The New Sudoku Players' Forum

by **Mauriès Robert** » Sun Nov 24, 2019 8:36 am

Hi,

Here is a rather complicated puzzle to solve. What resolution will be yours ?

31..8...6...519.8.8.....1..27...1.......6..1....8...935...9..31.3.254.....6.....2

puzzle: Show

Good sudoku
Robert

by **SpAce** » Mon Nov 25, 2019 12:34 am

Hi Robert,

I have no time to solve it normally right now, so I just tested how easily it would fall to targeted T&E. I smelled weakness in r6c7 so I chose it as my target. (Yes, I knew it was a backdoor.)

Steps 1,2 (normal solving):

Code: Select all: .------------------.------------------.------------------------. | 3 1 *4579^ | 47 8 27 | *4579^ *2457 6 | | 467 246 247 | 5 1 9 | 3 8 47 | | 8 459 4579 | 3467 2347 2367 | 1 2457 4579^ | :------------------+------------------+------------------------: | 2 7 *34589 | 349 34 1 | *4568 *456 *458 | | 49 4589 34589 | 3479 6 2357 | 2478-5 1 4578 | | 146 456 145 | 8 247 257 | 247-5 9 3 | :------------------+------------------+------------------------: | 5 248 2478 | 67 9 678 | 478 3 1 | | 179 3 178-9 | 2 5 4 | 6789 67 789^ | | 479 489 6 | 1 37 378 | *45789 *457 2 | '------------------'------------------'------------------------'

Step 1. 3x4-Fish *: (5)R149\c38[c7b6] => -5 r56c7 (gets rid of one of our targets, 5r6c7)

Step 2. Kite ^: (9)R1C9\b3[r8c3] => -9 r8c3 (helps eliminate 2r6c7 next)

Step 3. T&E (2)r6c7, after basics:

Code: Select all: .-----------------.---------.-------------------. | 3 1 a59 | 4 8 7 | b59 2 6 | | 467 246 247 | 5 1 9 | 3 8 47 | | 8 45 4579 | 6 2 3 | 1 47 c59 | :-----------------+---------+-------------------: | 2 7 3 | 9 4 1 | 568 56 58 | | 9 58 a5[8] | 3 6 2 | 47 1 47 | | 146 46 14 | 8 7 5 | *2* 9 3 | :-----------------+---------+-------------------: | 5 248 248 | 7 9 6 | 48 3 1 | | 17 3 17-8 | 2 5 4 | 6789 67 c(8)9 | | 47 9 6 | 1 3 8 | 457 457 2 | '-----------------'---------'-------------------'

(85)r51c3 = r1c7 - (5=98)r38c9 -> -8 r8c3 -> basics -> contradiction => -2 r6c7

Step 4. T&E (7)r6c7, after basics (n/a):

Code: Select all: .------------------.----------------------.---------------------. | 3 1 4579 | c47 8 c27 | d459 d2457 6 | | 467 246 247 | 5 1 9 | 3 8 e47 | | 8 459 4579 | 3467 b2347 2367 | 1 e2457 e4579 | :------------------+----------------------+---------------------: | 2 7 34589 | 349 g(3)4 1 | g4568 g456 f458 | | 49 4589 34589 | 3479 6 357 | 2 1 f458 | | 146 456 145 | 8 24 25 | *7* 9 3 | :------------------+----------------------+---------------------: | 5 248 2478 | 67 9 678 | 48 3 1 | | 179 3 178 | 2 5 4 | 689 67 789 | | 479 489 6 | 1 a[7]-3 378 | 4589 457 2 | '------------------'----------------------'---------------------'

(7)r9c5 = r3c5 - (7=24)r1c64 - (2|4)r1c78 = (24)b3p869 - r45c9 = (43)r4c875 -> -3 r9c5

-> basics -> contradiction => -7 r6c7; btte

Conclusion. It took two trivial normal steps, and then two T&E steps with basics and one relatively simple chain each. Not pretty or satisfying, but probably quite a bit easier than the normal solving route. At least my little chains avoided the need to use nested T&E.

by **Cenoman** » Mon Nov 25, 2019 4:21 pm

Hi Robert,
This puzzle is rated S.E. 9.0 Clearly, in the category of "sudoku for masochists" (the expression is not mine

)
Or, to put it less trivially, it is in the "grey zone" (not hard enough to be solved by exotic patterns, but not easily solved by advanced techniques)

Mauriès Robert wrote:What resolution will be yours ?

Well, I ask my solver... and even so, it's a hard work to sort the outputs.
Here is a not optimized sequence of chains + krakens in thirteen steps (without net, though)

Hidden Text: Show

by **Mauriès Robert** » Wed Nov 27, 2019 6:17 pm

Hi Cenoman, Hi SpAce,

I like your resolutions, one for mixing "reasonable" T&Es, the other for using short chains that build the solution step by step.
TDP can resolve, either in short steps like Cenoman, or by accepting "reasonable" disability like SpAce.
For me, the reasonable term means that the starting choice of the elements of a pair to build tracks (or chains) is above all the search for interaction leading to eliminations or validations, and that if during this process a contradiction appears, then so much the better.
Here is a resolution by TDP due to one of the users of my website.
It is based on the exploitation that can be made of the 4r5b6.

First we consider the track P(4r5c79) = {4r5c79, 9r5c1, ...} that we develop by an extension P(4r5c79).P(9r1) :
P(4r5c79).P(9r1c3) = {4r5c79, 9r5c1, 9r1c3, 9r9c1, ...} -> 5b5=∅ (see puzzle 1) contradiction =>
P(4r5c79) = P(4r5c79).P(9r1c7) = {4r5c79, 9r5c1, 9r1c7, 9r8C9, ..., 8r67c9, 56r4c78, 5r3c9,..., 27r1c78, 4r1c4,... } (see puzzle 2)

puzzle1: Show

puzzle2: Show

We then consider the antitrack P'(4r5c79) = {4r5c1234, ...} that we develop with an extension P'(4r5c79).P(578r5c9) :
P'(4r5c79).P(58r5c9) = {4r5c1234, 27r56c7, 4r4c789, 3r4c5, ..., 4r2c9, ...} (green track on puzzle 3)
P'(4r5c79).P(7r5c9) = {4r5c1234, 4r2c9,459r3c239,...} (purple track on puzzle 3)
=> P'(4r5c79) = {4r5c1234, 4r2c9, 6r3c6, 8r7c6, 6r7c4, 7r9c5, 3r9c6,...} (see puzzle3)

Comparing P(4r5c79) and P'(4r5c79) we deduce from this: r2c9=4, -7r13c3, but as we can develop P(4r5c79) more than we do, we realize that P(4r5c79) is invalid (8b4=∅), which allows us to place all the candidates of P'(4r5c79) as a solution to the puzzle.

puzzle3 et puzzle4: Show

At this stage, since we have understood that P'(4r5c79) is the valid track, it is sufficient to resume its construction from cell r5c9 (see puzzle 5) where all the candidates common to both green and purple branches are candidates of P'(4r5c79), which completes the puzzle.

puzzle5: Show

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