The New Sudoku Players' Forum

[SteveG48]

Code: Select all

 *-----------*
 |6..|9.3|..7|
 |...|..7|.2.|
 |2.3|.6.|1..|
 |---+---+---|
 |7..|...|9.1|
 |...|4..|...|
 |9.1|...|..6|
 |---+---+---|
 |...|.9.|7.8|
 |.5.|2..|...|
 |1..|5.8|...|
 *-----------*


[SpAce]

Code: Select all

.---------------------.-----------------.-------------------.
|  6    1       45    | 9   2       3   |  458   48    7    |
|  458  489     4589  | 1   45      7   |  6     2     3    |
|  2    7       3     | 8   6       5-4 |  1     9    a5#4  |
:---------------------+-----------------+-------------------:
|  7    248     2458  | 36  358     256 |  9     348   1    |
|  358  2368    2568  | 4   1       9   |  258   7     25   |
|  9    248     1     | 7   358     25  |  2458  348   6    |
:---------------------+-----------------+-------------------:
|  34   2346    246   | 36  9       1   |  7     5     8    |
| c38   5     cd79+68 | 2   47+3  ad6#4 | c34    1    b9-4+ |
|  1    39      79+   | 5   47+3    8   |  234   6    b49+2 |
'---------------------'-----------------'-------------------'

Extended UR+5 (79,47,49)r89c359 using mixed +internals (68r8c3), #externals (4r3c9, 4r8c6)

(4)r3c9 = r89c9 - (438)r8c713 == (64)r8c36 => -4 r3c6,r8c9; stte

uncompressed: Show

Code: Select all

.---------------------.-----------------.--------------------.
|  6    1       45    | 9   2       3   |  458   48     7    |
|  458  489     4589  | 1   45      7   |  6     2      3    |
|  2    7       3     | 8   6       5-4 |  1     9    ab5#4  |
:---------------------+-----------------+--------------------:
|  7    248     2458  | 36  358     256 |  9     348    1    |
|  358  2368    2568  | 4   1       9   |  258   7      25   |
|  9    248     1     | 7   358     25  |  2458  348    6    |
:---------------------+-----------------+--------------------:
|  34   2346    246   | 36  9       1   |  7     5      8    |
| e38   5     fg79+68 | 2   47+3  ah6#4 | d34    1     c9-4+ |
|  1    39      79+   | 5   47+3    8   |  234   6     c49+2 |
'---------------------'-----------------'--------------------'

(4)r3c9|r8c6 == [(4)r3c9 = r89c9 - (4=3)r8c7 - (3=8)r8c1 - (8)r8c3 == (6)r8c3 - (6=4)r8c6] => -4 r3c6,r8c9; stte

As a kraken:

Code: Select all

(4)r3c9
(4)r8c6
(6)r8c3 - (6=4)r8c6
(8)r8c3 - (8=3)r8c1 - (3=4)r8c7 - r89c9 = (4)r3c9

=> -4 r3c6,r8c9; stte

[pjb]

Code: Select all

 6       1       45     | 9      2      3      | 458    48     7     
f458     489     4589   | 1     e45     7      | 6      2      3     
 2       7       3      | 8      6     d45     | 1      9      45     
------------------------+----------------------+---------------------
 7       248     2458   |a36     358   b256    | 9      348    1     
g358     2368    2568   | 4      1      9      |i258    7     h25     
 9       248     1      | 7      358    25     |i2458   348    6     
------------------------+----------------------+---------------------
m34      2346    246    | 6-3    9      1      | 7      5      8     
l38      5       6789   | 2      347   c46     |k34     1      49     
 1       39      79     | 5      347    8      |j234    6      249   


(3=6)r4c4 - (6)r4c6 = (6-4)r8c6 = (4)r3c6 - (4=5)r2c5 - (5)r2c1 = (5-3)r5c1 - (5=2)r5c9 - (2)r56c7 = (2-3)r9c7 = (3)r8c7 - (3)r8c1 = (3)r7c1 => -3 r7c4; stte

Phil

[SpAce]

(3=6)r4c4 - (6)r4c6 = (6-4)r8c6 = (4)r3c6 - (4=5)r2c5 - (5)r2c1 = (5-3)r5c1 - (5=2)r5c9 - (2)r56c7 = (2-3)r9c7 = (3)r8c7 - (3)r8c1 = (3)r7c1 => -3 r7c4; stte

An interesting way to write a memory chain. Almost perfectly disguised as an AIC but the non-alternating link blows its cover.

[Mauriès Robert]

Hi Space,
I'm glad you point out that the sequence used by Phil is not an AIC but an "anti-track diagram" written with eureka.
I would have written in the symbolism of TDP:
P'(3r4c4) : (-3r4c4) => 6r4c4->6r8c6->4r3c6->5r2c5->[5r5c1->(3r78c1 and 2r5c9)->2r9c7->3r8c7]->3r7c1 => -3r7c4.
It is the element 3r78c1 that is missing in its sequence, but this leads to nested AICs I think ?
Robert

[SpAce]

I'm glad you point out that the sequence used by Phil is not an AIC but an "anti-track diagram" written with eureka.

I said it wasn't an AIC, but the rest is obviously your addition. Sure, it can be written as an anti-track diagram, but it's not an inherent property of the pattern. What describes it more accurately and generally is 'memory chain', like I said, or 'whip'. (An anti-track could be a basic AIC just as well.)

Such a pattern can be expressed in many commonly accepted ways, but Phil's is not one of them. Some valid ways to write it would be a Eureka-style memory chain (with memory markers), a nested AIC, a kraken column, a network diagram, Denis' notation, and a triangular matrix.

(Sorry if I don't fully count your construction diagram among them either, because it's so hard to read and without any clearly defined syntax rules. It's infinitely better than Phil's, though, because it doesn't disguise as something it's not. It's better to be ugly than to cheat )

I would have written in the symbolism of TDP:
P'(3r4c4) : (-3r4c4) => 6r4c4->6r8c6->4r3c6->5r2c5->[5r5c1->(3r78c1 and 2r5c9)->2r9c7->3r8c7]->3r7c1 => -3r7c4.
It is the element 3r78c1 that is missing in its sequence, but this leads to nested AICs I think ?

3r78c1 is not needed (5r5c1 is enough), but you're right that the easiest way to write it as an AIC is to use a nested one:

(3=6)r4c4 - r4c6 = (6-4)r8c6 = r3c6 - (4=5)r2c5 - r2c1 = r5c1 - [(5=2)r5c9 - r9c9 = (2-3)r9c7 = r8c7 - r8c1 = (3)r5c1] = (3)r7c1 => -3 r7c4; stte

(I've replaced Phil's original group node 2r56c7 with the simpler 2r9c9 in that and the following examples.)

As a matrix:

9x9 TM: Show

Code: Select all

4N4: 3r4c4 6r4c4
6C6: . . . 6r4c6 6r8c6
4C6: . . . . . . 4r8c6 4r3c6
2N5: . . . . . . . . . 4r2c5 5r2c5
5C1: . . . . . . . . . . . . 5r2c1 5r5c1
5N9: . . . . . . . . . . . . . . . 5r5c9 2r5c9
2R9: . . . . . . . . . . . . . . . . . . 2r9c9 2r9c7
3C7: . . . . . . . . . . . . . . . . . . . . . 3r9c7 3r8c7
3C1: 3r7c1 . . . . . . . . . . . . 3r5c1 . . . . . . 3r8c1
==========================================================
    -3r7c4


As a memory chain:

(3=6)r4c4 - r4c6 = (6-4)r8c6 = r3c6 - (4=5)r2c5 - r2c1 = (5*)r5c1 - (5=2)r5c9 - r9c9 = (2-3)r9c7 = r8c7 - r8*5c1 = (3)r7c1 => -3 r7c4; stte

As a whip:

whip[9]: r4c4{n3 n6} - c6n6{r4 r8} - c6n4{r8 r3} - r2c5{n4 n5} - c1n5{r2 r5} - r5c9{n5 n2} - r9n2{c9 c7} - c7n3{r9 r8} - c1n3{r8 .} ==> r7c4 ≠ 3; stte

As a kraken column / network diagram:

Code: Select all

(3)r7c1
||
(3)r5c1 - (5)r5c1 = r2c1 - (5=4)r2c5 - r3c6 = (4-6)r8c6 = r4c6 - (6=3)r4c4
||      /
||     '-----------------------------------------,
||                                              /
(3)r8c1 - r8c7 = (3-2)r9c7 = r9c9 - (2=5)r5c9 -'

=> -3 r7c4

[Cenoman]

Code: Select all

 +----------------------+-------------------+---------------------+
 |  6     1      45     |  9    2     3     |  458    48    7     |
 | b458   489    4589   |  1    4-5   7     |  6      2     3     |
 |  2     7      3      |  8    6    z45    |  1      9    y45    |
 +----------------------+-------------------+---------------------+
 |  7     248    2458   |  36  B358   256   |  9      348   1     |
 |  358   2368   2568   |  4    1     9     |  258    7     25    |
 |  9     248    1      |  7   B358   25    |  2458   348   6     |
 +----------------------+-------------------+---------------------+
 | b34    2346   246    |  36   9     1     |  7      5     8     |
 | b38    5      6789   |  2    347   46    |  34     1    y49    |
 |  1    a39     79     |  5   A347   8     | x234    6    y249   |
 +----------------------+-------------------+---------------------+

Kraken row (3)r9c257
(3)r9c2 - (3=485)r278c1
(3)r9c5 - (3=85)r46c5
(3-2)r9c7 = (2-945)r389c9 = (5)r3c6
=> -5 r2c5; ste

Could be written as an almost ALS W-Wing : [(5=483)r278c1 - r9c2 = r9c5 - (3=85)r46c5] = (3-2)r9c7 = (2-945)r389c9 = (5)r3c6 => -5 r2c5; ste

[Ngisa]

Code: Select all

+---------------------+------------------+--------------------+
| 6      1       458  | 9     2      3   | 458     48     7   |
| 458    489     4589 | 1     45     7   | 6       2      3   |
| 2      7       3    | 8     6     d45  | 1       9     c45  |
+---------------------+------------------+--------------------+
| 7      2468    2458 | 36    358    256 | 9       348    1   |
|j38-5  i2368    2568 | 4     1      9   | 258     7     a25  |
| 9      248     1    | 7     358    25  | 2458    348    6   |
+---------------------+------------------+--------------------+
| 34     2346    246  | 36    9      1   | 7       5      8   |
|f38     5      g6789 | 2     347   e46* |c3*4     1     b49  |
| 1     h39     g79   | 5     347    8   | 234     6     b249 |
+---------------------+------------------+--------------------+


A net
(5=2)r5c9 - (2=9|4)r89c9 - (4=3*)r8c7,(-4)r3c9 = r3c6 - (4=6*)r8c6 - (3*=8)r8c1 - (6*8=7|9)r89c3 - (9=3)r8c2 - r5c2 = (3)r5c1 => - 5r5c1; stte

Clement

[SteveG48]

Code: Select all

+---------------------+------------------+--------------------+
| 6      1       458  | 9     2      3   | 458     48     7   |
| 458    489     4589 | 1     45     7   | 6       2      3   |
| 2      7       3    | 8     6     d45  | 1       9     c45  |
+---------------------+------------------+--------------------+
| 7      2468    2458 | 36    358    256 | 9       348    1   |
|j38-5  i2368    2568 | 4     1      9   | 258     7     a25  |
| 9      248     1    | 7     358    25  | 2458    348    6   |
+---------------------+------------------+--------------------+
| 34     2346    246  | 36    9      1   | 7       5      8   |
|f38     5      g6789 | 2     347   e46* |c3*4     1     b49  |
| 1     h39     g79   | 5     347    8   | 234     6     b249 |
+---------------------+------------------+--------------------+


A net
(5=2)r5c9 - (2=9|4)r89c9 - (4=3*)r8c7,(-4)r3c9 = r3c6 - (4=6*)r8c6 - (3*=8)r8c1 - (6*8=7|9)r89c3 - (9=3)r8c2 - r5c2 = (3)r5c1 => - 5r5c1; stte

Clement

Nice solution, Clemont. You don't need a net if you write it this way (which doesn't change your solution at all):

(5=249)r589c9 - 4r3c9,r8c7 = ((46)r38c6)&((38)r8c17) - (6|8=793)b7p689 - 3r5c2 = 3r5c1 => -5 r5c1 ; stte

[Ngisa]

[quote="SteveG48"][quote="Ngisa"][code] Good, I can see. Thanks.

[pjb]

SpAce, I am curious to see which link in my chain is non-alternating. You may write it differently, but what I proposed is perfectly clear. BTW, can you point me to a link where rules for writing Eureka chains with memory are defined?

Phil

[SpAce]

Hi Phil,

SpAce, I am curious to see which link in my chain is non-alternating.

I already colored the two adjacent weak links red in my original post, but I guess they're not very visible. Perhaps this is:

(3=6)r4c4 - (6)r4c6 = (6-4)r8c6 = (4)r3c6 - (4=5)r2c5 - (5)r2c1 = (5-3)r5c1 - (5=2)r5c9 - (2)r56c7 = (2-3)r9c7 = (3)r8c7 - (3)r8c1 = (3)r7c1 => -3 r7c4; stte

See it now?

You may write it differently, but what I proposed is perfectly clear.

To you, perhaps. You might want to ask how many people here would agree with that claim. Obviously I don't, but I guess that counts for nothing. Apparently Robert agreed with me, though, and since no one else has said anything, I would guess they didn't disagree with my assessment either.

To be honest, I don't think there's anything to debate about it. The biggest problem with your chain is that it looks like an AIC, which gives the reader a false impression about its simplicity and interpretation. The whole reason why I suspected it couldn't be one was that I knew the puzzle was not solvable with a simple AIC. Otherwise I wouldn't have even bothered to read the chain, because I generally assume simple AICs to be correct.

You're of course free to use whatever ad hoc syntax you like for your memory chains, but if it happens to look like a normal AIC then you should at least tell the reader that it's not. Otherwise it's very confusing, especially for people who're just learning about AICs. Your chain had neither memory markers nor a label to warn the reader that it wasn't an AIC.

BTW, can you point me to a link where rules for writing Eureka chains with memory are defined?

No, because Eureka was designed to write AICs instead of memory chains. The latter is an unofficial extension, so somewhat different ad hoc syntaxes are expected and accepted. (Of course I think there's only one logical and readable way to do it, but that's just me.)

Yet there's one overarching rule about writing anything in Eureka, and it's that the links must be alternating. That rule should never be broken, whether one writes AICs, loops, discontinuous loops, krakens, network diagrams, or even memory chains. The same rule applies to Denis' chains as well, though they have somewhat different interpretation rules otherwise.

My preference of writing memory chains is explained in the lower half of this post. I don't claim it's official, but it's rather easy to argue why it's better than any alternatives that I've seen. Also, with that syntax it's not necessary to label the chain as a memory chain because it's obvious anyway. If no such markers are used, the chain should definitely be labeled to avoid confusion with normal AICs.

If one wants a simpler and cleaner way of writing memory chains, then I suggest looking at Denis' whip-notation. The price of the apparent simplicity is that it has less information (no z- and t-candidates), which makes it less intuitive and harder to read, imo. Nevertheless it's unambiguously defined and can be interpreted correctly if one knows that definition -- because the chain is always labeled as a 'whip'.

--
Btw, if the difference between AICs and memory chains is not clear to you, here it is. The links in AICs are between two adjacent nodes only. They must work independently of anything else in the chain. That's obviously not true in memory chains, which means they can't use the exact same syntax as AICs without causing confusion. Either memory markers (preferred) or a label is needed to distinguish them.

Furthermore, since AICs and memory chains are two different things, the latter shouldn't be called "Complex AICs" as you do on your site. Memory chains are not AICs, not even complex ones. Both simple and complex AICs must follow the same rule that all links apply to adjacent nodes only. (And both AICs and memory chains must follow the rule that all links alternate.)

[pjb]

SpAce
Still don't get it. Ignore the -3 and the chain alternates perfectly. The -3 is simply there to indicate the 3 at r5c1 is false , so the final link in the chain is valid.

Phil

[SpAce]

Still don't get it. Ignore the -3 and the chain alternates perfectly. The -3 is simply there to indicate the 3 at r5c1 is false , so the final link in the chain is valid.

It's obvious why it's there, but it's an invalid way to write it. I already explained why, and presented several valid alternatives earlier. The logic itself is correct, but your notation isn't as per our normal standards.

If you don't believe me, ask Steve, for example. He knows how to write both valid AICs and memory chains. I'm not particularly interested in debating this (or anything). Debates tend to get me banned around here.