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I'm still trying to get a handle on ERs in vanilla 9x9, so I'm really clueless with one in a jigsaw. This is Grid 2 of a Samurai jigsaw. I'm almost finished with the puzzle (Grids 1, 4, and 5 complete, and Grid 3 almost complete), so I really hate to quit now, especially since ER is my next technique to learn. Can someone please help me understand the logic here?

Richard Broughton's SudokuSolver shows as the next step:

Empty Rectangle on candidate 3 at n2(r1>c6) - r7c6=r7c7

The characteristics of an ER are as follows:

1) A block for which there is a cell that is in the same row or column as all occurrences of a candidate d in that block.

2) A strong link on candidate d that can see the cell described above

Then, all candidates d can be eliminated from all other cells that can see both the cell from 1) and the "other" end of the strong link.

To apply this to your puzzle, we can see that in block 2, cell r1c6 is in the same row or column as all occurrences of candidate 3 in that block. Furthermore, there is a strong link on r7c6 =3= r7c7. Thus, all cells that can see both r1c6 and r7c7 (excluding the cell from the strong link) can have 3 eliminated from them, ie r1c7 <> 3.

To see why: Suppose r7c7 = 3, then r1c7 <> 3. If r7c7 <> 3, then r7c6 = 3, so the 3 in block 2 must be in r1, so r1c7 <> 3.

enxio27 wrote:Richard Broughton's SudokuSolver shows as the next step:

Empty Rectangle on candidate 3 at n2(r1>c6) - r7c6=r7c7

3 at r1c7
would put two 3s in c6
( for r7 and for n2 )

as a finned X-wing —

(3) r7n2\c67 with "fin" = r1c245

or

(3) r7n2\r1c6 with "fin" = r7c7

Thanks for the explanations. I see the logic now, but how in the world do you go about identifying these in the first place?

Here's another one in the same grid. Is r8c6 the cell referred to in step 1? If so, I'm not sure how to follow from there. Can the strong link be in the same block as the first cell?

Empty Rectangle on candidate 3 at n9(c7>R8) - r8c8=r3c8

As an aside, I'm not sure how nonets are numbered in a jigsaw.

(BTW, Pat, I haven't gotten to finned X-wings yet. Should I work on those first?)

This ER would centre around cell r8c7 - the strong link is in column 8, leading to r3c7 <> 3.

The strong link cannot be in the same block.