## interesting one

Post the puzzle or solving technique that's causing you trouble and someone will help
Glyn wrote:I think this would produce the eliminations given by Ronk

(189=6)ALS:r9c235-(6=9)r7c1-(9=168)ALS:r9c235

The closure of the loop allows Carcul's eliminations at the peers of the ends of the weak links (ie the 6's and 9's in Box 7 outside the chain). The ends of the chain give the strong link between the values possible in r9c235 leading to Ronk's additional eliminations.

Although there are no "ends of the chain" for a continuous loop, you have hit upon the very heart -- i.e., the minimum number of cells -- required for this deduction. It is known as the (doubly-linked) ALS xz-rule, aka the Sue de Coq or two-sector disjoint subset (TSDS) technique.

Since it doesn't matter where you start a continuous loop, the shortest NL notation occurs when you duplicate the bivalue:

r7c1 -6- ALS:([r9c23,r9c5] =6|18|9=r9c23) -9- r7c1 - continuous loop
==> r7c2<>69, r8c123<>6, r9c6<>18, r9c8<>8

... although no one else writes "continuous loop" at the end. R9c5 is "split out" in the notation to indicate that digits 6&9 do not occur there. IOW r7c1 must see all occurrences of digits 6&9 in the ALS. I think Carcul would simply write ...

[r7c1]-6-[r9c235]-9-[r7c1], => r7c2<>6,9; r8c123<>6; r9c6<>1,8; r9c8<>8

In AIC notation: (189=186)ALS:r9c235 - (6=9)r7c1 - loop
==> r7c2<>69, r8c123<>6, r9c6<>18, r9c8<>8

... although most people only write the locked digits 18 once in the ALS.

The eliminations are identical if r9c5 is the bivalue and [r7c1,r9c23] is the ALS.
ronk
2012 Supporter

Posts: 4764
Joined: 02 November 2005
Location: Southeastern USA

Storm_norm wrote:I'll toss this one in as bonus.

Code: Select all
` *--------------------------------------------------------------* | 3      6      1    | 58     58     4   | 9      2      7     | | 459    7      49   | 2      3      69  | 8      15     1456  | | 2459   2458   489  | 7      69     1   | 356    35     456   | |--------------------+-------------------+---------------------| | 8      124    4679 | 135    4579   239 | 1256   1579   12569 | | 129    3      5    | 6      79     8   | 4      179    129   | | 12469  124    4679 | 15     4579   29  | 1256   8      3     | |--------------------+-------------------+---------------------| | 156    158    68   | 4      2      7   | 135    1359   1589  | | 47     48     3    | 9      1      5   | 27     6      28    | | 157    9      2    | 38     68     36  | 157    4      15    | *--------------------------------------------------------------*`

1) [r3c3]=8=[r3c2]=2=[r3c1]-2-[r5c1]=2=[r5c9]-2-[r8c9]-8-[r8c2](-4-
-[r3c2])-4-[r46c2]=4|9=[r5c1]=1=[r5c8]-1-[r2c8]-5-[r2c1]=5|8=[r3c3], => r3c3 = 8; r6c1<>2; r4c9<>2; r3c2<>4.

2) [r7c8]=9=[r7c9]=8=[r8c9]-8-[r8c2]-4-[r46c2]=4|9=[r5c1]=2=[r5c9]
=1=[r5c8](-1-[r7c8])-1-[r23c8]-3,5-[r7c8], => r7c8<>1,3,5.

3) [r5c1]=9|4=[r46c2]-4-[r8c2]-8-[r8c9]-2-[r5c9]=2=[r5c1], => r5c1<>1.

4) [r5c5]-9-[r6c6]-2-[r6c7]-5-[r3c7]-6-[r3c5]-9-[r5c5], => r5c5<>9 and the puzzle is solved.
Carcul

Posts: 724
Joined: 04 November 2005

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