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by **ArkieTech** » Fri Mar 01, 2013 3:42 am

Code: Select all: *-----------* |...|3.8|.6.| |9..|.1.|...| |35.|...|...| |---+---+---| |...|..3|.4.| |7.2|...|1.5| |.9.|2..|...| |---+---+---| |...|...|.83| |...|.2.|..9| |.8.|4.6|...| *-----------*

by **pjb** » Fri Mar 01, 2013 4:47 am

A continuous nice loop:

Code: Select all: 124 1247 147 | 3 59 8 | 59 6 1247 9 2467 4678 | 567 1 2457 | 23578 2357 2478 3 5 14678 | 679 d4679 2479 | 2789 1279 12478 ---------------------+----------------------+--------------------- 1568 16 156 | 15679 c5679 3 | 2789 4 2678 7 346 2 |b69 8 a49 | 1 39 5 14568 9 13456 | 2 ce4567 1457 | 378 37 678 ---------------------+----------------------+--------------------- 12456 12467 14567 | 1579 579 1579 | 46 8 3 1456 13467 134567 | 8 2 157 | 46 15 9 15 8 9 | 4 3 6 | 257 1257 127

(4=9) r5c6 - (9=6) r5c4 - r46c5 = (6-4) r3c5 = (4) r6c5 - loop => r4c45 <>9, r5c8<>9, r4c4<>6, r6c6<>4, r3c5<>7,9; stte

Phil

by **daj95376** » Fri Mar 01, 2013 5:22 am

A recent puzzle had a 4-SIS L2-Ring ... as does this puzzle. What are the odds?

Code: Select all: +--------------------------------------------------------------------------------+ | 124 1247 147 | 3 59 8 | 59 6 1247 | | 9 2467 4678 | 567 1 2457 | 23578 2357 2478 | | 3 5 14678 | 679 a4679g 2479 | 2789 1279 12478 | |--------------------------+--------------------------+--------------------------| | 1568 16 156 | 15679 5679f 3 | 2789 4 2678 | | 7 d346 2 | e69 8 c49 | 1 39 5 | | 14568 9 13456 | 2 b4567f 1457 | 378 37 678 | |--------------------------+--------------------------+--------------------------| | 12456 12467 14567 | 1579 579 1579 | 46 8 3 | | 1456 13467 134567 | 8 2 157 | 46 15 9 | | 15 8 9 | 4 3 6 | 257 1257 127 | +--------------------------------------------------------------------------------+ # 143 eliminations remain (4)r3c5 = r6c5 - r5c6 = (4-6)r5c2 = r5c4 - r46c5 = (6)r3c5 - loop => r3c5<>79, r5c2<>3, r6c6<>4, r4c4<>6 -also- (4)r5c6 = (4-6)r5c2 = r5c4 - (6579=5794)r1467c5 - loop => r3c5<>79, r5c2<>3, r6c6<>4, r4c4<>6

by **Leren** » Fri Mar 01, 2013 9:10 am

Code: Select all: *-----------------------------------------------------------------------* | 124 1247 147 | 3 b59 8 | 59 6 1247 | | 9 2467 4678 | 567 1 2457 | 23578 2357 2478 | | 3 5 14678 | 679 4679 2479 | 2789 1279 12478 | |-----------------------+-----------------------+-----------------------| |c1568 c16 c156 | 15679 b5679 3 | 2789 4 2678 | | 7 46-3 2 |a69 8 a49 | 1 a39 5 | |c14568 9 c1346 | 2 b4567 1457 | 78-3 7-3 678 | |-----------------------+-----------------------+-----------------------| | 12456 12467 14567 | 1579 b579 1579 | 46 8 3 | | 1456 13467 13456 | 8 2 157 | 46 15 9 | | 15 8 9 | 4 3 6 | 257 1257 127 | *-----------------------------------------------------------------------*

als xy-wing: (3=6) r5c468 - (6=4) r1467c5 - (4=3) r4c123,r6c13 => r5c2, r6c78 <> 3; stte

Leren

by **David P Bird** » Fri Mar 01, 2013 12:12 pm

Here's a symmetrical chain confined to 3 digits in 2 boxes:

(9=6)r5c4 - (6)r23c4 = (6-4)r3c5 = (4)r23c6 - (4=9)r5c6 => r5c8 <> 9 stte

[Edit] Typo spotted by Leren (thanks)

by **aran** » Fri Mar 01, 2013 11:14 pm

Code: Select all: *-----------------------------------------------------------------------------* | 124 1247 147 | 3 59 8 | 59 6 1247 | | 9 2467 4678 | 567 1 2457 | 23578 2357 2478 | | 3 5 14678 | 679 4679 2479 | 2789 1279 12478 | |-------------------------+-------------------------+-------------------------| | 1568 16 156 | 15679 5679 3 | 2789 4 2678 | | 7 346 2 | 69 8 49 | 1 39 5 | | 14568 9 13456 | 2 4567 1457 | 378 37 678 | |-------------------------+-------------------------+-------------------------| | 12456 12467 14567 | 1579 579 1579 | 46 8 3 | | 1456 13467 134567 | 8 2 157 | 46 15 9 | | 15 8 9 | 4 3 6 | 257 1257 127 | *-----------------------------------------------------------------------------*

The DL-ALS version :
r5c46 {469}
b2 5 cells excluding r3c5 {245679}
dual links 4,6
{946} {642579} : =><9>r4c45 <9>r5c8 <4>r6c6 <6>r4c4 <7>r3c5 <9>r3c5

by **Leren** » Fri Mar 01, 2013 11:16 pm

David, there is a typo in your loop - first term should be (9=6)r5c4.

There is also a related symmetrical xy-wing loop in the same 2 boxes:

Code: Select all: *-----------------------------------------------------------------------* | 124 1247 147 | 3 b59 8 | 59 6 1247 | | 9 2467 4678 |b567 1 b2457 | 23578 2357 2478 | | 3 5 14678 |b679 46-79 b2479 | 2789 1279 12478 | |-----------------------+-----------------------+-----------------------| | 1568 16 156 | 157-69 567-9 3 | 2789 4 2678 | | 7 346 2 |a69 8 c49 | 1 3-9 5 | | 14568 9 13456 | 2 4567 157-4 | 378 37 678 | |-----------------------+-----------------------+-----------------------| | 12456 12467 14567 | 1579 579 1579 | 46 8 3 | | 1456 13467 134567 | 8 2 157 | 46 15 9 | | 15 8 9 | 4 3 6 | 257 1257 127 | *-----------------------------------------------------------------------* (9=6) r5c4 - (6=4) r1c5,r23c46 - (4=9) r5c6 => r3c5 <> 79, r4c4 <> 69, r4c5 <> 9, r5c8 <> 9, r6c6 <> 4; stte

Also, your multisector AHS method works here:

Code: Select all: *---------------------------------------------------------------------------------* | 124 1247 147 | 3 59 8 | 59 6 1247 | | 9 2467 4678 | 567 1 2457 | 23578 2357 2478 | | 3 5 14678 | 679 a46-79 2479 | 2789 1279 12478 | |--------------------------+---------------------------+--------------------------| | 1568 16 156 |b157-69 ab567-9 3 | 2789 4 2678 | | 7 346 2 | 69 8 49 | 1 39 5 | | 14568 9 13456 | 2 ab4567 b157-4 | 378 37 678 | |--------------------------+---------------------------+--------------------------| | 12456 12467 14567 | 1579 579 1579 | 46 8 3 | | 1456 13467 134567 | 8 2 157 | 46 15 9 | | 15 8 9 | 4 3 6 | 257 1257 127 | *---------------------------------------------------------------------------------* AHS1 (46) r346c5; AHS2 (157) r4c45,r6c56 => r3c5 <> 79, r4c4 <> 69, r4c5 <> 9, r6c6 <> 4; stte

Leren

by **Leren** » Sat Mar 02, 2013 1:50 am

Just realised that there is a simple solution to this puzzle.

There are 2 Kites (4 & 6) both with pincer cells r3c5 and r5c2. Neither makes any direct eliminations
but together they => r3c5 <> 79, r5c2 <> 3; stte. How simple is that !

Leren

by **ArkieTech** » Sat Mar 02, 2013 3:48 am

Leren wrote:Just realised that there is a simple solution to this puzzle.

There are 2 Kites (4 & 6) both with pincer cells r3c5 and r5c2. Neither makes any direct eliminations
but together they => r3c5 <> 79, r5c2 <> 3; stte. How simple is that !

Leren

beautiful

It must have a name 8-)

Loop

4r3c5=r6c5-r5c6=(4-6)r5c2=r4c2-r4c5=(6-4)r3c5

by **Leren** » Sat Mar 02, 2013 6:24 am

Arkietech wrote: It must have a name

Actually it does have a name, I call it the 2 digit pattern overly method. The "patterns" can be any AIC starting and ending with strong links on the same digit,
ie any pattern where at least one of the pincer cells must be true, so it applies to any combination of kites, skyscrapers, w-wings, xy-wings etc etc. You can also "join"
the patterns in different ways (ie when the pincer cells don't necessarily co-incide but can see each other) to form various constructions, but the 2 digit pattern overly
is a real killer when it works.

Leren

by **aran** » Sat Mar 02, 2013 8:56 am

A Hidden Remote Pair.

by **daj95376** » Sat Mar 02, 2013 4:16 pm

ArkieTech wrote:It must have a name

I called it a 4-SIS L2-Ring in my solution (above). I guess that wasn't acceptable ... nor the two extra eliminations necessary.

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