The New Sudoku Players' Forum

[daj95376]

Thanks again daj, so many patterns!


This here is a whack of odditty.

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. . . | . . 3 | 6 . 5
. . 8 | 6 . . | . 1 .
. 1 . | . 5 . | 7 . 4
---------------------
. 4 . | . 3 . | . . 1
. . 9 | 4 . 1 | 8 . .
1 . . | . 8 . | . 9 .
---------------------
4 . 2 | . 9 . | . 5 .
. 7 . | . . 4 | 9 . .
9 . 1 | 8 . . | . . .

You're welcome wapati. Lots of variety in your puzzle: Singles, Locked Candidates (1), Naked Pairs, Swordfish, Jellyfish, Unique Rectangle Type 1, XY-Chains, and a BUG+1 to finish.

[daj95376]

It is a tad busy, pattern wise.

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3 . . | . . . | . . .
. 2 . | . 4 9 | 3 . .
. . 8 | 2 . . | . 7 .
---------------------
. . 3 | . 8 . | . 9 .
. 1 . | 4 . 3 | . 2 .
. 6 . | . 2 . | 8 . .
---------------------
. 4 . | . . 7 | 9 . .
. . 6 | 9 5 . | . 8 .
. . . | . . . | . . 1

All of the pattern eliminations for <1> in this puzzle are really just one mandatory assignment -- [r6c8]=1.

Code: Select all

# [r6c8]<>1 => [r4c7]=1 & [r6c6]=1 => [r3] to be void of <1>
 *--------------------------------------------------------------------*
 | 3      59     14     | 156    7      8      | 12456  456-1  24569  |
 | 67     2      17     | 156    4      9      | 3      56-1   8      |
 | 46     59     8      | 2      3      156    | 1456   7      4569   |
 |----------------------+----------------------+----------------------|
 | 2      7      3      | 156    8      156    | 45-1   9      45     |
 | 8      1      5      | 4      9      3      | 67     2      67     |
 | 49     6      49     | 7      2      5-1    | 8      1-35   35     |
 |----------------------+----------------------+----------------------|
 | 5      4      2      | 8      1      7      | 9      36     36     |
 | 1      3      6      | 9      5      24     | 247    8      247    |
 | 79     8      79     | 3      6      24     | 245    45     1      |
 *--------------------------------------------------------------------*


To paraphrase one thread on chains, it says that a chain with only three cells (i.e., two links) is of no use. Maybe, but I find a lot of assignments by setting the end-points to true and looking for contradictions. Anyway, just a thought.
(note: X-Colors gives the same results in this puzzle.)

[ravel]

To paraphrase one thread on chains, it says that a chain with only three cells (i.e., two links) is of no use.

?? Its a turbot fish/2 strong links (your assignment only works, because r3c67 are conjugated).

[ronk]

To paraphrase one thread on chains, it says that a chain with only three cells (i.e., two links) is of no use. Maybe, but I find a lot of assignments by setting the end-points to true and looking for contradictions. Anyway, just a thought.

For all three discontinuous loops implying an exclusion, the cycle-length = 5.

r12c8-1-r6c8=1=r6c6-1-r3c6=1=r3c7-1-r12c8, implies r12c8<>1

r4c7-1-r6c8=1=r6c6-1-r3c6=1=r3c7-1-r4c7, implies r4c7<>1

r6c6-1-r3c6=1=r3c7-1-r12c8=1=r6c8-1-r6c6, implies r6c6<>1

Chop off the weak link on each end, and the chain-length = 3, as you say. So I think there's a very good chance whomever you've paraphrased was speaking about the cycle length of a continuous loop -- for example, an xy-loop or an x-wing.

[daj95376]

So I think there's a very good chance whomever you've paraphrased was speaking about the cycle length of a continuous loop -- for example, an xy-loop or an x-wing.

I was (mis)quoting someone who was talking strictly about making conclusions based on chains in general.

I then tried to add that checking for contradictions can often be beneficial when a cell has 2/3 strong links for a single digit. Simply assigning the single digit value to the non-central cells often produces an immediate and obvious contradiction. Here's a trivial example that I run into all of the time with Skyscrapers.

Code: Select all

# Skyscraper [c59] => [r4c7]<>X => [r6c9]=X
# -or-
# [r4c7]=X=[r6c9]-X-[r1c9]
# [r4c7]=X & [r1c9]=X => [c5] void of X => [r6c9]=X
*-----------------------------*
| .  .  . | .  X  . | .  .  X |
| .  .  . | .  /  . | .  .  / |
| .  .  . | .  /  . | .  .  / |
|---------+---------+---------|
| .  .  . | .  X  . | X  /  / |
| .  .  . | .  /  . | /  /  / |
| .  .  . | .  /  . | /  /  X |
|---------+---------+---------|
| .  .  . | .  /  . | .  .  / |
| .  .  . | .  /  . | .  .  / |
| .  .  . | .  /  . | .  .  / |
*-----------------------------*


[wapati]

This one has some variety of pattern methods but some cancel others.

These are in here, you may not see them all:
x-wing, xy-wing, xyz-wing, skyscraper, turbot and swordfish.

Code: Select all

. . .|1 . .|7 3 .
. . .|. 7 5|. . 6
. . .|2 . 3|. . 4
-----+-----+-----
9 . 7|. . .|5 2 .
. 3 .|. . .|. 6 .
. 5 6|. . .|9 . 3
-----+-----+-----
7 . .|3 . 8|. . .
6 . .|5 9 .|. . .
. 8 3|. . 2|. . .

[wapati]

There is a fairly robust jellyfish in here but it may well be eliminated before you get to it!

Code: Select all

. 1 2 | 6 . . | . 4 7
3 . . | . . . | . . 2
6 . . | . 1 . | 8 . .
---------------------
2 . . | 8 3 . | . . .
. . 8 | 1 . 6 | 4 . .
. . . | . 2 5 | . . 3
---------------------
. . 9 | . 6 . | . . 1
4 . . | . . . | . . 8
1 6 . | . . 2 | 5 9 .

[wapati]

There are some big fish in here.

Swords may cancel jellies.

Code: Select all

. 6 .|. 9 5|2 . 7
9 . .|2 . .|. 5 .
. . 2|. . .|. . 3
-----+-----+-----
. 2 .|. 7 4|. . 1
4 . .|8 . 1|. . 5
7 . .|3 5 .|. 2 .
-----+-----+-----
2 . .|. . .|7 . .
. 7 .|. . 3|. . 2
5 . 4|7 1 .|. 8 .

[wapati]

There is a sword and a jelly, although two swords can do it.
(With xy-wings and maybe a sky?)

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. 8 . | . . 5 | . . .
4 . 5 | 6 1 . | . . .
. 1 . | 8 . 3 | 6 . .
---------------------
. 5 4 | . 8 . | 1 . 2
. 2 . | 1 . 4 | . 8 .
1 . 8 | . 2 . | 4 6 .
---------------------
. . 1 | 4 . 8 | . 9 .
. . . | . 6 1 | 7 . 3
. . . | 7 . . | . 4 .

[wapati]

Hmmm.

Lots.

Code: Select all

. . . | 2 . . | . . 8
. 5 2 | . . 8 | 1 3 .
. 1 . | . . . | 2 7 .
---------------------
2 . . | 9 1 . | . 8 .
. . . | 6 . 4 | . . .
. 8 . | . 2 5 | . . 1
---------------------
. 2 5 | . . . | . 4 .
. 3 4 | 8 . . | 9 5 .
8 . . | . . 3 | . . .


[Carcul]

This here is a whack of odditty.

Code: Select all

 *-----------------------------------------------------------*
 | 27    9     4     | 127   127   3     | 6     8     5     |
 | 2357  235   8     | 6     4     27    | 23    1     9     |
 | 236   1     36    | 9     5     8     | 7     23    4     |
 |-------------------+-------------------+-------------------|
 | 8     4     67    | 27    3     9     | 5     267   1     |
 | 2356  2356  9     | 4     267   1     | 8     2367  236   |
 | 1     236   367   | 5     8     267   | 4     9     236   |
 |-------------------+-------------------+-------------------|
 | 4     8     2     | 37    9     67    | 1     5     367   |
 | 36    7     5     | 123   126   4     | 9     236   8     |
 | 9     36    1     | 8     267   5     | 23    4     2367  |
 *-----------------------------------------------------------*


1. [r8c8]=2=[r1c1]-2-[r3c1]=3=[r3c8]-2-[r8c8], => r2c12/r45c8<>2.

2. [r8c1]-3-[r9c2]-6-[r9c5]-7-[r5c5]=7=[r5c8]-7-[r4c8]-6-[r8c8]-3-[r8c1], => r8c1<>3.

Carcul

[wapati]

I didn't see any "big fish" here but a swarm of pansize!

Code: Select all

. . . | . . 2 | . 9 .
. . . | 6 1 4 | . . 7
. . . | 9 3 . | 4 . .
---------------------
. 4 2 | . . . | . 6 1
. 5 6 | . . . | 3 7 .
3 9 . | . . . | 2 4 .
---------------------
. . 4 | . 5 9 | . . .
5 . . | 7 6 3 | . . .
. 6 . | 2 . . | . . .


[wapati]

There are up to 3 swords here, one is required (as far as I can see).
UR and BUG available, xys, sky and Turbots are optional.

Code: Select all

. . . | . 8 . | . 6 .
. . . | 3 6 . | . 7 4
. . 2 | . . 9 | . . .
---------------------
. 8 . | . 1 . | 6 . .
2 6 . | 8 . 3 | . 5 1
. . 7 | . 9 . | . 3 .
---------------------
. . . | 4 . . | 8 . .
8 2 . | . 5 6 | . . .
. 9 . | . 2 . | . . .

[wapati]

Tad bad.

Jelly is there, not too strong.

Code: Select all

. . . | . . 3 | 1 6 .
. 7 . | 8 2 . | . . 9
. . 6 | . . . | . . 4
---------------------
. 6 . | . 3 . | . . 5
. 3 . | 6 . 2 | . 1 .
8 . . | . 1 . | . 4 .
---------------------
6 . . | . . . | 3 . .
9 . . | . 5 4 | . 7 .
. 5 3 | 1 . . | . . .


[wapati]

If you are strong on Turbot, this is easy.

There are a lot of small patterns here. Have fun!

Code: Select all

8 . 2|. 9 .|6 3 .
. 4 .|. . .|. . 9
6 . 9|2 . .|. . 5
-----+-----+-----
. . 7|. 8 4|. . .
9 . .|1 . 2|. . 7
. . .|5 7 .|9 . .
-----+-----+-----
5 . .|. . 9|1 . 6
3 . .|. . .|. 5 .
. 2 6|. 1 .|3 . 8