The New Sudoku Players' Forum

[jiesushang]

Hey，guys，as the #001，I design another question. （Actually，I have designed ten interesting questions.I will post all of them one by one.）
UR can be used.
Now，try to find all the eliminations under the current PM.

Welcome to discuss with me.

The picture links here --> https://ibb.co/jyxmkVT

[marek stefanik]

I'll begin. I haven't found a way to use the 2479 cells in r13 and the missing 7 in r7c9. Nothing I found is rank0, not even partially.

We begin with an xyz-wing in b12 and a rank1 almost-MSLS in b369:

Code: Select all

.---------------------------------.---------------------------------.---------------------------------.
| 123456789 a16         2479      |b136        123–6      2479      | 123456789  123456789  2479      |
| 123456789  123456789  123456789 | 123456789 b36         123456789 | 123456789  123456789  123456789 |
| 123456789  123456789  2479      | 123456789  2479       123456789 | 2479       123456789 #2367      |
:---------------------------------+---------------------------------+---------------------------------:
| 123456789  123456789  123456789 | 123456789  123456789  123456789 | 123456789  123456789  123456789 |
| 123456789  456        123456789 | 123456789  456        123456789 |#19         123456789 #3679      |
| 123456789  123456789  123456789 | 123456789  123456789  123456789 | 123456789  123456789 #367       |
:---------------------------------+---------------------------------+---------------------------------:
| 123456789  123456789  123458    | 123456789  456        1238      |#2358      #2358       145689–23 |
| 123456789  456        18        | 123456789  123456789  1458      | 123456789  123456789 #35678     |
| 123456789  123456789  123456789 | 123456789  123456789  123456789 |#158        123456789 #35678     |
'---------------------------------'---------------------------------'---------------------------------'

(6=1)r1c2 – (1=36)b2p15 => –6r1c5
9 truths: r579c7, r7c8, r35689c9 (#-marked cells)
10 links: 1c7, 2r7, 2c9, 3r7, 3c9, 5b9, 6c9, 7c9, 8b9, 9b6
=> –23r7c9

Now it gets more difficult. I will try to notate the next step as an AIC net, but no promises.

Code: Select all

.---------------------------------.---------------------------------.---------------------------------.
|123456789 bc16         2479      |b136      ab123        2479      | 13456789–2 13456789–2 479–2     |
| 123456789  123456789  123456789 |123456789 bc36         123456789 | 123456789  123456789  123456789 |
| 123456789  123456789  2479      | 13456789–2 479–2      13456789–2| 2479       123456789 #2367      |
:---------------------------------+---------------------------------+---------------------------------:
| 123456789  123456789  123456789 | 123456789  123456789  123456789 | 123456789  123456789  123456789 |
| 123456789 d456        123456789 | 123456789 d456        123456789 |#19         123456789 #3679      |
| 123456789  123456789  123456789 | 123456789  123456789  123456789 | 123456789  123456789 #367       |
:---------------------------------+---------------------------------+---------------------------------:
| 123456789 123456789 ef123458    | 123456789 d456       f1238      |#2358      #2358       145689    |
| 123456789 d456       f18        | 123456789 123456789 ef1458      | 123456789  123456789 #35678     |
| 123456789  123456789  123456789 | 123456789 123456789   123456789 |#158        123456789 #35678     |
'---------------------------------'---------------------------------'---------------------------------'

2r1c5 = (136b2p125 & r1c245) – (1r1c2 | 3r2c5) = (6r1c2 & r2c5) – ((6=45)r58c2 & r57c5) – ((4|5)r7c3 | r8c6) =UR 18r78c36= (2|3)r7c36 – 23r7c78 =#= 2r3c9 => –2r1c789, –2r3c456

The hidden section proves an extra elimination (-1r1c7), which I will not try to notate as an AIC net.

Multilink: Show

Code: Select all

+----------+----------+----------+
| .  .  .  | .  .  .  | .  .  .  |
| .  .  .  | .  .  .  | .  .  .  |
| .  .  .  | .  .  .  | .  .  .  |
+----------+----------+----------+
| .  .  .  | .  .  .  | .  .  .  |
| .#*45 .  | .#*45 .  | .  .  .  |
| .  .  .  | .  .  .  | .  .  .  |
+----------+----------+----------+
| .  .#1458| .#*45 18 | .  .  .  |
| .#*45 18 | .  .*1458| .  .  .  |
| .  .  .  | .  .  .  | .  .  .  |
+----------+----------+----------+

UR 18r78c36 – at most 3 true candidates, i.e. 3-link
For each digit x:
2L x# = xr57c25b7 / 2
2L x* = xr58c25b8 / 2
7L A (all marked candidates) = ([2]4#, [2]4*, [2]5#, [2]5*, [3](UR 18) + r7c36, r8c36) / 2

Code: Select all

+----------+----------+----------+
| .  6  .  | 6  .  .  | .  .  .  |
| .  .  .  | .  6  .  | .  .  .  |
| .  .  .  | .  .  .  | .  .  .  |
+----------+----------+----------+
| .  .  .  | .  .  .  | .  .  .  |
| . 456 .  | . 456 .  | .  .  .  |
| .  .  .  | .  .  .  | .  .  .  |
+----------+----------+----------+
| .  . 1458| . 456 18 | .  .  .  |
| . 456 18 | .  . 1458| .  .  .  |
| .  .  .  | .  .  .  | .  .  .  |
+----------+----------+----------+

9L B = ([7]A, 6r1, 6c25, 6b2 + r5c25, r7c356, r8c236) / 2
(A, the cells of A, and the 6s)

Finally, we can prove the eliminations:

Code: Select all

.---------------------------------.---------------------------------.---------------------------------.
| 123456789 #16         2479      |#136       #123        2479      | 123456789  123456789  2479      |
| 123456789  123456789  123456789 | 123456789 #36         123456789 | 123456789  123456789  123456789 |
| 123456789  123456789  2479      | 123456789  2479       123456789 | 2479       123456789 #2367      |
:---------------------------------+---------------------------------+---------------------------------:
| 123456789  123456789  123456789 | 123456789  123456789  123456789 | 123456789  123456789  123456789 |
| 123456789 #456        123456789 | 123456789 #456        123456789 |#19         123456789 #3679      |
| 123456789  123456789  123456789 | 123456789  123456789  123456789 | 123456789  123456789 #367       |
:---------------------------------+---------------------------------+---------------------------------:
| 123456789  123456789 #123458    | 123456789 #456       #1238      |#2358      #2358       145689    |
| 123456789 #456       #18        | 123456789  123456789 #1458      | 123456789  123456789 #35678     |
| 123456789  123456789  123456789 | 123456789  123456789  123456789 |#158        123456789 #35678     |
'---------------------------------'---------------------------------'---------------------------------'

21 truths: r1c245, r2c5, r3c9, r5c2579, r6c9, r7c35678, r8c2369, r9c79 (#-marked cells)
22 links: [9]B, 1r1, 1c7, 2r7, 3r7, 3c9, 3b2, 5b9, 6c9, 7c9, 8b9, 9b6, [2]placeholder
where instead of the placeholder we put 2r1b3 for –2r1c789 or 2r3b2 for –2r3c456
In either case we also get -1r1c7.

Marek

[jiesushang]

Without a little tip，this training will be so difficult.
Technically，if R7C36 has one 23，we can get an almost MSLS .That is to say R3C9=2.
On the other hand，if R7C3orR8C6 has one 45，we can make 136xyz-wing be a group.That is to say R1C5=2.
Then,let me prove （2）R3C9 -- （2）R1C5.
When R3C9=2 and R1C5=2，paying attention to those （479）R13C35679，I mark R3C5=a.
Because of UR in R13C59，R1C9 can't equal R3C5.So，I mark R1C9=b.
Then，we can mark all of them：R1C7=c、R3C7=c ==> R1C3=a、R3C3=b.
Then，let's think about R13C359.They can compose 2ab UR.It's contradictory.
So，we can get （2）R3C9 -- （2）R1C5.
Based on this，the almost MSLS and xyz-wing group become a real Rank=0 structure.

The answer links here --> https://ibb.co/CwfF9fw

I'm gald to discuss with you.

jiesushang

[marek stefanik]

Because of UR in R13C59...

I don't understand, there is no UR in r13c59. The missing 479 in r1c5 always resolve it.

Marek

[m_b_metcalf]

The picture links here --> https://ibb.co/jyxmkVT

But where is the 729- digit string?

[jiesushang]

Because it isn't a standard sukaku，although there is no 479 in R1C5，it also will be AR.

jiesushang