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[SpAce]

(135=6|7|8)r278c9 - (6781=4)r9c7892 - (4)r2c2 = (remote triple, type 1: <135>r2c79,r8c9) => -135 r3c9; stte

Nice!!

I don't know if the "remote triple" term has been used before

It has, here, but I don't think it meant the same thing. Seems more like what I would call a Grouped RP (like your first example), i.e. only capable of double-digit eliminations like a normal RP -- though a bit hard to tell from those examples. I think StrmCkr agreed with that assessment in some discussion, if I remember correctly.

Yours seems more like the real thing, anyhow, because of the triple-digit elimination! However, can it ever exist usefully as anything but an almost-pattern? At least this example would degenerate into a naked triple (with locked 1s in box3) and then a normal grouped RP (with just a double-digit elimination) without the spoiler. I can't really see how that could be avoided with any unspoiled form (kind of like a Finned Sashimi fish). Can you?

and "type 1" is only meant to suggest the possiblity of other types existing.

I'm not a big fan of arbitrary type numbers, so I'd probably delay using any until a real need for such typing is established. I think we need more samples of these! Could there be similar almost-remote-quads (and possibly bigger) as well? A very interesting pattern!

[blue]

However, can it ever exist usefully as anything but an almost-pattern? At least this example would degenerate into a naked triple (with locked 1s in box3) and then a normal grouped RP (with just a double-digit elimination) without the spoiler. I can't really see how that could be avoided with any unspoiled form (kind of like a Finned Sashimi fish). Can you?

Good point.
No, I can't see it existing without a spoiler.

I'm not a big fan of arbitrary type numbers (...)

Me either.

I think we need more samples of these! Could there be similar almost-remote-quads (and possibly bigger) as well? A very interesting pattern!

Here are a couple of "free standing" remote triple patterns.
The cell count is up by 4, compared to what we have in this thread.

Code: Select all

+-----------+--------------+
| . .   .   | .   .   -abc |
| . abc .   | abc .   abc  |
| . .   .   | .   .   -abc |
+-----------+--------------+
| . abc .   | .   .   .    |
| . abc .   | .   .   abc  |
| . .   abc | abc abc .    |
+-----------+--------------+

Code: Select all

+-------------+--------------+
| .   .   .   | .   -abc .   |
| .   abc .   | abc -abc abc |
| .   .   .   | .   -abc .   |
+-------------+--------------+
| .   abc .   | .   abc  .   |
| abc .   abc | .   .    abc |
| .   .   .   | .   abc  .   |
+-------------+--------------+

[SpAce]

Here are a couple of "free standing" remote triple patterns.
The cell count is up by 4, compared to what we have in this thread.

Code: Select all

+-----------+--------------+
| . .   .   | .   .   -abc |
| . abc .   | abc .   abc  |
| . .   .   | .   .   -abc |
+-----------+--------------+
| . abc .   | .   .   .    |
| . abc .   | .   .   abc  |
| . .   abc | abc abc .    |
+-----------+--------------+

Beautiful! I also think the RP-notation I suggested some time ago would work with these too:

(a/b/c)r8c9 = r9c78 - r9c3 = r78c2 - r2c2 = (a/b/c)r2c79 => -abc r13c9

(What we have is basically three parallel grouped X-Chains. In RPs we have two.)

Code: Select all

+-------------+--------------+
| .   .   .   | .   -abc .   |
| .   abc .   | abc -abc abc |
| .   .   .   | .   -abc .   |
+-------------+--------------+
| .   abc .   | .   abc  .   |
| abc .   abc | .   .    abc |
| .   .   .   | .   abc  .   |
+-------------+--------------+

Also nice! Shouldn't the r2c8 be emptied first by the r2 triple, though? Then the links work:

Code: Select all

+-------------+--------------+
| .   .   .   | .   -abc .   |
| .   abc .   | abc .    abc |
| .   .   .   | .   -abc .   |
+-------------+--------------+
| .   abc .   | .   abc  .   |
| abc .   abc | .   .    abc |
| .   .   .   | .   abc  .   |
+-------------+--------------+

(a/b/c)r79c8 = r8c9 - r8c13 = r7c2 - r2c2 = (a/b/c)r2c79 => -abc r13c8

Since all of these can be seen as multiple grouped X-Chains (like RPs), I'm wondering if more complicated cases exist where that's not possible. In other words, can some of the triples (or possibly larger LSs) be spread into three boxes within a chute and still make it work? I'm imagining that would require fishy patterns. A simple example:

Code: Select all

+------------+------------+---------------+
| .   .   .  | .   .   .  | .    .    .   |
| .  abc  .  | .  abc  .  | .    abc  .   |
| .   .   .  | .   .   .  | .    .    .   |
+------------+------------+---------------+
| .   .   .  | .   .   .  | .   -abc  .   |
| .  abc  .  | .   .   .  | abc  .    abc |
| .   .   .  | .   .   .  | .   -abc  .   |
+------------+------------+---------------+
| .   .   .  | .   .   .  | .    .    .   |
| .  abc  .  | .  abc  .  | .    abc  .   |
| .   .   .  | .   .   .  | .    .    .   |
+------------+------------+---------------+

Triple-3x4-Fish: (a/b/c)R258\c258b6 => -abc r46c8

Of course the same result is achieved with three separate fishes, but that's true about the chained versions as well. Every "free-standing" RP or (non-fishy) RT can be seen as two or three (grouped) X-Chains, so by itself it doesn't really give any new solving power (except that such chains/fishes are easier to see because of the naked pairs/triples revealing the links).

However, that observation leads me back to the earlier comment about the almost-form. I think that might actually be the most powerful way to use these patterns because it gives multi-digit weak links enabling exotic chain propagation possibilities and/or wonderful OTP-eliminations (like eleven's). Then the pattern's simultaneous multi-shot capability is actually essential. Would you agree with that?

An Almost-Triple-Fish:

Code: Select all

+------------+------------+---------------+
| .   .   .  | /   .   .  | .    .    .   |
| .  abc  .  | /  abc  .  | .    abc  .   |
| .   .   .  | d   .   .  | .    abcd .   |
+------------+------------+---------------+
| .   .   .  | /   .   .  | .   -abc  .   |
| .  abcd .  | d   .   .  | abc  .    abc |
| .   .   .  | /   .   .  | .   -abc  .   |
+------------+------------+---------------+
| .   .   .  | /   .   .  | .    .    .   |
| .  abc  .  | /  abc  .  | .    abc  .   |
| .   .   .  | /   .   .  | .    .    .   |
+------------+------------+---------------+

(abc=d)r283c8 - r3c4 = r5c4 - r5c2 = (a/b/c)R258\c258b6 => -abc r46c8

Even there the triple-shot capability is not essential because the same eliminations are available with three separate moves (one for each fish).

Here's where it really shines, though:

Code: Select all

+------------+------------+---------------+
| .   .   .  | .   .   .  | .    .    .   |
| .  abc  .  | .  abc  .  | .    abc  .   |
| .   .   .  | .   .   .  | .    .    .   |
+------------+------------+---------------+
| .   .   .  | .   .   .  | .    .    .   |
| .  abcd .  | .   .   .  | abc  -d   abc |
| -d  -d  -d | .   .   .  | .    abcd .   |
+------------+------------+---------------+
| .   .   .  | .   .   .  | .    .    .   |
| .  abc  .  | .  abc  .  | .    abc  .   |
| .   .   .  | .   .   .  | .    .    .   |
+------------+------------+---------------+

(d)r5c2 = (a/b/c)R258\c258b6 - (a|b|c=d)r6c8 => -d r5c8,r6c123

I don't think that's possible without the multi-digit weak link (or a complicated net).

[StrmCkr]

Code: Select all

+-----------------+--------------------+----------------------+
| 1   2      35   | 45    345     6    | 7      8     9       |
| 46  (345)  3568 | 7     1358    9    | (135)  2     (135)   |
| 7   9      358  | 1258  12358   38   | 1345   6     4-135   |
+-----------------+--------------------+----------------------+
| 2   8      4    | 15    9       37   | 16     1357  167     |
| 35  7      1    | 6     48      2    | 9      35    48      |
| 35  6      9    | 1458  134578  3478 | 48     17    2       |
+-----------------+--------------------+----------------------+
| 46  1345   2356 | 248   2478    478  | 13568  9     (13567) |
| 8   (35)   7    | 9     6       1    | 2      4     (35)    |
| 9   (14)   26   | 3     2478    5    | (168)  (17)  (1678)  |
+-----------------+--------------------+----------------------+

(14) @ R9C2
4r9C2 = (135) @ r2c279
R2C2 = (5 or 3 )
||
r8c29 = 3 & 5 or 5 & 3 {and reduces r2c79 to a pair of 13 or 15)
=>> r3c9 <> 1,3,5 { hidden remote pair}

(14) @ r9c1
1R9C2 = ls b(678)@ r9c789 => ls c (135) R278C9
=>> R3C9 <> 1,3,5