## Templates with UAs (UnAvoidable Sets)

Advanced methods and approaches for solving Sudoku puzzles

### Templates with UAs (UnAvoidable Sets)

This post moved here to start a new thread at daj95376's request. The forum software assigns ownership according to the oldest post, but this is really daj95376's thread.

here daj95376 wrote:
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`....5...9.5.1...3.....37...2..6..8...6..1..7...4..5.....9.....2.3...1.6.8.....4.. ;136;elev;117;2BN D1D3 +--------------------------------------------------------------------------------+ |  13467   12478   123678  |  248     5       2468    |  1267    1248    9       | |  4679    5       2678    |  1       24689   24689   |  267     3       4678    | |  1469    12489   1268    |  2489    3       7       |  1256    12458   14568   | |--------------------------+--------------------------+--------------------------| |  2       179     1357    |  6       479     349     |  8       1459    1345    | |  359     6       358     |  23489   1       23489   |  2359    7       345     | |  1379    1789    4       |  23789   2789    5       |  12369   129     136     | |--------------------------+--------------------------+--------------------------| |  14567   147     9       |  34578   4678    3468    |  1357    158     2       | |  457     3       257     |  245789  24789   1       |  579     6       578     | |  8       127     12567   |  23579   2679    2369    |  4       159     1357    | +--------------------------------------------------------------------------------+ # 179 eliminations remain Templates: 56 59 16 50 32 20 87 26 28 <2489>   accepted = 23 template combinations...                                                              47 eliminations`

My utility program finds the same template counts and, without using uniqueness, finds 34 acceptable template combinations. After manually discarding the combinations with unavoidable set (48)r13c48, there remain the 18 below (where givens are not shown). What are your other 5 combinations?

18 acceptable <2489>-templates: Show
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`   V   V             V   V                                                       .2.4.8...4...9.2.898.2...4......4.9...89.2..4.9..8..2..4.....8...284.9......29....2.4...8.4...892..98.2...4..9...4.....8..29.4...89..2..4...8.....294...8....2..9..2.4...8.4...892..98.2...4.....94.....8..29.4.9.8...2..4...8.....294...8....2..9..2.4...8.4...892..9.82...4..9...4......8.29.4.8..9..2..4...8.....294...8....2..9..2.4...8.4...892...982...4.....94...9..8.2..4.8....92..4...8.....294...8....2..9..2.4...8.4...892...982...4.....94......8.29.498.....2..4...8.....294...8....2..9..2.4...8.4...892...982...4......4.9.9..8.2..4.8..9..2..4...8.....2.4.9.8...92.....2.4...8.4...982..98.2...4......4.9...89.2..4.9.8...2..4..8......2.4.9.8....29....2.4...8.4...982..98.2...4......4.9...89.2..4.9..8..2..4.8.......2.4.9.8....29....2.4...8.4...982...982...4......4.9.9..8.2..4.8.9...2..4..8......2.4.9.8....29....8.2...4.4...892..92.4...8..9...4.....8..29.4...89..2..4...8.....294...8....2..9..8.2...4.4...892..92.4...8.....94.....8..29.4.9.8...2..4...8.....294...8....2..9..8.2...4.4...982..92.4...8......4.9...89.2..4.9.8...2..4..8......2.4.9.8....29....8.2...4.4...982..92.4...8......4.9...89.2..4.9..8..2..4.8.......2.4.9.8....29....8.2...4.4...982..92.4....8.....4.9...89.2..4.9..8..2..4.....8...284.9......29.....82...4.4...892..92.4...8..9...4......8.29.4.8..9..2..4...8.....294...8....2..9....2.8.4.4.8..92..92.4...8..9...4......8.29.4.8..9..2..4..8......294...8....2..9..8.2...4.9...842..42.9...8.....49.....8..29.4.9.8...2..4...8.....249...8....2..9.`

daj95376 wrote:r1c4,r2c1,r3c4,r4c6,r5c69,r6c8,r7c2,r8c35 locked for candidates <2489>

All ten of these are not in the same "class" and shouldn't be shown together like this IMO. The cells r1c4 and r3c4 are limited to candidates <2489> before the templates technique and are thus strong-inference-sets. The other eight cells are limited to candidates <2489> after discarding unacceptable template sets and are thus weak-inference-sets.

Last edited by ronk on Fri Jul 13, 2012 11:59 am, edited 2 times in total.
ronk
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### Re: Templates: With/without Unavoidable Sets

ronk wrote:My utility program finds the same template counts and, without using uniqueness, finds 34 acceptable template combinations. After manually discarding the combinations with unavoidable set (48)r13c48, there remain the 18 below (where givens are not shown). What are your other 5 combinations?

Step #1: sorted my 23 results

Step #3: generated a list of my 7 results that weren't in your results

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`...8..2494.8.29...92.4...8.29...48.....2.89.4.84.9..2..49.8...2..294...88....249....8.2.494.8..92..92.4...8.29...48.....2.89.4.84.9..2..49.8...2..294...88...2.49..2.8...494.8.29....9.4..28.2....489.9..2.8..4.84.9..2..49.8...2..2.4.9.88..9.24...2.8...494.8.29....9.4..28.2...948.....2.89.4984....2..49.8...2..294...88....249..2.8...494.8.29....9.4..28.2...948..9..2.8..4.84...92..49.8...2..294...88....249..2.8...494.8.29...9..4..28.29...48.....2.89.4.84.9..2..49.8...2..294...88....249..2.8...494.8.92....9.4..28.2....489.9..2.8..4.849...2..49.8...2..2.4.9.88...294..`

Step #4: generated a list of your 2 results that weren't in my results

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`...2.8.494.8..92..92.4...8.29...48.....8.29.4.84.9..2..49.8...2..294...88...2.49. +-----------------------+ | . . . | 2 . 8 | . 4 9 | | 4 . 8 | . . 9 | 2 . . | | 9 2 . | 4 . . | . 8 . | |-------+-------+-------| | 2 9 . | . . 4 | 8 . . | | . . . | 8 . 2 | 9 . 4 | | . 8 4 | . 9 . | . 2 . | |-------+-------+-------| | . 4 9 | . 8 . | . . 2 | | . . 2 | 9 4 . | . . 8 | | 8 . . | . 2 . | 4 9 . | +-----------------------+   # contains <28> UR r15c46`

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`.2.4...894...982..98.2...4.2....489...89.2..4.94.8..2..498....2..2.4.9.88...294.. +-----------------------+ | . 2 . | 4 . . | . 8 9 | | 4 . . | . 9 8 | 2 . . | | 9 8 . | 2 . . | . 4 . | |-------+-------+-------| | 2 . . | . . 4 | 8 9 . | | . . 8 | 9 . 2 | . . 4 | | . 9 4 | . 8 . | . 2 . | |-------+-------+-------| | . 4 9 | 8 . . | . . 2 | | . . 2 | . 4 . | 9 . 8 | | 8 . . | . 2 9 | 4 . . | +-----------------------+   # not sure which filter disabled this combination`
Last edited by daj95376 on Wed Jul 11, 2012 1:27 am, edited 1 time in total.
daj95376
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### Re: Templates: with/without UnAvoidable Sets

ronk wrote:
daj95376 wrote:r1c4,r2c1,r3c4,r4c6,r5c69,r6c8,r7c2,r8c35 locked for candidates <2489>

All ten of these are not in the same "class" and shouldn't be shown together like this IMO. The cells r1c4 and r3c4 are limited to candidates <2489> before the templates technique and are thus strong-inference-sets. The other eight cells are limited to candidates <2489> after discarding unacceptable template sets and are thus weak-inference-sets.

My logic simply flags those cells where a <2489> value is always assigned in the accepted template combinations. It doesn't distinguish between original cells with/without additional candidates.
daj95376
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### Re: Templates: With/without Unavoidable Sets

daj95376 wrote:Step #3: generated a list of my 7 results that weren't in your results

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`...8..2494.8.29...92.4...8.29...48.....2.89.4.84.9..2..49.8...2..294...88....249....8.2.494.8..92..92.4...8.29...48.....2.89.4.84.9..2..49.8...2..294...88...2.49..2.8...494.8.29....9.4..28.2....489.9..2.8..4.84.9..2..49.8...2..2.4.9.88..9.24...2.8...494.8.29....9.4..28.2...948.....2.89.4984....2..49.8...2..294...88....249..2.8...494.8.29....9.4..28.2...948..9..2.8..4.84...92..49.8...2..294...88....249..2.8...494.8.29...9..4..28.29...48.....2.89.4.84.9..2..49.8...2..294...88....249..2.8...494.8.92....9.4..28.2....489.9..2.8..4.849...2..49.8...2..2.4.9.88...294..`

Thanks for the quick response. All seven of these have the same unavoidable set in r13c48. Interesting that your software seems to work OK when the '4' and '8' in these four cells is reversed in other <2489>-templates.
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` . . . | 8 . . | 2 4 9 4 . 8 | . 2 9 | . . . 9 2 . | 4 . . | . 8 .-------+-------+------- 2 9 . | . . 4 | 8 . . . . . | 2 . 8 | 9 . 4 . 8 4 | . 9 . | . 2 .-------+-------+------- . 4 9 | . 8 . | . . 2 . . 2 | 9 4 . | . . 8 8 . . | . . 2 | 4 9 .`

daj95376 wrote:Step #4: generated a list of your 2 results that weren't in my results

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`...2.8.494.8..92..92.4...8.29...48.....8.29.4.84.9..2..49.8...2..294...88...2.49. +-----------------------+ | . . . | 2 . 8 | . 4 9 | | 4 . 8 | . . 9 | 2 . . | | 9 2 . | 4 . . | . 8 . | |-------+-------+-------| | 2 9 . | . . 4 | 8 . . | | . . . | 8 . 2 | 9 . 4 | | . 8 4 | . 9 . | . 2 . | |-------+-------+-------| | . 4 9 | . 8 . | . . 2 | | . . 2 | 9 4 . | . . 8 | | 8 . . | . 2 . | 4 9 . | +-----------------------+   # contains <28> UR r15c46`

Having done it manually, missing one is not a big surprise.

daj95376 wrote:
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`.2.4...894...982..98.2...4.2....489...89.2..4.94.8..2..498....2..2.4.9.88...294.. +-----------------------+ | . 2 . | 4 . . | . 8 9 | | 4 . . | . 9 8 | 2 . . | | 9 8 . | 2 . . | . 4 . | |-------+-------+-------| | 2 . . | . . 4 | 8 9 . | | . . 8 | 9 . 2 | . . 4 | | . 9 4 | . 8 . | . 2 . | |-------+-------+-------| | . 4 9 | 8 . . | . . 2 | | . . 2 | . 4 . | 9 . 8 | | 8 . . | . 2 9 | 4 . . | +-----------------------+   # not sure which filter disabled this combination`

I find nothing wrong with this one. If I place an 'X' at r1c1, gsf's solver with the "-gtm.0" option finds valid sub-puzzles, with multiple solutions of course.
ronk
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### Re: Templates: With/without Unavoidable Sets

ronk wrote:Thanks for the quick response. All seven of these have the same unavoidable set in r13c48. Interesting that your software seems to work OK when the '4' and '8' in these four cells is reversed in other <2489>-templates.
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` . . . | 8 . . | 2 4 9 4 . 8 | . 2 9 | . . . 9 2 . | 4 . . | . 8 .-------+-------+------- 2 9 . | . . 4 | 8 . . . . . | 2 . 8 | 9 . 4 . 8 4 | . 9 . | . 2 .-------+-------+------- . 4 9 | . 8 . | . . 2 . . 2 | 9 4 . | . . 8 8 . . | . . 2 | 4 9 .`

Code: Select all
`.2.4...894...982..98.2...4.2....489...89.2..4.94.8..2..498....2..2.4.9.88...294.. +-----------------------+ | . 2 . | 4 . . | . 8 9 | | 4 . . | . 9 8 | 2 . . | | 9 8 . | 2 . . | . 4 . | |-------+-------+-------| | 2 . . | . . 4 | 8 9 . | | . . 8 | 9 . 2 | . . 4 | | . 9 4 | . 8 . | . 2 . | |-------+-------+-------| | . 4 9 | 8 . . | . . 2 | | . . 2 | . 4 . | 9 . 8 | | 8 . . | . 2 9 | 4 . . | +-----------------------+   # not sure which filter disabled this combination`

I find nothing wrong with this one. If I place an 'X' at r1c1, gsf's solver with the "-gtm.0" option finds valid sub-puzzles, with multiple solutions of course.

Yes, I have a bug to track down in my detection of UR patterns. It may be a byproduct from stripping down another version of my templates solver in order to obtain just 4-templates results. (see additional details below)

As for your second <2489> grid, inserting all givens and loading into Simple Sudoku results in a puzzle with zero solutions.

I get my 4-templates results by stripping down a version of my templates solver that solves scenarios 2-templates through 7-templates, iteratively. However, in order to maintain some of the functional logic, I have to perform calls to 2-templates and 3-templates prior to performing 4-templates; but, none of these routines are allowed to perform eliminations. A flag is set if a template entry is determined to be inactive at some point. I suspect that one of the four templates in your second <2489> grid was marked inactive prior to my performing the 4-templates pass.

Regards, Danny
daj95376
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### Re: Templates: With/without Unavoidable Sets

daj95376 wrote:As for your second <2489> grid, inserting all givens and loading into Simple Sudoku results in a puzzle with zero solutions.

Aha, I think k-templates should involve only 'k' digits, so including the other "9-k" digits never even occurred to me.

daj95376 wrote:I have a bug to track down in my detection of UR patterns.

After you find the bug, I'll be very interested in your revised number of exclusions, which I expect will be approx 60 versus the prior 47.
ronk
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### Re: Templates: with/without UnAvoidable Sets

I'm working on a new templates analyzer that properly addresses 4-templates only.

Fortunately, the analyzer problems do not appear to be in my (originating source) 2/7-templates solver. (output below)

Note #1: The number of templates for several values decrease before getting to <2489>.

Note #2: ronk's second <2489> grid doesn't occur in my output because (at least) one of its four templates was disabled in an earlier 2/3-templates pass involving digits other than <2489>.

Note #3: r3c4<>8 would have occurred at <2489> if it hadn't already occurred at <248>.

Hidden Text: Show
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`Output from templates solver "Solver27ur" -- detection of UR collisions enabled.Diagnostics shows: a specific <48> UR pattern was detected, and a list of the accepted <2489> patterns.....5...9.5.1...3.....37...2..6..8...6..1..7...4..5.....9.....2.3...1.6.8.....4.. +-----------------------+ | . . . | . 5 . | . . 9 | | . 5 . | 1 . . | . 3 . | | . . . | . 3 7 | . . . | |-------+-------+-------| | 2 . . | 6 . . | 8 . . | | . 6 . | . 1 . | . 7 . | | . . 4 | . . 5 | . . . | |-------+-------+-------| | . . 9 | . . . | . . 2 | | . 3 . | . . 1 | . 6 . | | 8 . . | . . . | 4 . . | +-----------------------+ +--------------------------------------------------------------------------------+ |  13467   12478   123678  |  248     5       2468    |  1267    1248    9       | |  4679    5       2678    |  1       24689   24689   |  267     3       4678    | |  1469    12489   1268    |  2489    3       7       |  1256    12458   14568   | |--------------------------+--------------------------+--------------------------| |  2       179     1357    |  6       479     349     |  8       1459    1345    | |  359     6       358     |  23489   1       23489   |  2359    7       345     | |  1379    1789    4       |  23789   2789    5       |  12369   129     136     | |--------------------------+--------------------------+--------------------------| |  14567   147     9       |  34578   4678    3468    |  1357    158     2       | |  457     3       257     |  245789  24789   1       |  579     6       578     | |  8       127     12567   |  23579   2679    2369    |  4       159     1357    | +--------------------------------------------------------------------------------+ # 179 eliminations remain +-----------------------+ | . . . |*8 . . | .*4 . | | 4 . 8 | . . . | . . . | | . . . |*4 . . | .*8 . | |-------+-------+-------| | . . . | . . 4 | 8 . . | | . . . | . . 8 | . . 4 | | . 8 4 | . . . | . . . | |-------+-------+-------| | . 4 . | . 8 . | . . . | | . . . | . 4 . | . . 8 | | 8 . . | . . . | 4 . . | +-----------------------+   # one of 36 <48>-templates containing a UR pattern Templates: 56 59 16 50 32 20 87 26 28 <248>   accepted = 331 template combinations <248>   <>8  r3c4 r1c4   locked for candidates *** 3-template completed Templates: 56 59 16 50 32 20 87 24 28   *** 2-template (reduction pass only) completed Templates: 56 58 16 50 32 20 87 24 28   *** 3-template (reduction pass only) completed Templates: 56 37 16 24 32 20 87 19 28   *** 3-template (reduction pass only) completed Templates: 56 37 16 23 32 19 87 19 27.2.4...894...982...982...4.2....489.9..8.2..4.849...2..49.8...2..2.4.9.88...294...2.4.8..94...9.2.898.2...4.2....489...89.2..4.94.8..2..49....82..284.9..8...294...2.4...894...982..98.2...4.2....489...89.2..4.94.8..2..498....2..2.4.9.88...294...2.4...894...892..98.2...4.29...48....8..29.4..489..2..49..8..2..294...88...2.49..2.4...894...892..98.2...4.2...948....8..29.4.948...2..49..8..2..294...88...2.49..2.4...894...892..9.82...4.29...48.....8.29.4.84.9..2..49..8..2..294...88...2.49..2.4...894...892...982...4.2...948..9..8.2..4.84...92..49..8..2..294...88...2.49..2.4...894...892...982...4.2...948.....8.29.4984....2..49..8..2..294...88...2.49..2.4...894...892...982...4.2....489.9..8.2..4.84.9..2..49..8..2..2.4.9.88..92.4...2.4...894...982..98.2...4.2....489...89.2..4.948...2..49.8...2..2.4.9.88...294...8.2...494...892..92.4...8.29...48....8..29.4..489..2..49..8..2..294...88...2.49..8.2...494...892..92.4...8.2...948....8..29.4.948...2..49..8..2..294...88...2.49..8.2...494...982..92.4...8.2....489...89.2..4.948...2..49.8...2..2.4.9.88...294...8.2...494...982..92.4...8.2....489...89.2..4.94.8..2..498....2..2.4.9.88...294...8.2...494...982..92.4....82....489...89.2..4.94.8..2..49....82..284.9..8...294....82...494...892..92.4...8.29...48.....8.29.4.84.9..2..49..8..2..294...88...2.49..8.2...499...842..42.9...8.2...498....8..29.4.948...2..49..8..2..249...88...2.49. <2489>   accepted = 17 template combinations <2489>   <>2  r1c3678,r2c356,r3c378,r5c47,r6c457,r8c45,r9c2346   -21 <2489>   <>4  r1c126,r2c59,r3c29,r4c89,r5c46,r7c1456,r8c1        -16 <2489>   <>8  r1c4,r2c3,r5c6,r8c5                                - 4 <2489>   <>9  r5c6,r6c8,r9c5                                     - 3 <2489>   <>1  r6c8,r7c2                                          - 2 <2489>   <>3  r4c6,r5c69                                         - 3 <2489>   <>5  r5c9,r8c3                                          - 2 <2489>   <>6  r2c157,r9c5                                        - 4 <2489>   <>7  r2c17,r7c2,r8c35,r9c5                              - 6                                                                  ===                                                                   61 eliminations r1c4,r2c157,r3c4,r4c6,r5c69,r6c8,r7c2,r8c35,r9c5   locked for candidates *** 4-template completed   c4b5  Locked Candidate 1              <> 3    r79c4   c1b7  Locked Candidate 1              <> 5    r5c1   c4b8  Locked Candidate 1              <> 7    r6c4 Templates: 18 2 6 3 16 3 7 8 14 <13>   accepted = 42 template combinations <13>   <>1  r3c1 <36>   accepted = 9 template combinations <36>   <>3  r6c7 <46>   accepted = 6 template combinations <46>   <>4  r2c6,r3c1,r4c5,r8c4 <46>   <>9  r2c1,r4c6,r8c5 r2c1,r4c6,r8c5   locked for candidates <69>   accepted = 19 template combinations <69>   <>9  r4c2 *** 2-template completed   c2    Naked  Pair                     <> 17   r136c2     b2  Naked  Triple                   <> 689  r3c4 Templates: 11 2 5 2 16 3 4 8 7 <39>   accepted = 17 template combinations <39>   <>9  r6c4 <69>   accepted = 10 template combinations <69>   <>9  r6c7 <78>   accepted = 10 template combinations <78>   <>5  r8c9 <78>   <>7  r9c4 <78>   <>8  r7c4 <78>   <>9  r6c5 r6c5,r8c9   locked for candidates *** 2-template completed r6  b4  Locked Candidate 2              <> 9    r5c1Solution:123456789457189236698237145271694853365812974984375621549768312732941568816523497`
daj95376
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### Re: Templates: with/without UnAvoidable Sets

daj95376 wrote:Note #2: ronk's second <2489> grid doesn't occur in my output because (at least) one of its four templates was disabled in an earlier 2/3-templates pass involving digits other than <2489>.

Note #3: r3c4<>8 would have occurred at <2489> if it hadn't already occurred at <248>.

That makes 62 exclusions. By using all the available <2489>-column-sis as a proxy for <2489>-templates and then adding r13c4 cell-sis, XSudo finds 60 exclusions, missing the r2c3<>8 and r2c5<>6 in your results.

I see no reason whatsoever for r2c3<>8, as no accepted 4-template even has a digit there.

The reason for the r2c5<>6 discrepancy was a bit trickier to find, but it's caused by discarding the template set noted in #2 above. It should not be discarded IMO, because the discard is based on information beyond that available with just the <2489>-templates.

[edit: "<2489>" was "<2468>" in 3 plcs]
Last edited by ronk on Thu Jul 12, 2012 6:58 pm, edited 1 time in total.
ronk
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### Re: Templates: with/without UnAvoidable Sets

ronk wrote:That makes 62 exclusions. By using all the available <2468>-column-sis as a proxy for <2468>-templates and then adding r13c4 cell-sis, XSudo finds 60 exclusions, missing the r2c3<>8 and r2c5<>6 in your results.

I see no reason whatsoever for r2c3<>8, as no accepted 4-template even has a digit there.

I suspect that your answer is (at least partially) in these 2-template patterns. They all contain r2c3=8 ... and ... they all contain a UR pattern.

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`...2.8.....8...2....2....8.2.....8.....8.2....8.....2.....8...2....2...882..........2.8.....8...2...2......82.....8.....8.2....8.....2........82..2.8....8...2.......2.8.....8...2...2.....8.2.....8.....8.2....8.....2.....8...2....2...88.2.........2.8.....8...2...2.....8.2.....8.....8.2....8.....2.....8...2..2.....88...2.......8.2.....8...2....2....8.2.....8.....2.8....8.....2.....8...2....2...882..........8.2.....8...2...2......82.....8.....2.8....8.....2........82..2.8....8...2.......8.2.....8...2...2.....8.2.....8.....2.8....8.....2.....8...2....2...88.2.........8.2.....8...2...2.....8.2.....8.....2.8....8.....2.....8...2..2.....88...2......2..8.....8..2..........282.....8.....8..2...8..2...........82...28....82..........4...8.4.8.........8...4......48.......8..4.84.......4..8........4...88.....4.....4.8.....8.....4.4......8......84....8.4....84..........4..8.4...8....8.....4.....4.8.....8.....4.4.....8.......84....8.4....84......4...8........4...88.....4.....4.8.....8.....44......8.......84....8.4....84.......4..8........4...88.....4.....4.8...4.8.............84......84....8.4....84.......4..8........4...88.....4.....8...4.4.8.........4...8......48.......8..4.84.......4..8........4...88.....4.....8.4.....8.....4.4......8......84....4.8....84..........4..8.4...8....8.....4.....8.4.....8.....4.4.....8.......84....4.8....84......4...8........4...88.....4.....8.4.....8.....44......8.......84....4.8....84.......4..8........4...88.....4.....8.4...4.8.............84......84....4.8....84.......4..8........4...88.....4..`

ronk wrote:The reason for the r2c5<>6 discrepancy was a bit trickier to find, but it's caused by discarding the template set noted in #2 above. It should not be discarded IMO, because the discard is based on information beyond that available with just the <2468>-templates.

You need to remember that my latest results were from running my templates solver before I make one more attempt at a template analyzer for just 4-template scennarios. As such, the solver should be expected to draw upon any accumulative information it collects on its way to the <2489>-template. As far as the analyzer goes, I'm still working on which constraints I wish to enforce prior to 4-template analysis.
daj95376
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Joined: 15 May 2006

### Re: Templates: with/without UnAvoidable Sets

daj95376 wrote:
ronk wrote:That makes 62 exclusions. By using all the available <2489>-column-sis as a proxy for <2489>-templates and then adding r13c4 cell-sis, XSudo finds 60 exclusions, missing the r2c3<>8 and r2c5<>6 in your results.

I see no reason whatsoever for r2c3<>8, as no accepted 4-template even has a digit there.

I suspect that your answer is (at least partially) in these 2-template patterns. They all contain r2c3=8 ... and ... they all contain a UR pattern.

Sorry, I had the exclusion rule backwards. Paraphrasing myself, "no accepted <2489>-template having a digit in r2c3" is exactly the reason r2c3<>8 is valid. Unfortunately, this seems to mean that templating and base\cover set logic, although not contradictory, might have different results.

daj95376 wrote:
ronk wrote:The reason for the r2c5<>6 discrepancy was a bit trickier to find, but it's caused by discarding the template set noted in #2 above. It should not be discarded IMO, because the discard is based on information beyond that available with just the <2489>-templates.

You need to remember that my latest results were from running my templates solver before I make one more attempt at a template analyzer for just 4-template scenarios.

I'd like to pursue this one later.

[edit: "<2489>" was "<2468>" in 4 plcs]
ronk
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Location: Southeastern USA

### Re: Templates with UAs (UnAvoidable Sets)

I stripped down a copy of my template solver software to where it should now only be analyzing a puzzle for 2-template, 3-template, and 4-template results. Use of URs, and template reduction after resolving clues/givens, has been removed. This comes as close as I can get to what ronk probably wants for comparison purposes. So, here's my "template analyzer" results for the above puzzle.

Hidden Text: Show
Code: Select all
`....5...9.5.1...3.....37...2..6..8...6..1..7...4..5.....9.....2.3...1.6.8.....4.. +-----------------------+ | . . . | . 5 . | . . 9 | | . 5 . | 1 . . | . 3 . | | . . . | . 3 7 | . . . | |-------+-------+-------| | 2 . . | 6 . . | 8 . . | | . 6 . | . 1 . | . 7 . | | . . 4 | . . 5 | . . . | |-------+-------+-------| | . . 9 | . . . | . . 2 | | . 3 . | . . 1 | . 6 . | | 8 . . | . . . | 4 . . | +-----------------------+ +--------------------------------------------------------------------------------+ |  13467   12478   123678  |  248     5       2468    |  1267    1248    9       | |  4679    5       2678    |  1       24689   24689   |  267     3       4678    | |  1469    12489   1268    |  2489    3       7       |  1256    12458   14568   | |--------------------------+--------------------------+--------------------------| |  2       179     1357    |  6       479     349     |  8       1459    1345    | |  359     6       358     |  23489   1       23489   |  2359    7       345     | |  1379    1789    4       |  23789   2789    5       |  12369   129     136     | |--------------------------+--------------------------+--------------------------| |  14567   147     9       |  34578   4678    3468    |  1357    158     2       | |  457     3       257     |  245789  24789   1       |  579     6       578     | |  8       127     12567   |  23579   2679    2369    |  4       159     1357    | +--------------------------------------------------------------------------------+ # 179 eliminations remain Templates: 56 59 16 50 32 20 87 26 28 *** 2-template completed *** 3-template completed <2489>   accepted = 34 template combinations <2489>   <>2  r9c2,r1239c3,r689c4,r68c5,r56c7,r13c8         -14 <2489>   <>4  r1c126,r2c59,r3c29,r4c89,r5c46,r7c1456,r8c1   -16 <2489>   <>8  r8c5                                          - 1 <2489>   <>9  r5c6,r6c8                                     - 2 <2489>   <>1  r6c8,r7c2                                     - 2 <2489>   <>3  r4c6,r5c69                                    - 3 <2489>   <>5  r5c9,r8c3                                     - 2 <2489>   <>6  r2c1                                          - 1 <2489>   <>7  r2c1,r7c2,r8c35                               - 4                                                             ===                                                              45 eliminations r1c4,r2c1,r3c4,r4c6,r5c69,r6c8,r7c2,r8c35   locked for candidates <2489> *** 4-template completed`
daj95376
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### Re: Templates with UAs (UnAvoidable Sets)

daj95376 wrote:I stripped down a copy of my template solver software to where it should now only be analyzing a puzzle for 2-template, 3-template, and 4-template results. Use of URs, and template reduction after resolving clues/givens, has been removed. This comes as close as I can get to what ronk probably wants for comparison purposes. So, here's my "template analyzer" results for the above puzzle.

This agrees 100% with my templating utility and can be 100% emulated (for lack of a better word) by Xsudo. However, I didn't mean for the use of URs to be removed. When you have time, would you please add it again? I'm primarily interested in what now happens with your previously posted r2c3<>8 and r2c5<>6. (I'm feeling guilty asking you for this stuff, so I best get busy and add the uniqueness to my own templating utility.)

FWIW here are the Xsudo logic diagrams for both without UR (on left/top) and with UR (on right/bottom).

logic diagrams: Show

logic set without UR: Show
Code: Select all
`000050009050100030000037000200600800060010070004005000009000002030001060800000400     25 Truths = {2C235678 4C125689 8C25689 9C125678 13N4}     50 Links = {2r123569 4r13457 8r13678 9r3469 2n1 1367n2 8n3 8n5 245n6 5n7 136n8 5n9 2b2368 4b2378 8b235 9b2489}     45 Eliminations, 4 Assignments --> r7c1456<>4, r1239c3<>2, r1c126<>4, r6c457<>2, r234c9<>4, r5c6<>349,      r8c5<>278, r9c24<>2, r13c8<>2, r2c1<>67, r5c9<>35, r6c8<>19, r7c2<>17,      r8c3<>57, r2c5<>4, r3c2<>4, r4c6<>3, r4c8<>4, r5c7<>2, r5c4<>4, r8c4<>2, r8c1<>4,      r5c9=4, r6c8=2, r7c2=4, r8c3=2`

logic set with UR: Show
Code: Select all
`000050009050100030000037000200600800060010070004005000009000002030001060800000400     25 Truths = {2C235678 4C125689 8C25689 9C125678 13N4}     50 Links = {2r123569 4r13457 8r13678 9r3469 2n1 1367n2 8n3 89n5 245n6 25n7 36n8 5n9 2b238 4b2378 8b235 9b2489}     AUR points {aur 4r1c4 8r3c8 }     60 Eliminations, 7 Assignments --> r1c3678<>2, r7c1456<>4, r9c2346<>2, r5c6<>3489, r1c126<>4, r2c356<>2,      r3c378<>2, r6c457<>2, r234c9<>4, r8c5<>278, r9c5<>679, r2c17<>6, r2c17<>7,      r5c47<>2, r13c4<>8, r5c9<>35, r6c8<>19, r7c2<>17, r8c3<>57, r2c5<>4,      r3c2<>4, r4c6<>3, r4c8<>4, r5c4<>4, r8c4<>2, r8c1<>4,      r2c7=2, r5c6=2, r5c9=4, r6c8=2, r7c2=4, r8c3=2, r9c5=2 `
ronk
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### Re: Templates with UAs (UnAvoidable Sets)

ronk wrote:This agrees 100% with my templating utility and can be 100% emulated (for lack of a better word) by Xsudo. However, I didn't mean for the use of URs to be removed. When you have time, would you please add it again? I'm primarily interested in what now happens with your previously posted r2c3<>8 and r2c5<>6. (I'm feeling guilty asking you for this stuff, so I best get busy and add the uniqueness to my own templating utility.)

I was just tired enough last night that I forgot the objective of this thread, and fixated on getting output that would agree with your results. Here's my template analyzer output with UR tracking enabled.

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` +--------------------------------------------------------------------------------+ |  13467   12478   123678  |  248     5       2468    |  1267    1248    9       | |  4679    5       2678    |  1       24689   24689   |  267     3       4678    | |  1469    12489   1268    |  2489    3       7       |  1256    12458   14568   | |--------------------------+--------------------------+--------------------------| |  2       179     1357    |  6       479     349     |  8       1459    1345    | |  359     6       358     |  23489   1       23489   |  2359    7       345     | |  1379    1789    4       |  23789   2789    5       |  12369   129     136     | |--------------------------+--------------------------+--------------------------| |  14567   147     9       |  34578   4678    3468    |  1357    158     2       | |  457     3       257     |  245789  24789   1       |  579     6       578     | |  8       127     12567   |  23579   2679    2369    |  4       159     1357    | +--------------------------------------------------------------------------------+ # 179 eliminations remain Templates: 56 59 16 50 32 20 87 26 28 *** 2-template completed <248>   accepted = 331 template combinations <248>   <>8  r3c4 r1c4   locked for candidates <248> *** 3-template completed ### removed <248+x>-templates that eliminate only   r3c4<>8 <2489>   accepted = 17 template combinations <2489>   <>2  r1c3678,r2c356,r3c378,r5c47,r6c457,r8c45,r9c2346   -21 <2489>   <>4  r1c126,r2c59,r3c29,r4c89,r5c46,r7c1456,r8c1        -16 <2489>   <>8  r2c3,r13c4,r8c5,r5c6                               - 5 <2489>   <>9  r5c6,r6c8,r9c5                                     - 3 <2489>   <>1  r6c8,r7c2                                          - 2 <2489>   <>3  r4c6,r5c69                                         - 3 <2489>   <>5  r5c9,r8c3                                          - 2 <2489>   <>6  r2c157,r9c5                                        - 4 <2489>   <>7  r2c17,r7c2,r8c35,r9c5                              - 6                                                                  ===                                                                   62 eliminations r1c4,r2c157,r3c4,r4c6,r5c69,r6c8,r7c2,r8c35,r9c5   locked for candidates <2489> *** 4-template completed`