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[daj95376]

# original puzzle

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 *-----------*
 |..1|59.|..3|
 |6..|..2|..8|
 |...|...|14.|
 |---+---+---|
 |..6|..9|.51|
 |...|2.5|...|
 |53.|8..|6..|
 |---+---+---|
 |.15|...|...|
 |3..|9..|..4|
 |8..|.21|9..|
 *-----------*

# after a number of reductions

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*--------------------------------------------------------------------*
 | 4      28     1      | 5      9      678    | 27     67     3      |
 | 6      79     3      | 1      4      2      | 5      79     8      |
 | 27     5      89     | 36(7)  3(78)  36     | 1      4      269    |
 |----------------------+----------------------+----------------------|
 | 27     28     6      | 347    37     9      | 48     5      1      |
 | 1      49     89     | 2      6      5      | 34     38     7      |
 | 5      3      47     | 8      1      47     | 6      29     29     |
 |----------------------+----------------------+----------------------|
 | 9      1      5      | 3467   378    347    | 237    23678  26     |
 | 3      67     2      | 9      5      678    | 78     1      4      |
 | 8      467    47     | 367    2      1      | 9      36     5      |
 *--------------------------------------------------------------------*

At this point, my solver makes the following assignments.

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r1c7    =  2     Templates -- Pass B
r3c1    =  2     Templates -- Pass B
r4c2    =  2     Templates -- Pass B

How is this possible? If you examine [b1], you find a Naked Quad in <2789> where [r3c1]=7 forces [r3c3]=8 and, together, they force minirow [r3b2] to have two candidates -- <3> and <6> -- for three cells. Thus, [r3c1]=2 and the puzzle cracks (with the other two assignments being made in the process).

Now, it occurs to me that class 222(2) n-tuple in a box might be a good place to start when forcing chains are considered.

[ronk]

Maybe it is detecting the pure bilocation chain ...

r3c1-7-r2c2=7=r2c8=9=r3c9=2=r3c1, implying r3c1<>7

... which can be found with advanced coloring.

[gsf]

Code: Select all

r1c7    =  2     Templates -- Pass B
r3c1    =  2     Templates -- Pass B
r4c2    =  2     Templates -- Pass B

How is this possible?

3 x cycles on 7 ( - for weak link, strong otherwise, last cell linked to first to form cycle)

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[76]-[31][22]-[63][41]- => [76]^7
[86]-[31][22]-[63][41]- => [86]^7
[17]-[87][82]-[22][31]- => [17]^7


some of the weak links like [41]-[76] are (collapsed) hinges

[daj95376]

Thanks ronk and gsf for the additional insight into solving this puzzle.