The New Sudoku Players' Forum

[shye]

Code: Select all

+-------+-------+-------+
| 9 8 7 | 6 . . | . 5 . |
| 4 5 . | . . . | . 6 7 |
| . . . | . . 5 | . . . |
+-------+-------+-------+
| . . 4 | . 5 . | 7 . . |
| 5 7 . | 9 . 3 | . . . |
| . . . | . 2 . | . . 5 |
+-------+-------+-------+
| . . 5 | . . 4 | . . 8 |
| 8 4 . | . 6 . | . 7 9 |
| . 3 . | . 8 . | . 4 6 |
+-------+-------+-------+
9876...5.45.....67.....5.....4.5.7..57.9.3.......2...5..5..4..884..6..79.3..8..46

estimated rating: 7.2

[P.O.]

Code: Select all

PAIR ROW: ((8 3 7) (1 2)) ((8 6 8) (1 2)) 
(((8 4 8) (1 2 3 5)) ((8 7 9) (1 2 3 5)))

PAIR COL: ((1 6 2) (1 2)) ((8 6 8) (1 2)) 
(((2 6 2) (1 2 8 9)) ((4 6 5) (1 6 8)) ((6 6 5) (1 6 7 8)) ((9 6 8) (1 2 7 9)))

12r1c6 => r2c7 <> 3,8,9
 r1c6=1 - r8n1{c6 c3} - r2n1{c3 c7}
 r1c6=2 - r8n2{c6 c3} - r2n2{c3 c7}

intersections:
((((9 0) (3 7 3) (1 2 3 4 8 9)) ((9 0) (3 8 3) (1 2 3 8 9)))
 (((8 0) (3 7 3) (1 2 3 4 8 9)) ((8 0) (3 8 3) (1 2 3 8 9))))

QUAD COL: ((2 7 3) (1 2)) ((7 7 9) (1 2 3)) ((8 7 9) (3 5)) ((9 7 9) (1 2 5))
(((1 7 3) (1 2 3 4)) ((3 7 3) (1 2 3 4 8 9)) ((5 7 6) (1 2 4 6 8)) ((6 7 6) (1 3 4 6 8 9)))

ste.


[yzfwsf]

g-Whip[7]: Supposing 4r3c4 would causes 7 to disappear in Box 2 => r3c4<>4
4r3c4 - 4r6(c4=c7) - 6c7(r6=r5) - 8c7(r5=r23) - 8r3(c8=c7) - 9c7(r3=r2) - 9r3(c8=c5) - 7b2(p8=.)
stte

[Cenoman]

Code: Select all

 +------------------------+--------------------------+--------------------------+
 |  9      8      7       |  6       fa134     12    |  1234     5       1234   |
 |  4      5     c123     | b1238     b139     89    |  12389    6       7      |
 |  1236   126    1236    |ga347-128 ga347-19  5     |  123489   12389   1234   |
 +------------------------+--------------------------+--------------------------+
 |  1236   1269   4       | e18        5      d68    |  7        12389   123    |
 |  5      7      1268    |  9        e14      3     |  12468    128     124    |
 |  136    169    13689   |  1478      2      d678   |  134689   1389    5      |
 +------------------------+--------------------------+--------------------------+
 |  1267   1269   5       |  1237      1379    4     |  123      123     8      |
 |  8      4     c12      |  35        6       12    |  35       7       9      |
 |  127    3     c129     |  1257      8      d79    |  125      4       6      |
 +------------------------+--------------------------+--------------------------+

(743)b2p278 = r2c45 - (3=129)r289c3 - (9=678)r469c6 - (8=14)b5p15 - r1c5 = (47)r3c45 => -128 r3c4, -19 r3c5 (+347 r3c45); lclste

[shye]

thank you for your solves!
here's my own solution

Code: Select all

.-------------------.---------------------.-----------------------.
| 9     8     7     | 6      k134    12   |k*1234    5      #123-4|
| 4     5    #123   | 1238    139    1289 | *12389   6       7    |
|*1236 *126  *1236  | 123478  13479  5    | *123489 *12389 k*1234 |
:-------------------+---------------------+-----------------------:
| 1236  1269  4     | 18      5      168  |  7       12389   123  |
| 5     7     1268  | 9       1-4    3    |  12468   128    k124  |
| 136   169   13689 | 1478    2      1678 |  134689  1389    5    |
:-------------------+---------------------+-----------------------:
| 1267  1269  5     | 1237    1379   4    | *123    #123     8    |
| 8     4     12    | 1235    6      12   | *1235    7       9    |
| 127   3     129   | 1257    8      1279 | *125     4       6    |
'-------------------'---------------------'-----------------------'

let x represent 123
x in b139 covered by r3, c7
3 of x to appear in #ed cells => remote triple, -4r1c9

solves with a two-string kite
4r1c5 = r1c7 - r3c9 = r5c9
=> -4r5c5 stte

[Cenoman]

let x represent 123
x in b139 covered by r3, c7
3 of x to appear in #ed cells => remote triple, -4r1c9

Nice first step !
Thank you for this not so hard puzzle, enabling the possibility of this effective technique.
I was aware of its existence while reading some use of it by you, by marek stefanik and by mith (sorry if I forget other players), but I'm unable to spot it.
So my question: could you (or any other expert) provide a link to a description and rationale of the "remote triple" pattern ?

[yzfwsf]

thank you for your solves!
here's my own solution

Code: Select all

.-------------------.---------------------.-----------------------.
| 9     8     7     | 6      k134    12   |k*1234    5      #123-4|
| 4     5    #123   | 1238    139    1289 | *12389   6       7    |
|*1236 *126  *1236  | 123478  13479  5    | *123489 *12389 k*1234 |
:-------------------+---------------------+-----------------------:
| 1236  1269  4     | 18      5      168  |  7       12389   123  |
| 5     7     1268  | 9       1-4    3    |  12468   128    k124  |
| 136   169   13689 | 1478    2      1678 |  134689  1389    5    |
:-------------------+---------------------+-----------------------:
| 1267  1269  5     | 1237    1379   4    | *123    #123     8    |
| 8     4     12    | 1235    6      12   | *1235    7       9    |
| 127   3     129   | 1257    8      1279 | *125     4       6    |
'-------------------'---------------------'-----------------------'

let x represent 123
x in b139 covered by r3, c7
3 of x to appear in #ed cells => remote triple, -4r1c9

solves with a two-string kite
4r1c5 = r1c7 - r3c9 = r5c9
=> -4r5c5 stte

My solver can find this solution path:

Code: Select all

Death Blossom Complex Type 3(MSLS): Set have degrees of freedom of 2-1234589{r12789c7} => r3c4<>1,r3c5<>1,r3c4<>2,r3c4<>3,r3c5<>3,r5c7<>1,r6c7<>1,r5c7<>2,r6c7<>3,r1c9<>4,r3c7<>1,r3c7<>2,r3c7<>3
  4r1c7-(4=1236){r3c1239}
  8r2c7,9r2c7-(89=12346){r3c123789}
2-String Kite: 4 in r1c7,r6c4 connected by b2p27 => r6c7 <> 4
stte


[shye]

Nice first step !
Thank you for this not so hard puzzle, enabling the possibility of this effective technique.
I was aware of its existence while reading some use of it by you, by marek stefanik and by mith (sorry if I forget other players), but I'm unable to spot it.
So my question: could you (or any other expert) provide a link to a description and rationale of the "remote triple" pattern ?

thanks! sorry for the late response
i usually just call a pattern a remote triple when i am able to prove 3 cells (not all in the same house) must be a set of 3 unique digits, and i think while this is in line with that, the elimination of 4r1c9 is not typically what the triples are used for
maybe some kind of mutant multifish is a better name. or perhaps not naming it is the best way about it

a bit of a vague answer sorry... someone else might have a more rigid definition on hand?

[eleven]

I wondered, how hard it would be to eliminate 4r1c9 without that nice trick.

Code: Select all

+-------------------------+-------------------------+--------------------------+
| 9       8       7       | 6       134     12      | d1234    5       123-4   |
| 4       5       123     | 1238    139     89      | d12389   6       7       |
| 1236    126     1236    |b123478 b13479   5       |ca123489 c12389  a1234    |
+-------------------------+-------------------------+--------------------------+
| 1236    1269    4       | 18      5       68      |  7       12389   123     |
| 5       7       1268    | 9       14      3       |  12468   128     124     |
| 136     169     13689   | 1478    2       678     |  134689  1389    5       |
+-------------------------+-------------------------+--------------------------+
| 1267    1269    5       | 1237    1379    4       | d123     123     8       |
| 8       4       12      | 35      6       12      | d35      7       9       |
| 127     3       129     | 1257    8       79      | d125     4       6       |
+-------------------------+-------------------------+-------------------------+

4r3c79 = (47-8|9)r3c45 = 89r3c78 - (8|9=12354)r27891c7 => -4r1c9
This is a kind of complementary elimination. It seems to me, that it works, if you get the remote triple and vice versa.
I had seen similar complementary eliminations, but never found a rule for them.

[Cenoman]

thanks! sorry for the late response
i usually just call a pattern a remote triple when i am able to prove 3 cells (not all in the same house) must be a set of 3 unique digits, and i think while this is in line with that, the elimination of 4r1c9 is not typically what the triples are used for
maybe some kind of mutant multifish is a better name. or perhaps not naming it is the best way about it

a bit of a vague answer sorry... someone else might have a more rigid definition on hand?

Thank you for responding. You have not to apologize for the delay.
My concern is not the name. The name is clear, and similar to the remote pair (two cells not in the same house having each a different digit from a pair); furthermore, it is fully appropriate here. You justify the remote triple with this sentences

let x represent 123
x in b139 covered by r3, c7

My question was: which (minimal) criteria must be met to prove a remote triple pattern ? Is there some conceptual post somewhere elaborating this ?
If you use it with your instinct, or rather with your own knowledge, don't worry.
Anyhow, thank you for the puzzle and your solution. They provide a good training !

[Cenoman]

4r3c79 = (47-8|9)r3c45 = 89r3c78 - (8|9=12354)r27891c7 => -4r1c9

Your chain, yzfwsf's second solution, and shye's justification of the remote triple (1,2,3 covered by r3, c7) made me search a symmetrical solution (I mean symmetrical roles for r3 and c7) Cell r3c7 is the issue.

Code: Select all

 +------------------------+--------------------------+--------------------------+
 |  9      8      7       |  6         134     12    | B1234     5       1234   |
 |  4      5      123     |  1238      139     89    | B12389    6       7      |
 | A1236  A126   A1236    |  123478    13479   5     | C123489  A12389  A1234   |
 +------------------------+--------------------------+--------------------------+
 |  1236   1269   4       |  18        5       68    |  7        12389   123    |
 |  5      7      1268    |  9         14      3     |  12468    128     124    |
 |  136    169    13689   |  1478      2       678   |  134689   1389    5      |
 +------------------------+--------------------------+--------------------------+
 |  1267   1269   5       |  1237      1379    4     | B123      123     8      |
 |  8      4     c12      |  35        6       12    | B35       7       9      |
 |  127    3     c129     |  1257      8      d79    | B125      4       6      |
 +------------------------+--------------------------+--------------------------+

I found this from my old learning document about ALS's, AALS's, ...
Consider AALS (1234689)r3c12389 [A], AALS(1234589)r12789c7 [B], AAAAALS(123489)r3c7 [C]

Code: Select all

        C   
      /   \
 123489  123489
    /       \
   A - 489 - B

RC: Restricted Common
A, B, C are linked two by two by RCs 4, 8, 9 that can exist each only once (in b3). Each RC 4,8,9 has a constraint degree 2. In addition, C is linked to A and B by RCs 1, 2, 3 that can exist each twice at most (in b1 and b9). Each RC 1,2,3 has a constraint degree 1. So the freedom degree of the net is:
5 + 2 + 2 - 3*2 - 3*1 = 0 => -4r1c9 (in sight of all instances of digit 4 in A, B, C)

Another much simpler solution:
MSLS 11 cells r3c12389, r12789c7, r3c7; 11 links: 489b3, 123r3, 123c7 => -4 r1c9, -123 r3c45, r56c7

In eleven's way:
(12345689) at r3c12389, r12789c7, r3c7: 8 digits in 11 cells, 5 digits can be there only once: 5, 6, 4, 8, 9, other 3 digits 1, 2, 3 must be there twice => +489 b3p14789 (-4r1c9) and eliminations of 123 in r3c45, r56c7.

[yzfwsf]

Another much simpler solution:
MSLS 11 cells r3c12389, r12789c7, r3c7; 11 links: 489b3, 123r3, 123c7 => -4 r1c9, -123 r3c45, r56c7

Yes, actually my solver also sees it as MSLS for cell 11 to find the elimination, and gives the MSLS keyword in the hint.