The New Sudoku Players' Forum

[ArkieTech]

Code: Select all

 *-----------*
 |..4|1..|...|
 |...|.38|.2.|
 |8.2|...|43.|
 |---+---+---|
 |.3.|..2|7..|
 |..1|8.3|...|
 |7..|...|...|
 |---+---+---|
 |...|..6|.87|
 |...|...|9.4|
 |.9.|..1|.62|
 *-----------*


Play/Print this puzzle online

[SteveG48]

Code: Select all

 *-----------------------------------------------------------------------------*
 | 3       56      4       | 1       2       59      | 568     7       5689    |
 | 1569    1567    5679    | 4       3       8       | 156     2       156     |
 | 8       15      2       | 567     56      579     | 4       3       159     |
 *-------------------------+-------------------------+-------------------------|
 | 4569    3       5689    | 569     1569    2       | 7       1459    1568    |
 | 24569   2456    1       | 8       7       3       | 256     459     56      |
 | 7       2568    5689    | 569     1569    4       | 12568   159     3       |
 *-------------------------+-------------------------+-------------------------|
 | 1245    1245    35      | 2359    459     6       | 135     8       7       |
 | 1256    125678  35678   | 2357   a58     a57      | 9       1-5     4       |
 |b45      9       3578    |b357    b458     1       |c35      6       2       |
 *-----------------------------------------------------------------------------*


(5=78)r8c56 - (78=3)r9c145 - (3=5)r9c7 => -5 r8c8 ; lclste

Or better,

(5=7)r8c6 - (7=8)r9c1457 - (8=5)r8c5 => -5 r8c12348 ; lclste

[ArkieTech]

or

Code: Select all

 *-----------------------------------------------------------------------------*
 | 3       56      4       | 1       2       59      | 568     7       5689    |
 | 1569    1567    5679    | 4       3       8       | 156     2       156     |
 | 8       15      2       | 567     56      579     | 4       3       159     |
 |-------------------------+-------------------------+-------------------------|
 | 4569    3       5689    | 569     1569    2       | 7       1459    1568    |
 | 24569   2456    1       | 8       7       3       | 256     459     56      |
 | 7       2568    5689    | 569     1569    4       | 12568   159     3       |
 |-------------------------+-------------------------+-------------------------|
 | 1245    1245    35      | 239-5   49-5    6       | 135     8       7       |
 | 126-5   12678-5 3678-5  | 237-5  a58     c57      | 9       1-5     4       |
 |b45      9       3578    |b37-5   b48-5    1       |b35      6       2       |
 *-----------------------------------------------------------------------------*
(5=8)r8c5-(8=3457)r9c1457-(7=5)r8c6 => -5r79c45,r8c12348; lclste


[Leren]

Code: Select all

*--------------------------------------------------------------------------------*
| 3       56      4        | 1       2       59       | 568     7       5689     |
| 1569    1567    5679     | 4       3       8        | 156     2       156      |
| 8       15      2        | 567     56      579      | 4       3       159      |
|--------------------------+--------------------------+--------------------------|
| 4569    3       5689     | 569     1569    2        | 7       1459    1568     |
| 24569   2456    1        | 8       7       3        | 256     459     56       |
| 7       2568    5689     | 569     1569    4        | 12568   159     3        |
|--------------------------+--------------------------+--------------------------|
| 1245    1245    35       | 239-5   49-5    6        | 135     8       7        |
| 126-5   12678-5 3678-5   | 23-57  e58     a57       | 9       1-5     4        |
| 45      9      c78-35    |b37-5   d48-5    1        | 35      6       2        |
*--------------------------------------------------------------------------------*

(5=7) r8c6 - r9c4 = (7-8) r9c3 = r9c5 - (8=5) r8c5 Loop => - 5 r79c45, r8c12348, - 7 r8c4, - 35 r9c3; lclste

Leren

<edit> Recognised loop condition and added - 7 r8c4 and - 35 r9c3 on advice from daj95376 - thanks Danny.

Leren

[7b53]

All three solutions above => r8c56 = 5
another...
(78)r8c56 -(78)r9c45 = no solution => one of r8c56 must be 5.
r9c45 cannot be (78) ; then r9c3 = (78)

[daj95376]

Code: Select all

 *-----------------------------------------------------------------------------*
 | 3       56      4       | 1       2       59      | 568     7       5689    |
 | 1569    1567    5679    | 4       3       8       | 156     2       156     |
 | 8       15      2       | 567     56      579     | 4       3       159     |
 *-------------------------+-------------------------+-------------------------|
 | 4569    3       5689    | 569     1569    2       | 7       1459    1568    |
 | 24569   2456    1       | 8       7       3       | 256     459     56      |
 | 7       2568    5689    | 569     1569    4       | 12568   159     3       |
 *-------------------------+-------------------------+-------------------------|
 | 1245    1245    35      | 2359    459     6       | 135     8       7       |
 | 1256    125678  35678   | 2357   a58     a57      | 9       1-5     4       |
 |b45      9       3578    |b357    b458     1       |c35      6       2       |
 *-----------------------------------------------------------------------------*


(5=78)r8c56 - (78=3)r9c145 - (3=5)r9c7 => -5 r8c8 ; lclste

Or better,

(5=7)r8c6 - (7=8)r9c1457 - (8=5)r8c5 => -5 r8c12348 ; lclste

Hmmm!!! A wrinkle in the logic of your first chain.

(5=78)r8c56 - (78=345)r9c145 - (35=empty)r9c7 !!!

Your second chain ignores the eliminations for 5 in [box 8]. Read Dan's chain r-to-l to match your chain and see the missed eliminations.

_

[daj95376]

Code: Select all

*--------------------------------------------------------------------------------*
| 3       56      4        | 1       2       59       | 568     7       5689     |
| 1569    1567    5679     | 4       3       8        | 156     2       156      |
| 8       15      2        | 567     56      579      | 4       3       159      |
|--------------------------+--------------------------+--------------------------|
| 4569    3       5689     | 569     1569    2        | 7       1459    1568     |
| 24569   2456    1        | 8       7       3        | 256     459     56       |
| 7       2568    5689     | 569     1569    4        | 12568   159     3        |
|--------------------------+--------------------------+--------------------------|
| 1245    1245    35       | 239-5   49-5    6        | 135     8       7        |
| 126-5   12678-5 3678-5   | 237-5  e58     a57       | 9       1-5     4        |
| 45      9      c3578     |b37-5   d48-5    1        | 35      6       2        |
*--------------------------------------------------------------------------------*

(5=7) r8c6 - r9c4 = (7-8) r9c3 = r9c5 - (8=5) r8c5 => - 5 r79c45, r8c12348; lclste

Your chain is a continuous loop, so you can add these eliminations: -7 r8c4; -3 r9c3

Unfortunately, no real help, again.
_

[daj95376]

The only stte solution found by my solver.

Code: Select all

 +--------------------------------------------------------------------------------+
 |  3       56      4       |  1       2       59      |  568     7       5689    |
 |  1569    1567    5679    |  4       3       8       |  156     2       156     |
 |  8       15      2       |  567     56      579     |  4       3       159     |
 |--------------------------+--------------------------+--------------------------|
 |  4569    3       5689    |  569     1569    2       |  7      f1459    1568    |
 |  24569   2456    1       |  8       7       3       | e256    f459    e56      |
 |  7      c2568    5689    |  569     1569    4       | d12568  f159     3       |
 |--------------------------+--------------------------+--------------------------|
 |  1245    1245    35      |  2359    459     6       |  135     8       7       |
 |  1256   b125678  35678   |  2357   a58      57      |  9      g15      4       |
 |  45      9       3578    |  357     458     1       |  35      6       2       |
 +--------------------------------------------------------------------------------+
 # 115 eliminations remain

 (5=8)r8c5 - r8c2 = (8-2)r6c2 = r6c7 - (2=56)r5c79 - (5)r456c8 = (5)r8c8 - loop

  =>  -56 r6c2; -58 r8c3; -5 r4c9,r6c7,r8c1246

 stte


_

[SteveG48]

(5=78)r8c56 - (78=3)r9c145 - (3=5)r9c7 => -5 r8c8 ; lclste

Or better,

(5=7)r8c6 - (7=8)r9c1457 - (8=5)r8c5 => -5 r8c12348 ; lclste

Hmmm!!! A wrinkle in the logic of your first chain.

(5=78)r8c56 - (78=345)r9c145 - (35=empty)r9c7 !!!

Yes, I noticed that. That's what led me to look at it again. A very interesting puzzle.

Your second chain ignores the eliminations for 5 in [box 8]. Read Dan's chain r-to-l to match your chain and see the missed eliminations.

_

Yes, I'm bad about missing eliminations. I didn't want to go back again.

[Leren]

daj95376 wrote: Your chain is a continuous loop, so you can add these eliminations: -7 r8c4; -3 r9c3

I can also add - 5 r9c3 for a total of 12 eliminations - edited my post accordingly. Still requires a lclste finish.

Leren

[Sudtyro2]

I'd like to briefly revisit the b789 floor of the November 8, 2014 puzzle, shown below.

Code: Select all

  ----------------------+------------------+---------------
 |  1245  1245    35    |  2359   459   6  |  135  8    7  |
 |  1256  125678  35678 |  2357   58    57 |  9    1-5  4  |
 |  45    9       3578  |  357    458   1  |  35   6    2  |
  ---------------------------------------------------------

In studying this grid segment, I used a simple, 1-color algorithm that generated one possible network solution for the -5r8c8 elimination (EE) starting with the Kraken cell (458)r9c5.

Code: Select all

4r9c5 – (4=5)r9c1 –- 5r9c4
 ||                /  ||
 ||               /  3r9c4 – (3=5)r9c7 –--- EE
 ||              /    ||                  /
 ||             /    7r9c4 – (7=5)r8c6 --
 ||            /                        /
5r9c5 ---------                        /
 ||                                   /
8r9c5 – (8=5)r8c5 --------------------


This type of network is easy to derive manually (in minutes), but it does lack the more familiar appearance of a conventional chain. So here's a first attempt at “linearizing” one of these networks:
Start by dropping all explicit weak links to the EE.
Reverse the bottom branch of the starting Kraken cell to begin an AIC:

Code: Select all

            4r9c5 - (4=5)r9c1 –- ...
             ||                /   
            5r9c5 ------------     
             ||
(5=8)r8c5 – 8r9c5

The Kraken cell segment and its two upper branches are equivalent (I think) to:
(8=45)r9c15, which is both an ALS and an ANP, and reads, if 8r9c5 is false, then the NP(45)r9c15 is true, along with the two possible positions of the 5-digit. The chain so far then becomes:

Code: Select all

(5=8)r8c5 – (8=45)r9c15 - ...

This leaves only the second Kraken cell, (357)r9c4 and its branches. The Kraken cell itself can be written as:
(5=3|7)r9c4, where the (|) symbol is the XOR logical operator, which helps to distinguish a pair of XOR'd digits from a pair of AND'd digits. The node reads, if 5r9c4 is false, then 3 or 7 must be true. The chain so far then becomes:

Code: Select all

(5=8)r8c5 – (8=45)r9c15 – (5=3|7)r9c4 - ...

The two remaining branches of the Kraken cell are equivalent to:
(37=5)r8c6,r9c7 where the 37 pair is logically AND'd. The node reads, if 3 and 7 are not both true (i.e. logically false), then one or both of 5r8c6,5r9c7 must be true. The AIC is then completed as:

Code: Select all

(5=8)r8c5 – (8=45)r9c15 – (5=3|7)r9c4 – (37=5)r8c6,r9c7 => -5r8c8

My first (negative) thought is that it looks like an AIC, but the last node refers to two cells that are not peers. Is this legit?

OK...bracing for the impact! Hey, Gurth, I feel your “notation” pain!

SteveC

[eleven]

In my eyes this is an attempt to write an xyz-wing followed by an xy-wing as one chain, an unnatural way for a manual solver.
If 5r9c4 would not lead to a contradiction (because of the xyz-wing), before it leads to the xy-wing elimination, my preferred way to denote it, would be as an almost xy-wing.

[aran]

Sudtyro 2
What you have identified without naming it is an XY-wing.
As a recognized structure, this can be used in the chain to generate both concision and interest.
(5=8)r8c5-(8=45)r9c15-5r9c4=XY-5r8c8 => <5>r8c8
How much descriptive detail the XY wing requires is a matter of opinon.
XY-W (r9c47+r8c8) appears much too long.
XY is concise but perhaps not excessively so, it being clear from the chain after all that
(i) r9c4 = XY cell
(ii) Z = 5

[eleven]

Again, these are just notation tricks. You could write as well:
xyz-wing 458r8c5,r9c15, xy-wing 357r8c7,r9c47 => r8c8,r9c5<>5

xyz-wing: (5=8)r8c5-(8=45)r9c15 =>r9c4<>5
xy-wing: (5=7)r8c7-(7=3)r9c4-(3=5)r9c7=>r8c8,r9c5<>5

[Sudtyro2]

Thx to eleven and aran for your feedback! I find the interpretation of “Almost XY-Wing” to be very interesting and that it could appear as it did (in aran's chain) as ...-5r9c4=XY. Looking back now at the original network, it's clear that eliminating 5r9c4 from the Kraken cell (357)r9c4 would leave the segment shown below:

Code: Select all

   3r9c4 – (3=5)r9c7 –--- EE
    ||                  /
   7r9c4 – (7=5)r8c6 --

And this is simply the discontinuous loop formed by the remaining XY-Wing that would eliminate the EE.

I guess my original intent here was to form the AIC (without embedded patterns) by using only relatively simple links. I have a whole folder reserved for “Wings” but would have never thought to consider an Almost-Wing!

SteveC