The New Sudoku Players' Forum

by **ghfick** » Sun Mar 05, 2023 7:41 pm

A frequency distribution of the SE of the 49,158 17-clue puzzles:

Code: Select all: SE | Freq. Percent Cum. ---------------+----------------------------------- ED=1.2/1.2/1.2 | 117 0.24 0.24 ED=1.5/1.2/1.2 | 15,585 31.70 31.94 ED=1.5/1.5/1.5 | 1,531 3.11 35.06 ED=1.7/1.2/1.2 | 2,603 5.30 40.35 ED=1.7/1.5/1.5 | 245 0.50 40.85 ED=2.0/1.2/1.2 | 8,348 16.98 57.83 ED=2.0/1.5/1.5 | 1,166 2.37 60.20 ED=2.0/2.0/2.0 | 10 0.02 60.22 ED=2.3/1.2/1.2 | 444 0.90 61.13 ED=2.3/1.5/1.5 | 60 0.12 61.25 ED=2.3/2.0/2.0 | 1 0.00 61.25 ED=2.5/1.2/1.2 | 184 0.37 61.63 ED=2.5/1.5/1.5 | 21 0.04 61.67 ED=2.5/2.0/2.0 | 2 0.00 61.67 ED=2.5/2.3/2.3 | 1 0.00 61.67 ED=2.6/1.2/1.2 | 8,575 17.44 79.12 ED=2.6/1.5/1.5 | 1,110 2.26 81.38 ED=2.6/2.0/2.0 | 7 0.01 81.39 ED=2.6/2.3/2.3 | 2 0.00 81.39 ED=2.6/2.6/2.6 | 2 0.00 81.40 ED=2.8/1.2/1.2 | 512 1.04 82.44 ED=2.8/1.5/1.5 | 101 0.21 82.65 ED=3.0/1.2/1.2 | 308 0.63 83.27 ED=3.0/1.5/1.5 | 85 0.17 83.45 ED=3.2/1.2/1.2 | 31 0.06 83.51 ED=3.2/1.5/1.5 | 6 0.01 83.52 ED=3.4/1.2/1.2 | 481 0.98 84.50 ED=3.4/1.5/1.5 | 77 0.16 84.66 ED=3.4/2.0/2.0 | 2 0.00 84.66 ED=3.4/3.4/2.6 | 9 0.02 84.68 ED=3.6/1.2/1.2 | 15 0.03 84.71 ED=3.6/1.5/1.5 | 6 0.01 84.72 ED=3.8/1.2/1.2 | 2 0.00 84.72 ED=3.8/1.5/1.5 | 1 0.00 84.73 ED=4.0/1.2/1.2 | 16 0.03 84.76 ED=4.2/1.2/1.2 | 979 1.99 86.75 ED=4.2/1.5/1.5 | 138 0.28 87.03 ED=4.4/1.2/1.2 | 37 0.08 87.11 ED=4.4/1.5/1.5 | 3 0.01 87.11 ED=4.5/1.2/1.2 | 292 0.59 87.71 ED=4.5/1.5/1.5 | 38 0.08 87.78 ED=4.6/1.2/1.2 | 140 0.28 88.07 ED=4.6/1.5/1.5 | 11 0.02 88.09 ED=4.7/1.2/1.2 | 7 0.01 88.11 ED=4.8/1.2/1.2 | 1 0.00 88.11 ED=5.0/1.2/1.2 | 2 0.00 88.11 ED=5.2/1.2/1.2 | 4 0.01 88.12 ED=5.6/1.2/1.2 | 526 1.07 89.19 ED=5.6/1.5/1.5 | 53 0.11 89.30 ED=5.7/1.2/1.2 | 33 0.07 89.36 ED=5.7/1.5/1.5 | 4 0.01 89.37 ED=5.8/1.2/1.2 | 1 0.00 89.38 ED=6.2/1.2/1.2 | 2 0.00 89.38 ED=6.2/1.5/1.5 | 2 0.00 89.38 ED=6.5/1.2/1.2 | 18 0.04 89.42 ED=6.5/1.5/1.5 | 2 0.00 89.42 ED=6.6/1.2/1.2 | 2,387 4.86 94.28 ED=6.6/1.5/1.5 | 350 0.71 94.99 ED=6.6/2.6/2.6 | 1 0.00 94.99 ED=6.7/1.2/1.2 | 494 1.00 96.00 ED=6.7/1.5/1.5 | 53 0.11 96.11 ED=6.7/2.0/2.0 | 2 0.00 96.11 ED=6.7/2.3/2.3 | 4 0.01 96.12 ED=6.7/2.6/2.6 | 1 0.00 96.12 ED=6.7/6.7/2.6 | 1 0.00 96.12 ED=6.8/1.2/1.2 | 56 0.11 96.24 ED=6.8/1.5/1.5 | 8 0.02 96.25 ED=6.9/1.2/1.2 | 15 0.03 96.28 ED=6.9/1.5/1.5 | 3 0.01 96.29 ED=7.0/1.2/1.2 | 13 0.03 96.32 ED=7.0/1.5/1.5 | 1 0.00 96.32 ED=7.1/1.2/1.2 | 901 1.83 98.15 ED=7.1/1.5/1.5 | 122 0.25 98.40 ED=7.1/2.0/2.0 | 1 0.00 98.40 ED=7.2/1.2/1.2 | 428 0.87 99.27 ED=7.2/1.5/1.5 | 47 0.10 99.37 ED=7.2/2.0/2.0 | 2 0.00 99.37 ED=7.2/3.4/2.6 | 1 0.00 99.37 ED=7.3/1.2/1.2 | 60 0.12 99.50 ED=7.3/1.5/1.5 | 19 0.04 99.53 ED=7.4/1.2/1.2 | 2 0.00 99.54 ED=7.6/1.2/1.2 | 43 0.09 99.63 ED=7.6/1.5/1.5 | 5 0.01 99.64 ED=7.7/1.2/1.2 | 27 0.05 99.69 ED=7.7/1.5/1.5 | 10 0.02 99.71 ED=7.8/1.2/1.2 | 34 0.07 99.78 ED=7.8/1.5/1.5 | 8 0.02 99.80 ED=7.9/1.2/1.2 | 5 0.01 99.81 ED=7.9/1.5/1.5 | 1 0.00 99.81 ED=8.2/1.2/1.2 | 5 0.01 99.82 ED=8.2/1.5/1.5 | 1 0.00 99.82 ED=8.3/1.2/1.2 | 46 0.09 99.91 ED=8.3/1.5/1.5 | 10 0.02 99.93 ED=8.4/1.2/1.2 | 7 0.01 99.95 ED=8.4/1.5/1.5 | 2 0.00 99.95 ED=8.5/1.2/1.2 | 13 0.03 99.98 ED=8.8/1.2/1.2 | 2 0.00 99.98 ED=8.9/1.2/1.2 | 3 0.01 99.99 ED=8.9/1.5/1.5 | 2 0.00 99.99 ED=9.0/1.2/1.2 | 2 0.00 100.00 ED=9.1/1.5/1.5 | 1 0.00 100.00 ---------------+----------------------------------- Total | 49,158 100.00

Under 4% of these puzzles have an SE of 7.0 or higher. There are a large number of 6.6 and 6.7 puzzles. The 6.6 rating contains the Turbot Fish and perhaps other techniques of some interest. There are certainly some fun puzzles hidden in this list. How to find them though?

by **ghfick** » Sun Mar 05, 2023 11:38 pm

I tried:

........1.......2...3..4..5.....6....7..3.4..21.....8.....1.......25......9...7.. ED=6.7/6.7/2.6

Fun! Only one bi-value cell and no 'easy' exclusions apart from one LC.

To send the puzzle to stte, there are several one-steppers: three different dual empty rectangles or six essentially different finned/sashimi swordfish

by **P.O.** » Mon Mar 06, 2023 12:24 pm

a solution by a reasoning on templates.
we know that the puzzle has a unique solution so we need to find only one template per value.
there are three clues for value 2 in cells 17,46 and 67 and there are seventeen cells with a candidate for 2.
a template is a set of nine disconnected cells
to get the template for 2 we need six cells that complement the three already given.
now the difficult part with pen and paper:
with the seventeen candidate cells only five set of six disconnected cells can be formed to complement the three cells already given
one of the five is therefore the correct one
without a process of trial and error we can observe that those five sets have one cell in common, cell 42
therefore that cell must be set to 2
it is enough to solve the puzzle

it is not necessary to assume uniqueness when solving with templates the reasoning is the same with a puzzle with multiple solutions only combinatorics is more complicated.

Hidden Text: Show

Code: Select all: Initialization: #VT: (6 5 94 92 138 527 89 856 511) 456789 245689 245678 356789 26789 235789 3689 34679 1 1456789 45689 145678 1356789 6789 135789 3689 2 346789 16789 2689 3 16789 26789 4 689 679 5 34589 34589 458 145789 24789 6 12359 13579 2379 5689 7 568 1589 3 12589 4 1569 269 2 1 456 4579 479 579 3569 8 3679 345678 234568 245678 346789 1 3789 235689 34569 234689 134678 3468 14678 2 5 3789 13689 13469 34689 134568 234568 9 3468 468 38 7 13456 23468 Value: 2 Value Cells: (17 46 67) Candidate Cells: (2 3 5 6 20 23 32 34 36 42 45 56 57 61 63 74 81) Union csets: (2 3 5 . 20 23 . 34 36 42 . 56 57 61 63 74 81) Complementary Sets: 5 (2 23 34 42 57 81) (3 23 34 42 56 81) (3 23 34 42 63 74) (3 23 36 42 61 74) (5 20 34 42 57 81) Value 2 to set in cell: (42) Candidate 2 to be eliminated in cells: (6 32 45) (5 17 20 34 42 46 57 67 81) (3 17 23 36 42 46 61 67 74) (3 17 23 34 42 46 63 67 74) . - - . X - . . • . - X . - - . . • . - X . - - . . • . . . . . . . 2 . . . . . . . . 2 . . . . . . . . 2 . . X • . - • . . • . - • . X • . . • . - • . X • . . • . . . . - • X . - . . . . - • - . X . . . . - • X . - . • . . • X • . - . • . . • X • . - . • . . • X • . - 2 • . . . . . • . 2 • . . . . . • . 2 • . . . . . • . . - X . • . - . - . - - . • . X . - . - - . • . - . X . . . 2 • . . . . . . . 2 • . . . . . . . 2 • . . . . . - • . . . • . X . X • . . . • . - . X • . . . • . - (3 17 23 34 42 46 56 67 81) (2 17 23 34 42 46 57 67 81) . - X . - - . . • . X - . - - . . • . . . . . . . 2 . . . . . . . . 2 . . - • . X • . . • . - • . X • . . • . . . . - • X . - . . . . - • X . - . • . . • X • . - . • . . • X • . - 2 • . . . . . • . 2 • . . . . . • . . X - . • . - . - . - X . • . - . - . . . 2 • . . . . . . . 2 • . . . . . - • . . . • . X . - • . . . • . X

by **ghfick** » Mon Mar 06, 2023 7:29 pm

P.O. wrote:
now the difficult part with pen and paper:
with the seventeen candidate cells only five set of six disconnected cells can be formed to complement the three cells already given

I really like your template display. It makes the process very clear. I do have one question. How do you determine that you have found all the complementary sets?
As a pen and paper solver, I can see, in this puzzle, that there are at least five sets. How do you know that there are not more than five?

by **P.O.** » Mon Mar 06, 2023 8:07 pm

i dont think there is really an easy way to do it and certainly that is why the technique is little used by manual solvers
it is a combinatorial problem: with 17 cells 12376 combinations of 6 cells can be formed, checking which combination has its 6 cells pairwise disconnected gives the answer: only 5.
i dont do it exactly that way for as i compute the templates i already have the complementary sets, although in a certain way it amounts to making the same calculation.

by **Leren** » Mon Mar 06, 2023 10:25 pm

Code: Select all: *--------------------------------------------------------------------------------* | 456789 b245689 a245678 | 356789 26789 35789-2 | 3689 34679 1 | | 1456789 45689 145678 | 1356789 6789 135789 | 3689 2 346789 | | 16789 b2689 3 | 16789 26789 4 | 689 679 5 | |--------------------------+--------------------------+--------------------------| | 34589 34589 458 | 145789 24789 6 | 1259 1579 279 | | 5689 7 568 | 1589 3 f12589 | 4 1569 e269 | | 2 1 456 | 4579 479 579 | 3569 8 3679 | |--------------------------+--------------------------+--------------------------| | 345678 234568 245678 | 346789 1 3789 | 235689 34569 234689 | | 134678 3468 14678 | 2 5 3789 | 13689 13469 34689 | | 134568 c234568 9 | 3468 468 38 | 7 13456 d23468 | *--------------------------------------------------------------------------------*

(2) r1c3 = r13c2 - r9c2 = r9c9 - r5c9 = r5c6 => - 2 r1c6; stte

Leren

by **eleven** » Tue Mar 07, 2023 11:51 am

Here the hard part for maual solvers is just to find the strong links (A-E).

Code: Select all: +-------+-------+-------+ | . ^ A | . ^ D | . . 1 | | . . . | . . . | .*2 . | | . E 3 | . E 4 | . . 5 | +-------+-------+-------+ | . . . | . D 6 | C . ^ | | . 7 . | . 3 # | 4 . D | |*2 1 . | . . . | . 8 . | +-------+-------+-------+ | . ^ A | . 1 . | C . ^ | | . . . |*2 5 . | . . . | | . B 9 | . . . | 7 . B | +-------+-------+-------+

Wherever you start an alternating chain, you will come to r5c6 (which has 3 strong links D)
e.g.

Hidden Text: Show

So, after localizing the strong links you can't miss the eliminations here.

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