      18     6   | | 7      2      9    | 1368   368    368  | 4      5      18  | |--------------------+--------------------+-------------------| | 9      68     2    | 368    7      1    | 356    4      358 | | 368    1      7    | 5      368    4    | 2      9      38  | | 4      5      368  | 2      9      368  | 136    18     7   | |--------------------+--------------------+-------------------| | 36     9      4    | 136    356    7    | 8      2      135 | | 2      68     3568 | 4      13568  3568 | 135    7      9   | | 1      7      358  | 38     2      9    | 35     6      4   | *-------------------------------------------------------------*`

If r6c6 is not “8” then [r8c2]-8-[r9c3]=8=[r9c4]-8-[r4c4]=8=[r5c5]=6=
[r5c1]-6-[r4c2]-8-[r8c2]. But this is incompatible with the X-Wing in cells [r26c38]. So, r6c6=8 and the puzzle is solved.

Carcul
Carcul

Posts: 724
Joined: 04 November 2005

Wapati wrote:This one has a sword, but other patterns overlap so you don't need it, may not find it.

Code: Select all
` *----------------------------------------------------------* | 368    368    2   | 9      7      18 | 4      5      16  | | 4      68     1   | 3      5      28 | 26     7      9   | | 9      5      7   | 4      12     6  | 23     13     8   | |-------------------+------------------+-------------------| | 1268   7      68  | 28     3      4  | 5      9      126 | | 5      2468   468 | 1      28     9  | 36     38     7   | | 128    9      3   | 5      6      7  | 18     4      12  | |-------------------+------------------+-------------------| | 7      148    489 | 6      189    3  | 18     2      5   | | 2368   12368  689 | 28     1289   5  | 7      168    4   | | 268    1268   5   | 7      4      12 | 9      168    3   | *----------------------------------------------------------*`

[r5c5]-2-[r3c5]-1-[r3c8]-3-[r5c8]-8-[r5c5], => r5c3<>8, which implies that r4c4<>8 and the puzzle is solved.

Alternatively: [r5c5]-2-[r3c5]-1-[r3c8]-3-[r5c8]-8-[r5c3]=8=[r4c3]-8-[r4c4]-2-[r5c5], => r5c5<>2 solving the puzzle.

Carcul
Carcul

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Joined: 04 November 2005

Interesting puzzle. The swordfish is reuired by pattern hunters, I believe.

Code: Select all
`. . 9 | . . . | . . .. . 1 | 9 . . | 6 7 .8 6 . | . 2 . | . 1 .---------------------. 4 . | 3 1 . | . . .. . 6 | 2 . 9 | 7 . .. . . | . 5 6 | . 2 .---------------------. 5 . | . 9 . | . 8 6. 3 8 | . . 5 | 1 . .. . . | . . . | 3 . .`
wapati
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