platinum blonde full path

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platinum blonde full path

Postby champagne » Tue Jan 27, 2026 2:17 pm

.......12........3..23..4....18....5.6..7.8.......9.....85.....9...4.5..47...6...

Platinum Blonde is a relatively old puzzle
With a rating Sudoku Explainer 10.6/1.2/1.2, it looks relatively low in the family of hardest puzzles.

It has been the first sudoku identified by “abi” as a variant of the Exocet having one target made of 2 cells with a locked extra digit (4r7c89).
“blue” as far as I remember has seen later a variant with a target of 3 digits with 2 extra digits locked, but I did not store this variant.

After the “golden nugget” not yet solved by “yzfwsf” 'code, I wanted to see if this sudoku was solved.

It is and, surprise, the sudoku has also a MSLS giving , with the Exocet, a cleaned PM solved with about 20 more steps of various solving technics by “yzfwsf”’ code.

I’ll copy in the next post this path, till the point STTE;

I wanted also to see if the strategy to clear remaining options in the Exocet could be applied with relatively short “contradiction” sequences, this will be shown in the following posts.

The start PM after hidden single 5r9c3
Code: Select all
35678 34589 34679 |4679   5689   4578   |679    1      2     
15678 14589 4679  |124679 125689 124578 |679    56789  3     
15678 1589  2     |3      15689  1578   |4      56789  6789 
------------------------------------------------------------
237   2349  1     |8      236    234    |23679  234679 5     
235   6     349   |124    7      12345  |8      2349   149     
23578 23458 347   |1246   12356  9      |12367  23467  1467     
------------------------------------------------------------
1236  123   8     |5      1239   1237   |123679 234679 14679
9     123   36    |127    4      12378  |5      23678  1678     
4     7     5     |129    12389  6      |1239   2389   189     


And the solution grid

Code: Select all
1=839 465 712
2=146 782 953
3=752 391 486

4=391 824 675
5=564 173 829
6=287 659 341

7=628 537 194
8=913 248 567
9=475 916 238
champagne
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Posts: 7847
Joined: 02 August 2007
Location: France Brittany

yzfwsf full path for platinum blonde

Postby champagne » Tue Jan 27, 2026 2:39 pm

Here below the path copied from "yzfwsf" solver

Hidden Text: Show
Code: Select all
Hidden Single: 5 in r9 => r9c3=5
MSLS:15 Cells r5689c3489, 15 Links 49r5,467r6,67r8,9r9,3c3,12c4,23c8,1c9,8b9
17 Eliminations:r2c4,r7c9<>1,r47c8,r2c4<>2,r47c8,r1c3<>3,r5c6,r6c2<>4,r6c57<>6,r6c17,r8c6<>7,r9c57<>9
Almost Locked Set XY-Wing: A=r123456c1{1235678}, B=b4p478{2358}, C=r1256c3{34679}, X,Y=6, 3, Z=2 =>  r4c2<>2
Junior Exocet:Base Cells-r1c7,r2c7;Target Cells-r4c8,r4c9,r7c8,r7c9;Cross Cells-r347c123456   
Target Cells Check: r4c8<>46,r7c8<>6,r7c9<>6
Check X-Rule:r2c7<>6,r1c7<>6
True Base digits seen by base cells or both targets: r2c8<>7,r3c8<>7,r3c9<>7,r4c7<>7,r7c7<>7,r8c8<>7r2c8<>9,r3c8<>9,r3c9<>9,r4c7<>9,r7c7<>9,r9c8<>9
True Base digits in non-'S' cells: r1c1<>7,r1c6<>7,r2c1<>7,r2c6<>7r1c2<>9,r1c5<>9,r2c2<>9,r2c5<>9
Almost Locked Set XY-Wing: A=r5c14689{123459}, B=b4p1478{23578}, C=r4c8{79}, X,Y=9, 7, Z=3 =>  r5c3<>3
Grouped AIC Type 2: 9r3c2 = r4c2 - (9=7)r4c8 - r4c1 = (7-3)r6c3 = (3-6)r8c3 = (6-1)r7c1 = 1r23c1 => r3c2<>1
Almost Locked Set XY-Wing: A=r3c289{5689}, B=r3c12589{156789}, C=r4c12567{234679}, X,Y=9, 7, Z=58 =>  r3c6<>5 r3c6<>8
ALS Discontinuous Nice Loop: (1=2345786)r6c1235789 - r4c7 = r7c7 - r7c1 = (6-3)r8c3 = r6c3 - (3=2581)r6c1257 => r6c4<>1,r6c4<>2
Uniqueness Test 3: 79 in r12c47 => r5c4 <> 4
Complex Grouped AIC Type 2: 9r3c5 = r3c2 - r12c3 = r9c9(r129\c3479) - 8r9c9 = 8r3c9,r9c5{FW} => r3c5<>8
Region Forcing Chain: Each 3 in c6 true in turn will all lead to: r4c1<>2
3r4c6 - (3=267)r4c157
3r5c6 - (3=462)b5p237
(3-7)r7c6 = 7r3c6 - 7r3c1 = 7r4c1
3r8c6 - 3r8c3 = (3-7)r6c3 = 7r4c1
Hidden Triple: 258 in r5c1,r6c1,r6c2 => r5c1<>3,r6c1<>3,r6c2<>3
H-Wing: (1=2)r5c4 - (2=5)r5c1 - r5c6 = 5r6c5 => r6c5<>1
Locked Candidates 1 (Pointing): 1 in b5 => r5c9<>1
Naked Pair: in r5c3,r5c9 => r5c8<>49,
Hidden Triple: 479 in r4c8,r6c8,r7c8 => r6c8<>236
Naked Triple: in r4c8,r5c9,r6c8 => r6c9<>47,
Locked Candidates 1 (Pointing): 7 in b6 => r7c8<>7
Swordfish:9c258\r347  => r7c9<>9
S-Wing: 1r5c4 = r5c6 - (1=7)r3c6 - r7c6 = 7r8c4 => r8c4<>1
AIC Type 2: (2=7)r8c4 - r8c9 = (7-4)r7c9 = (4-9)r7c8 = 9r7c5 => r7c5<>2
AIC Type 2: (1=6)r6c9 - (6=4)r6c4 - r6c8 = (4-9)r7c8 = 9r9c9 => r9c9<>1
Grouped AIC Type 2: 6r4c5 = r4c7 - r7c7 = r7c1 - (6=3)r8c3 - r6c3 = 3r4c12 => r4c5<>3
Empty Rectangle : 3 in b5 connected by c3 => r8c6 <> 3
Region Forcing Chain: Each 4 in r1 true in turn will all lead to: r1c4<>7
(4-3)r1c2 = 3r1c1 - (3=7)r4c1 - 7r6c3 = 7r8c4(c347\r1268)
4r1c3 - 4r5c3 = 4r5c9 - (4=7)r7c9 - 7r8c9 = 7r8c4
4r1c4
4r1c6 - (4=263)r4c567 - 3r4c12 = (3-7)r6c3 = 7r8c4(c347\r1268)
Uniqueness Test 7: 79 in r12c37; 2*biCell + 1*conjugate pairs(7r1) => r2c3 <> 9
Cell Forcing Chain: Each candidate in  r7c6 true in turn will all lead to: r2c6<>1
1r7c6
2r7c6 - 2r89c4 = (2-1)r5c4 = 1r5c6
3r7c6 - 3r79c5 = 3r6c5 - (3=476)r6c348 - (6=2)r4c5 - 2r2c5 = 2r2c6
7r7c6 - (7=1)r3c6
Cell Forcing Chain: Each candidate in  r7c6 true in turn will all lead to: r8c6<>2,r2c6<>8
1r7c6 - (1=263)r7c127 - 3r7c56 = (3-8)r9c5 = 8r8c6
2r7c6 - (2=163)r7c127 - 3r7c56 = (3-8)r9c5 = 8r8c6
3r7c6 - 3r79c5 = 3r6c5 - (3=476)r6c348 - (6=2)r4c5 - 2r2c5 = 2r2c6
7r7c6 - (7=129)r589c4 - (9=8)r9c9 - 8r9c5 = 8r8c6
Region Forcing Chain: Each 2 in r6 true in turn will all lead to: r3c2<>8
(2-8)r6c1 = 8r6c2
2r6c2 - (2=13)r78c2 - 3r8c3 = 3r6c3 - (3=794)r4c128 - 9r4c2 = 9r3c2
2r6c5 - (2=463)b5p237 - 4r4c6 = (4-9)r4c2 = 9r3c2
2r6c7 - (2=583)r6c125 - 3r45c6 = 3r7c6 - (3=1269)r7c1257 - 9r3c5 = 9r3c2
Region Forcing Chain: Each 3 in c1 true in turn will all lead to: r1c1<>5
3r1c1
3r4c1 - (3=2469)r4c2567 - (9=5)r3c2
3r7c1 - 3r8c23 = 3r8c8 - (3=2)r5c8 - (2=5)r5c1
Cell Forcing Chain: Each candidate in  r7c6 true in turn will all lead to: r4c6<>2
1r7c6 - 1r9c45 = 1r9c7 - (1=235784)r6c123578 - 4r6c4 = 4r4c6
2r7c6
3r7c6 - 3r5c6 = 3r5c8 - (3=62)r4c57
7r7c6 - 7r3c6 = 7r3c1 - (7=362)r4c157
Hidden Pair: 26 in r4c5,r4c7 => r4c7<>3
Empty Rectangle : 3 in b6 connected by c3 => r8c8 <> 3
Locked Candidates 2 (Claiming): 3 in r8 => r7c1<>3,r7c2<>3
L2-Wing: 6r7c1 = (6-3)r8c3 = r8c2 - r1c2 = 3r1c1 => r1c1<>6
Broken Wing: {r1c35,r4c57,r7c17,r3c1}, guardian-{r2c135,r1c4,r3c5} => r2c4<>6
Grouped AIC Type 1: 2r2c6 = r2c5 - r4c5 = (2-6)r4c7 = r7c7 - r7c1 = (6-3)r8c3 = (3-2)r8c2 = 2r7c12 => r7c6<>2
Almost Locked Set XZ-Rule: A=r37c6 {137},B=b5p2347 {12346}, X=3, Z=1 => r5c6<>1
Hidden Single: 1 in r5 => r5c4=1
Locked Candidates 2 (Claiming): 2 in c4 => r9c5<>2
Grouped Discontinuous Nice Loop: 2r2c6 = (2-8)r2c5 = r1c56 - (8=3)r1c1 - (3=7)r4c1 - r3c1 = (7-1)r3c6 = r78c6 - r9c5 = r9c7 - r6c7 = (1-6)r6c9 = r6c4 - (6=2)r4c5 - r5c6 = 2r2c6 => r2c6=2
Empty Rectangle : 4 in b4 connected by c6 => r1c3 <> 4
S-Wing: 2r5c1 = r5c8 - (2=6)r4c7 - r7c7 = 6r7c1 => r7c1<>2
Locked Candidates 2 (Claiming): 2 in c1 => r6c2<>2
Grouped Discontinuous Nice Loop: 2r4c5 = (2-6)r4c7 = (6-1)r6c9 = r6c7 - r9c7 = r9c5 - r23c5 = (1-7)r3c6 = r3c1 - r4c1 = r4c8 - (7=4)r6c8 - (4=6)r6c4 - (6=2)r4c5 => r4c5=2
Hidden Single: 6 in r4 => r4c7=6
Hidden Single: 6 in r6 => r6c4=6
Hidden Single: 6 in r7 => r7c1=6
Hidden Single: 4 in b5 => r4c6=4
Naked Single: r6c9=1
Naked Single: r8c3=3
Locked Candidates 2 (Claiming): 1 in c1 => r2c2<>1
Locked Candidates 2 (Claiming): 4 in c2 => r2c3<>4
Skyscraper : 3 in r7c6,r9c8 connected by r5c68 => r7c7,r9c5 <> 3
Naked Pair: in r8c6,r9c5 => r7c5<>1,r7c6<>1,
W-Wing: 58 in r1c6,r6c2 connected by 5r5 => r1c2<>8
XY-Chain: (5=8)r1c6 - (8=1)r8c6 - (1=2)r8c2 - (2=1)r7c2 - (1=2)r7c7 - (2=3)r6c7 - (3=5)r6c5 - (5=3)r5c6 - (3=7)r7c6 - (7=4)r7c9 - (4=9)r7c8 - (9=7)r4c8 - (7=3)r4c1 - (3=9)r4c2 - (9=5)r3c2 => r1c2,r3c5<>5
Locked Candidates 2 (Claiming): 5 in r1 => r2c5<>5
XY-Chain: (7=9)r1c7 - (9=4)r1c4 - (4=3)r1c2 - (3=9)r4c2 - (9=4)r5c3 - (4=7)r6c3 => r1c3<>7
Hidden Single: 7 in r1 => r1c7=7
Hidden Single: 9 in c7 => r2c7=9
XY-Chain: (5=8)r1c6 - (8=1)r8c6 - (1=2)r8c2 - (2=1)r7c2 - (1=2)r7c7 - (2=3)r6c7 - (3=5)r6c5 => r1c5,r5c6<>5
STTE


the 2 main points, reordered are
the known exocet
Code: Select all
Junior Exocet:Base Cells-r1c7,r2c7;Target Cells-r4c8,r4c9,r7c8,r7c9;Cross Cells-r347c123456   
Target Cells Check: r4c8<>46,r7c8<>6,r7c9<>6
Check X-Rule:r2c7<>6,r1c7<>6

and this MSLS that I had never seen before

MSLS:15 Cells r5689c3489, 15 Links 49r5,467r6,67r8,9r9,3c3,12c4,23c8,1c9,8b9



combining both, we get this cleaned PM

Code: Select all
3568  3458  4679  |4679   568    458    |79     1      2     
1568  1458  4679  |4679   12568  12458  |79     568    3     
15678 1589  2     |3      15689  1578   |4      568    68 
------------------------------------------------------------
237   2349  1     |8      236    234    |236    79     5     
235   6     349   |124    7      1235   |8      2349   149   
2358  2358  347   |1246   1235   9      |123    23467  1467     
------------------------------------------------------------
1236  123   8     |5      1239   1237   |1236   479    479 
9     123   36    |127    4      1238   |5      2368   1678     
4     7     5     |129    1238   6      |123    238    189


This will be the start to try to finish the path mainly thru the remaining exocet possible patterns.
champagne
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Posts: 7847
Joined: 02 August 2007
Location: France Brittany

path in exocet area

Postby champagne » Tue Jan 27, 2026 3:09 pm

One way to filter possible options for the Exocet is to consider the 2 UR threats
R12c37
R12c47

Here is a Pm cut to the cells to consider

Code: Select all
_     _     4679  |4679   _      _      |79b    _      _     
_     _     4679  |4679   _      _      |79b    _      _     
_     _     _     |_      15689  1578   |4      _      _   
------------------------------------------------------------
237   2349  _     |_      236    234    |236    79     _     t
_     6     349   |124    7      _      |_      _      _       
_     _     347   |1246   _      9      |_      _      _     
------------------------------------------------------------
1236  _     _     |_      1239   1237   |1236   479    479   tt
9     _     36    |127    4      1238   |_      _      _       
4     7     _     |129    _      6      |_      _      _         


Can not be 46r12c3 nor 46r12c4 (trivial, locked in targets)
Must be one and only one ‘4’ in r4


So we have four possible pairs in r12c3
47 49 67 69, with the other digits in r12c4

49 r12c3 is not possible in box 4
so we are left with 3 pairs in r12c3

69 the valid pair for r12c3
47 and 67 the 2 false pairs
We start showing 47 false forcing 4r4c6, first cell assigned
champagne
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Posts: 7847
Joined: 02 August 2007
Location: France Brittany


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