The New Sudoku Players' Forum

[blue]

OK for 1. and 2. (obvious)
But 3. is not proven.

OK, so: if 1r1c1 hasn't been asserted as a hidden single, then there are one or more additional cells in r1 (for example), with candidates for '1'.
From (2), T1-delete, allows each of those candidates to be eliminted, leaving a hidden single in r1.

[denis_berthier]

.
OK. That's the missing piece.
So, finally, template-depth 1 isn't an exception and T1bis is as strong as T1.
.

[denis_berthier]

.
Happy New Year to all.

Generally speaking, 17-clue puzzles are among the easiest (in the mean) to solve with the usual resolution rules; but they are among the hardest (still in the mean) to solve with templates; they have easy puzzles with very large numbers of templates.

You might think that this is not unexpected because a small number of clues should imply a larger number of candidates (and therefore supposedly a larger number of templates *). And this is indeed true at the start, as I showed in [HCCS2, Table 3.1]. But, as also shown in [HCCS2, Table 3.2], the situation is more contrasted after BRT ("after Singles"). Excluding 17c puzzles solvable in BRT:
- there are more candidates in the mean (153.3) than for the controlled-bias collection (129.6);
- there are fewer candidates in the mean (153.3) than for the old T&E(2) collections (eleven = 205.7, ph2010 = 234.4);
- there are fewer candidates in the mean (153.3) than in mith's T&E(3) collection (169.7) (in which no puzzle has template-depth >3).

I even found a few puzzles with large numbers of templates, but with very low SER:

Code: Select all

.......719......6..2.........4.7.....3....4.....91....7..6....8...3..2..1........ ED=4.4/1.2/1.2
.......81.6.5.....7........2..6..5....8....2.1..3......4..21....5....6........... ED=2.6/1.2/1.2
......1.3.8..2.........45...3.....2....5...7....1.....1..3..6..7...8......5...... ED=3.4/1.2/1.2
......1.5..4.7..........3..15.3........6...8..2...........512....6....7.8........ ED=2.0/1.2/1.2
......1.94...5........2.3.....1.9...5....7......3......13.......8.....4...9....2. ED=4.5/1.2/1.2

(*) this supposition is indeed false, as previously mentioned: there's no general correlation between the number of candidates after BRT and the template-depth of a puzzle.
.

[denis_berthier]

.
Following my post in the tridagon thread: http://forum.enjoysudoku.com/the-tridagon-rule-t39859-125.html, a friend asked me: can this be used in any way for solving by templates?

I don't think so.
My version of templates is pattern-based (but with a non standard use of patterns) and is compatible with using any other resolution rules - i.e. you can mix any resolution rules and templates in order to get a solution. But:
- will using the no-tridagon-in-solution pattern to eliminate a priori some templates make the template solution faster? I didn't try but I don't think so, though it may happen occasionally. Anyway, if speed of finding a solution is the purpose, templates are not the right method.
- will it provide a "nicer" template solution. I don't think so either. Templates are not interesting as a human solver method, except in exceptional cases. Using the no-tridagon-in-solution pattern may add a few such cases. (But anyway template-depth isn't related in any way to the other usual measures of difficulty of a puzzle. The hardest puzzles (template-wise) only need 4-digit templates, in very rare cases.) In the general case, any template that would be eliminated by the no-tridagon-in-solution pattern will be eliminated by the Sudoku constraints expressed as templates.
One question that arises if one tries to use the no-tridagon-in-solution 3-digit pattern in conjunction with templates is, where to put it in the hierarchy of complexity wrt to templates: the natural answer is between T2 and T3 or to include it in the T3 generation rules in order to block T3-templates before they can be generated, but nothing forbids to grant all the tridagon rules higher priority (which is the case with the standard SudoRules saliences).

Then, you may ask, what's the use of the no-tridagon-in-solution result? I think it stands by itself, as a complementary view of tridagons. Also, as a guard against looking for tridagons in solution grids.
.

[denis_berthier]

Following several questions in other threads and irrelevant answers to them, let me recall this old post:

So, finally, we have three different techniques for templates, based on equivalent definitions of a template[k]:
- the strongest one, introduced at the start of this thread;
- the old one, used by eleven and P.O.;
- the weakest one, defined while I tried to understand the latter.

In the three approaches, templates[1] eliminate candidates.
As for templates[k+1], k≥1:
- in the weakest approach, they can only eliminate candidates;
- in the medium approach, they can only eliminate templates[1]; (my cbg-000 results a few posts above show this is strictly stronger than the weakest approach, already at level T2);
- in the strongest approach, they can only eliminate templates[k].

The reasons for increasing power should be clear. Once level k+1 is reached and all the templates[k+1] are computed (which all the approaches must do):
- the weak approach can do nothing if it can't directly eliminate a candidate;
- the medium approach can do nothing if it can't directly eliminate a template[1] (which is easier than eliminating a candidate);
- the strong approach will not directly eliminate more candidates or templates[1], but is has a chance of eliminating templates[k], which may later lead to still more eliminations of smaller templates.

Note that this has absolutely nothing to do with "implementation". The differences are at the abstract logical level: different elimination rules.
.

[StrmCkr]

deleted.

[denis_berthier]

does this sound like what you are doing ?

Your rule Tk-delete dynamical seems to be weaker (it's what I called the intermediary version).

First thing to check: take the examples in the first page of this thread. Do you find any with Template-depth > 4 ?

[StrmCkr]

deleted.

[denis_berthier]

.
My purpose in choosing CLIPS for the implementation of CSP-Rules was to have an implementation as close as possible to the logical rules ("the rules are the code") and to avoid having to deal with implementation details you're talking of.
My rule Tk-delete is perfectly clear; it requires to keep track "dynamically" not only of 1-templates but of all the k'-templates for k' ≤ k.
.

[StrmCkr]

i seem to have gotten the structure codes operationalnow
i have subsets size 1-4 for inclusion/exclusion rules before sending it to the Tkdelete program

Ti k{1-4} at each K level, i check that the template considered can be used by at least 1 Ti representing each combo-set[0...8] - Ti (k) Digit-set if not its discarded before the
Tk math check that this Ti (K) has a representation for each of nCr (8,k-1) combos

Code: Select all

+-------------+-------------+-------------+
   ! 3   8   6   ! 79  27  29  ! 1   4   5   !
   ! 7   4   5   ! 6   8   1   ! 9   2   3   !
   ! 2   9   1   ! 3   4   5   ! 6   7   8   !
   +-------------+-------------+-------------+
   ! 1   5   38  ! 78  37  4   ! 2   9   6   !
   ! 4   2   39  ! 19  13  6   ! 8   5   7   !
   ! 6   7   89  ! 589 25  29  ! 4   3   1   !
   +-------------+-------------+-------------+
   ! 8   1   7   ! 2   9   3   ! 5   6   4   !
   ! 9   6   4   ! 15  15  7   ! 3   8   2   !
   ! 5   3   2   ! 4   6   8   ! 7   1   9   !
   +-------------+-------------+-------------+

T2-delete: digit 3 template 4437 cannot form Template[2] with digits {3,2}
T2-delete: digit 7 template 21156 cannot form Template[2] with digits {7,5}
T2-delete: digit 9 template 18644 cannot form Template[2] with digits {9,8}
T2-delete: digit 9 template 29024 cannot form Template[2] with digits {9,5}
FOUND HIDDEN-SUBSET: digits=3 cells=r4c3 sector=21 size=1
-> eliminate digit 8 templates={6697}
FOUND HIDDEN-SUBSET: digits=3 cells=r5c5 sector=22 size=1
-> eliminate digit 1 templates={36018}
FOUND HIDDEN-SUBSET: digits=9 cells=r1c6 sector=19 size=1
-> eliminate digit 2 templates={29577}
FOUND HIDDEN-SUBSET: digits=9 cells=r6c4 sector=22 size=1
-> eliminate digit 5 templates={43865}

[denis_berthier]

i have subsets size 1-4 for inclusion/exclusion rules before sending it to the Tkdelete program
[...]
FOUND HIDDEN-SUBSET: digits=3 cells=r4c3 sector=21 size=1

Using the word "subset" and "HIDDEN-SUBSET" to mean something that is probably not what one would expect is not a good idea.
AS fo checking if your program is correct, I've published lists of puzzles in T1 ... T4 at the beginning of this thread. No need to check T1 and T2 (they are the same). But you can use T3 and T4.
.

[StrmCkr]

the subsets would be your T1-assert, t1-delete
i had these broad based "rules" as well, analyzing single digit templates

i realized it matched hidden/naked subsets and asked can it be expanded to work as naked/hidden subsets.

templates at the sector slice level: makes it expandable by n digits.

A sector with n cells containing n digits => naked subset size n
A sector with n digits containing n cells => hidden subset size n

Accomplished by templates.
{The only difference is that it excludes templates}

....56..94.....1.3.89....4.21.648.....4.1.6.......3..2.....4....3197.......8.13..

this t3 puzzle on your lists is T2 on mine because I have subsets size 2-4 computing before my Tk code triggers resolution.

---------------------------

some times a 2nd set of eyes help pin down a subtle bug or point out a misstep.

..3......4...8..36..8...1...4..6..73...9..........2..5..4.7..686........7..6..5..

[Edit 2024 Nov 3]:Following the discovery of missing eliminations in T3, this puzzle is now solved in T3.

a hand full of the "t3" grids like this one report as t4.

I'm not asking you to read over this list of output:

instead could you point out where the new "missing" eliminations are caused by in your own code
then i have a spot to focus on for bug checks.

POM completion time: (10409.3377ms): Show

Code: Select all

T2-delete: digit 1 template 51 cannot form Template[2] with digits {1,3}
T2-delete: digit 1 template 75 cannot form Template[2] with digits {1,3}
T2-delete: digit 1 template 1791 cannot form Template[2] with digits {1,3}
T2-delete: digit 1 template 1809 cannot form Template[2] with digits {1,3}
T2-delete: digit 1 template 17283 cannot form Template[2] with digits {1,3}
T2-delete: digit 1 template 17307 cannot form Template[2] with digits {1,3}
T2-delete: digit 1 template 21673 cannot form Template[2] with digits {1,3}
T2-delete: digit 1 template 21685 cannot form Template[2] with digits {1,3}
T2-delete: digit 1 template 22479 cannot form Template[2] with digits {1,3}
T2-delete: digit 1 template 22489 cannot form Template[2] with digits {1,3}
T2-delete: digit 1 template 22491 cannot form Template[2] with digits {1,3}
T2-delete: digit 1 template 22501 cannot form Template[2] with digits {1,3}
T2-delete: digit 1 template 22503 cannot form Template[2] with digits {1,3}
T2-delete: digit 1 template 22563 cannot form Template[2] with digits {1,3}
T2-delete: digit 1 template 22587 cannot form Template[2] with digits {1,3}
T2-delete: digit 1 template 22611 cannot form Template[2] with digits {1,3}
T2-delete: digit 1 template 22635 cannot form Template[2] with digits {1,3}
T2-delete: digit 1 template 27663 cannot form Template[2] with digits {1,3}
T2-delete: digit 1 template 27681 cannot form Template[2] with digits {1,3}
T2-delete: digit 2 template 2961 cannot form Template[2] with digits {2,3}
T2-delete: digit 2 template 22785 cannot form Template[2] with digits {2,3}
T2-delete: digit 2 template 22797 cannot form Template[2] with digits {2,3}
T2-delete: digit 2 template 22953 cannot form Template[2] with digits {2,3}
T2-delete: digit 2 template 23085 cannot form Template[2] with digits {2,3}
T2-delete: digit 2 template 23409 cannot form Template[2] with digits {2,3}
T2-delete: digit 2 template 33153 cannot form Template[2] with digits {2,3}
T2-delete: digit 2 template 37231 cannot form Template[2] with digits {2,4}
T2-delete: digit 2 template 37473 cannot form Template[2] with digits {2,4}
T2-delete: digit 2 template 38047 cannot form Template[2] with digits {2,4}
T2-delete: digit 2 template 38337 cannot form Template[2] with digits {2,3}
T2-delete: digit 2 template 38349 cannot form Template[2] with digits {2,3}
T2-delete: digit 2 template 38505 cannot form Template[2] with digits {2,3}
T2-delete: digit 2 template 38959 cannot form Template[2] with digits {2,4}
T2-delete: digit 2 template 39214 cannot form Template[2] with digits {2,7}
T2-delete: digit 2 template 39215 cannot form Template[2] with digits {2,7}
T2-delete: digit 2 template 39247 cannot form Template[2] with digits {2,4}
T2-delete: digit 2 template 39259 cannot form Template[2] with digits {2,7}
T2-delete: digit 2 template 43533 cannot form Template[2] with digits {2,3}
T2-delete: digit 4 template 21049 cannot form Template[2] with digits {4,3}
T2-delete: digit 4 template 21061 cannot form Template[2] with digits {4,3}
T2-delete: digit 4 template 21337 cannot form Template[2] with digits {4,3}
T2-delete: digit 4 template 21349 cannot form Template[2] with digits {4,3}
T2-delete: digit 4 template 31417 cannot form Template[2] with digits {4,3}
T2-delete: digit 4 template 31429 cannot form Template[2] with digits {4,3}
T2-delete: digit 4 template 36601 cannot form Template[2] with digits {4,3}
T2-delete: digit 4 template 36613 cannot form Template[2] with digits {4,3}
T2-delete: digit 4 template 36901 cannot form Template[2] with digits {4,7}
T2-delete: digit 4 template 41785 cannot form Template[2] with digits {4,3}
T2-delete: digit 4 template 41797 cannot form Template[2] with digits {4,3}
T2-delete: digit 4 template 42085 cannot form Template[2] with digits {4,7}
T2-delete: digit 9 template 2931 cannot form Template[2] with digits {9,3}
T2-delete: digit 9 template 22755 cannot form Template[2] with digits {9,3}
T2-delete: digit 9 template 22971 cannot form Template[2] with digits {9,3}
T2-delete: digit 9 template 23049 cannot form Template[2] with digits {9,3}
T2-delete: digit 9 template 23379 cannot form Template[2] with digits {9,3}
T2-delete: digit 9 template 33123 cannot form Template[2] with digits {9,3}
T2-delete: digit 9 template 37443 cannot form Template[2] with digits {9,4}
T2-delete: digit 9 template 37489 cannot form Template[2] with digits {9,4}
T2-delete: digit 9 template 37777 cannot form Template[2] with digits {9,4}
T2-delete: digit 9 template 38305 cannot form Template[2] with digits {9,4}
T2-delete: digit 9 template 38307 cannot form Template[2] with digits {9,3}
T2-delete: digit 9 template 38523 cannot form Template[2] with digits {9,3}
T2-delete: digit 9 template 38593 cannot form Template[2] with digits {9,4}
T2-delete: digit 9 template 40657 cannot form Template[2] with digits {9,4}
T2-delete: digit 9 template 40945 cannot form Template[2] with digits {9,4}
T2-delete: digit 9 template 43497 cannot form Template[2] with digits {9,3}
T3-delete: digit 1 template 5244 cannot form Template[3] with digits {1,2,7}
T3-delete: digit 1 template 6984 cannot form Template[3] with digits {1,5,7}
T3-delete: digit 1 template 16465 cannot form Template[3] with digits {1,3,9}
T3-delete: digit 1 template 16476 cannot form Template[3] with digits {1,2,7}
T3-delete: digit 1 template 16477 cannot form Template[3] with digits {1,5,7}
T3-delete: digit 1 template 17281 cannot form Template[3] with digits {1,2,3}
T3-delete: digit 1 template 17292 cannot form Template[3] with digits {1,3,5}
T3-delete: digit 1 template 17293 cannot form Template[3] with digits {1,2,3}
T3-delete: digit 1 template 17305 cannot form Template[3] with digits {1,2,3}
T3-delete: digit 1 template 21615 cannot form Template[3] with digits {1,5,9}
T3-delete: digit 1 template 22476 cannot form Template[3] with digits {1,3,5}
T3-delete: digit 1 template 22490 cannot form Template[3] with digits {1,5,7}
T3-delete: digit 1 template 22561 cannot form Template[3] with digits {1,3,7}
T3-delete: digit 1 template 22585 cannot form Template[3] with digits {1,3,7}
T3-delete: digit 1 template 22599 cannot form Template[3] with digits {1,3,7}
T3-delete: digit 1 template 26844 cannot form Template[3] with digits {1,5,7}
T3-delete: digit 1 template 26856 cannot form Template[3] with digits {1,5,9}
T3-delete: digit 1 template 27672 cannot form Template[3] with digits {1,2,9}
T3-delete: digit 1 template 27693 cannot form Template[3] with digits {1,3,5}
T3-delete: digit 2 template 367 cannot form Template[3] with digits {2,4,5}
T3-delete: digit 2 template 5518 cannot form Template[3] with digits {2,5,7}
T3-delete: digit 2 template 5519 cannot form Template[3] with digits {2,5,7}
T3-delete: digit 2 template 5551 cannot form Template[3] with digits {2,4,5}
T3-delete: digit 2 template 5563 cannot form Template[3] with digits {2,5,7}
T3-delete: digit 2 template 16783 cannot form Template[3] with digits {2,4,5}
T3-delete: digit 2 template 17599 cannot form Template[3] with digits {2,4,5}
T3-delete: digit 2 template 21921 cannot form Template[3] with digits {2,4,5}
T3-delete: digit 2 template 22784 cannot form Template[3] with digits {2,4,8}
T3-delete: digit 2 template 23073 cannot form Template[3] with digits {2,3,5}
T3-delete: digit 2 template 23087 cannot form Template[3] with digits {2,1,5}
T3-delete: digit 2 template 37362 cannot form Template[3] with digits {2,4,7}
T3-delete: digit 2 template 38059 cannot form Template[3] with digits {2,1,8}
T3-delete: digit 2 template 38063 cannot form Template[3] with digits {2,3,6}
T3-delete: digit 2 template 38336 cannot form Template[3] with digits {2,3,4}
T3-delete: digit 2 template 39246 cannot form Template[3] with digits {2,4,7}
T3-delete: digit 2 template 43247 cannot form Template[3] with digits {2,3,6}
T3-delete: digit 4 template 36325 cannot form Template[3] with digits {4,3,6}
T3-delete: digit 4 template 41479 cannot form Template[3] with digits {4,3,6}
T3-delete: digit 4 template 41491 cannot form Template[3] with digits {4,3,6}
T3-delete: digit 4 template 41509 cannot form Template[3] with digits {4,3,6}
T3-delete: digit 5 template 22772 cannot form Template[3] with digits {5,1,7}
T3-delete: digit 8 template 40337 cannot form Template[3] with digits {8,3,4}
T3-delete: digit 9 template 2065 cannot form Template[3] with digits {9,4,5}
T3-delete: digit 9 template 7249 cannot form Template[3] with digits {9,4,5}
T3-delete: digit 9 template 21891 cannot form Template[3] with digits {9,4,5}
T3-delete: digit 9 template 21937 cannot form Template[3] with digits {9,4,5}
T3-delete: digit 9 template 22753 cannot form Template[3] with digits {9,2,3}
T3-delete: digit 9 template 22754 cannot form Template[3] with digits {9,4,8}
T3-delete: digit 9 template 22969 cannot form Template[3] with digits {9,3,7}
T3-delete: digit 9 template 23047 cannot form Template[3] with digits {9,2,3}
T3-delete: digit 9 template 27121 cannot form Template[3] with digits {9,4,5}
T3-delete: digit 9 template 27937 cannot form Template[3] with digits {9,4,5}
T3-delete: digit 9 template 33121 cannot form Template[3] with digits {9,2,3}
T3-delete: digit 9 template 37776 cannot form Template[3] with digits {9,4,7}
T3-delete: digit 9 template 38306 cannot form Template[3] with digits {9,3,4}
T3-delete: digit 9 template 38521 cannot form Template[3] with digits {9,3,7}
T3-delete: digit 9 template 38592 cannot form Template[3] with digits {9,4,6}
T3-delete: digit 9 template 40944 cannot form Template[3] with digits {9,4,7}
T3-delete: digit 9 template 43495 cannot form Template[3] with digits {9,2,3}
T3-delete: digit 9 template 43783 cannot form Template[3] with digits {9,2,7}
T3-delete: digit 9 template 43787 cannot form Template[3] with digits {9,3,6}
T4-delete: digit 1 template 50 cannot form Template[4] with digits {1,2,3,5}
T4-delete: digit 1 template 60 cannot form Template[4] with digits {1,2,3,5}
T4-delete: digit 1 template 74 cannot form Template[4] with digits {1,5,7,9}
T4-delete: digit 1 template 86 cannot form Template[4] with digits {1,5,7,9}
T4-delete: digit 1 template 87 cannot form Template[4] with digits {1,5,7,9}
T4-delete: digit 1 template 157 cannot form Template[4] with digits {1,2,5,9}
T4-delete: digit 1 template 1788 cannot form Template[4] with digits {1,2,5,7}
T4-delete: digit 1 template 1790 cannot form Template[4] with digits {1,2,5,7}
T4-delete: digit 1 template 1800 cannot form Template[4] with digits {1,2,7,9}
T4-delete: digit 1 template 1808 cannot form Template[4] with digits {1,2,3,9}
T4-delete: digit 1 template 1812 cannot form Template[4] with digits {1,2,7,9}
T4-delete: digit 1 template 1820 cannot form Template[4] with digits {1,2,5,7}
T4-delete: digit 1 template 1821 cannot form Template[4] with digits {1,2,5,7}
T4-delete: digit 1 template 5186 cannot form Template[4] with digits {1,2,3,5}
T4-delete: digit 1 template 5187 cannot form Template[4] with digits {1,2,3,5}
T4-delete: digit 1 template 5210 cannot form Template[4] with digits {1,2,3,5}
T4-delete: digit 1 template 5211 cannot form Template[4] with digits {1,2,3,5}
T4-delete: digit 1 template 5222 cannot form Template[4] with digits {1,2,3,5}
T4-delete: digit 1 template 5223 cannot form Template[4] with digits {1,2,3,5}
T4-delete: digit 1 template 5232 cannot form Template[4] with digits {1,2,5,7}
T4-delete: digit 1 template 5233 cannot form Template[4] with digits {1,2,3,9}
T4-delete: digit 1 template 5245 cannot form Template[4] with digits {1,2,5,7}
T4-delete: digit 1 template 5256 cannot form Template[4] with digits {1,2,6,7}
T4-delete: digit 1 template 5257 cannot form Template[4] with digits {1,2,3,9}
T4-delete: digit 1 template 5268 cannot form Template[4] with digits {1,2,6,7}
T4-delete: digit 1 template 5269 cannot form Template[4] with digits {1,2,3,9}
T4-delete: digit 1 template 5341 cannot form Template[4] with digits {1,2,5,9}
T4-delete: digit 1 template 5358 cannot form Template[4] with digits {1,2,5,7}
T4-delete: digit 1 template 6926 cannot form Template[4] with digits {1,2,5,7}
T4-delete: digit 1 template 6927 cannot form Template[4] with digits {1,2,5,7}
T4-delete: digit 1 template 6944 cannot form Template[4] with digits {1,2,5,7}
T4-delete: digit 1 template 6945 cannot form Template[4] with digits {1,3,5,9}
T4-delete: digit 1 template 6956 cannot form Template[4] with digits {1,2,5,7}
T4-delete: digit 1 template 6957 cannot form Template[4] with digits {1,3,5,9}
T4-delete: digit 1 template 6972 cannot form Template[4] with digits {1,2,3,9}
T4-delete: digit 1 template 6985 cannot form Template[4] with digits {1,2,5,9}
T4-delete: digit 1 template 6990 cannot form Template[4] with digits {1,2,7,9}
T4-delete: digit 1 template 6996 cannot form Template[4] with digits {1,2,5,8}
T4-delete: digit 1 template 6997 cannot form Template[4] with digits {1,2,7,9}
T4-delete: digit 1 template 7002 cannot form Template[4] with digits {1,2,7,9}
T4-delete: digit 1 template 7020 cannot form Template[4] with digits {1,2,5,7}
T4-delete: digit 1 template 7021 cannot form Template[4] with digits {1,2,5,7}
T4-delete: digit 1 template 7039 cannot form Template[4] with digits {1,2,5,7}
T4-delete: digit 1 template 16418 cannot form Template[4] with digits {1,2,3,5}
T4-delete: digit 1 template 16419 cannot form Template[4] with digits {1,2,3,5}
T4-delete: digit 1 template 16443 cannot form Template[4] with digits {1,2,3,5}
T4-delete: digit 1 template 16464 cannot form Template[4] with digits {1,2,5,7}
T4-delete: digit 1 template 16488 cannot form Template[4] with digits {1,2,5,7}
T4-delete: digit 1 template 16489 cannot form Template[4] with digits {1,2,3,9}
T4-delete: digit 1 template 16500 cannot form Template[4] with digits {1,2,5,7}
T4-delete: digit 1 template 16501 cannot form Template[4] with digits {1,2,3,5}
T4-delete: digit 1 template 16572 cannot form Template[4] with digits {1,2,7,9}
T4-delete: digit 1 template 16573 cannot form Template[4] with digits {1,2,7,9}
T4-delete: digit 1 template 16590 cannot form Template[4] with digits {1,2,5,7}
T4-delete: digit 1 template 16591 cannot form Template[4] with digits {1,2,5,7}
T4-delete: digit 1 template 16602 cannot form Template[4] with digits {1,2,5,7}
T4-delete: digit 1 template 16603 cannot form Template[4] with digits {1,2,5,7}
T4-delete: digit 1 template 17280 cannot form Template[4] with digits {1,2,3,5}
T4-delete: digit 1 template 17282 cannot form Template[4] with digits {1,2,3,4}
T4-delete: digit 1 template 17304 cannot form Template[4] with digits {1,2,3,5}
T4-delete: digit 1 template 17306 cannot form Template[4] with digits {1,2,3,9}
T4-delete: digit 1 template 17316 cannot form Template[4] with digits {1,2,3,5}
T4-delete: digit 1 template 17317 cannot form Template[4] with digits {1,2,3,5}
T4-delete: digit 1 template 17318 cannot form Template[4] with digits {1,2,3,9}
T4-delete: digit 1 template 17319 cannot form Template[4] with digits {1,2,3,5}
T4-delete: digit 1 template 17424 cannot form Template[4] with digits {1,2,8,9}
T4-delete: digit 1 template 17425 cannot form Template[4] with digits {1,2,3,4}
T4-delete: digit 1 template 17448 cannot form Template[4] with digits {1,2,8,9}
T4-delete: digit 1 template 17449 cannot form Template[4] with digits {1,2,3,5}
T4-delete: digit 1 template 17460 cannot form Template[4] with digits {1,2,8,9}
T4-delete: digit 1 template 21614 cannot form Template[4] with digits {1,2,7,9}
T4-delete: digit 1 template 21626 cannot form Template[4] with digits {1,5,7,9}
T4-delete: digit 1 template 21627 cannot form Template[4] with digits {1,2,3,5}
T4-delete: digit 1 template 21660 cannot form Template[4] with digits {1,2,3,5}
T4-delete: digit 1 template 21672 cannot form Template[4] with digits {1,2,3,5}
T4-delete: digit 1 template 21684 cannot form Template[4] with digits {1,2,3,5}
T4-delete: digit 1 template 21699 cannot form Template[4] with digits {1,2,3,5}
T4-delete: digit 1 template 21708 cannot form Template[4] with digits {1,2,7,9}
T4-delete: digit 1 template 21709 cannot form Template[4] with digits {1,2,3,9}
T4-delete: digit 1 template 21723 cannot form Template[4] with digits {1,2,3,5}
T4-delete: digit 1 template 21726 cannot form Template[4] with digits {1,2,5,7}
T4-delete: digit 1 template 21727 cannot form Template[4] with digits {1,2,3,9}
T4-delete: digit 1 template 21738 cannot form Template[4] with digits {1,2,5,7}
T4-delete: digit 1 template 21739 cannot form Template[4] with digits {1,2,3,5}
T4-delete: digit 1 template 21747 cannot form Template[4] with digits {1,3,5,9}
T4-delete: digit 1 template 21756 cannot form Template[4] with digits {1,2,7,9}
T4-delete: digit 1 template 21771 cannot form Template[4] with digits {1,3,5,9}
T4-delete: digit 1 template 21774 cannot form Template[4] with digits {1,2,5,7}
T4-delete: digit 1 template 21786 cannot form Template[4] with digits {1,2,5,7}
T4-delete: digit 1 template 22478 cannot form Template[4] with digits {1,2,3,5}
T4-delete: digit 1 template 22488 cannot form Template[4] with digits {1,2,3,4}
T4-delete: digit 1 template 22500 cannot form Template[4] with digits {1,2,3,4}
T4-delete: digit 1 template 22502 cannot form Template[4] with digits {1,2,3,9}
T4-delete: digit 1 template 22560 cannot form Template[4] with digits {1,2,8,9}
T4-delete: digit 1 template 22562 cannot form Template[4] with digits {1,2,3,5}
T4-delete: digit 1 template 22573 cannot form Template[4] with digits {1,2,3,9}
T4-delete: digit 1 template 22584 cannot form Template[4] with digits {1,2,8,9}
T4-delete: digit 1 template 22596 cannot form Template[4] with digits {1,2,8,9}
T4-delete: digit 1 template 22597 cannot form Template[4] with digits {1,2,3,9}
T4-delete: digit 1 template 22610 cannot form Template[4] with digits {1,2,3,9}
T4-delete: digit 1 template 22647 cannot form Template[4] with digits {1,2,3,5}
T4-delete: digit 1 template 26798 cannot form Template[4] with digits {1,2,5,7}
T4-delete: digit 1 template 26799 cannot form Template[4] with digits {1,2,5,7}
T4-delete: digit 1 template 26816 cannot form Template[4] with digits {1,2,5,7}
T4-delete: digit 1 template 26817 cannot form Template[4] with digits {1,2,5,7}
T4-delete: digit 1 template 26828 cannot form Template[4] with digits {1,2,5,7}
T4-delete: digit 1 template 26829 cannot form Template[4] with digits {1,2,5,7}
T4-delete: digit 1 template 26857 cannot form Template[4] with digits {1,2,5,7}
T4-delete: digit 1 template 26862 cannot form Template[4] with digits {1,2,3,5}
T4-delete: digit 1 template 26868 cannot form Template[4] with digits {1,2,3,5}
T4-delete: digit 1 template 26869 cannot form Template[4] with digits {1,2,5,7}
T4-delete: digit 1 template 26874 cannot form Template[4] with digits {1,2,3,5}
T4-delete: digit 1 template 26892 cannot form Template[4] with digits {1,2,3,9}
T4-delete: digit 1 template 26893 cannot form Template[4] with digits {1,2,3,9}
T4-delete: digit 1 template 26910 cannot form Template[4] with digits {1,2,5,7}
T4-delete: digit 1 template 26911 cannot form Template[4] with digits {1,2,5,7}
T4-delete: digit 1 template 26922 cannot form Template[4] with digits {1,2,5,7}
T4-delete: digit 1 template 26923 cannot form Template[4] with digits {1,2,3,5}
T4-delete: digit 1 template 27660 cannot form Template[4] with digits {1,2,3,5}
T4-delete: digit 1 template 27662 cannot form Template[4] with digits {1,2,3,5}
T4-delete: digit 1 template 27673 cannot form Template[4] with digits {1,2,3,4}
T4-delete: digit 1 template 27678 cannot form Template[4] with digits {1,2,3,5}
T4-delete: digit 1 template 27680 cannot form Template[4] with digits {1,2,3,8}
T4-delete: digit 1 template 27684 cannot form Template[4] with digits {1,2,3,4}
T4-delete: digit 1 template 27685 cannot form Template[4] with digits {1,2,3,5}
T4-delete: digit 1 template 27690 cannot form Template[4] with digits {1,2,3,5}
T4-delete: digit 1 template 27692 cannot form Template[4] with digits {1,2,3,8}
T4-delete: digit 1 template 27744 cannot form Template[4] with digits {1,2,5,7}
T4-delete: digit 1 template 27745 cannot form Template[4] with digits {1,2,3,5}
T4-delete: digit 1 template 27756 cannot form Template[4] with digits {1,2,5,7}
T4-delete: digit 1 template 27757 cannot form Template[4] with digits {1,2,5,7}
T4-delete: digit 1 template 27769 cannot form Template[4] with digits {1,2,3,5}
T4-delete: digit 1 template 27781 cannot form Template[4] with digits {1,2,7,9}
T4-delete: digit 2 template 2972 cannot form Template[4] with digits {2,1,3,5}
T4-delete: digit 2 template 2973 cannot form Template[4] with digits {2,1,3,5}
T4-delete: digit 2 template 5550 cannot form Template[4] with digits {2,1,7,9}
T4-delete: digit 2 template 5682 cannot form Template[4] with digits {2,1,5,8}
T4-delete: digit 2 template 5683 cannot form Template[4] with digits {2,1,5,7}
T4-delete: digit 2 template 5806 cannot form Template[4] with digits {2,1,5,7}
T4-delete: digit 2 template 5807 cannot form Template[4] with digits {2,1,5,7}
T4-delete: digit 2 template 5838 cannot form Template[4] with digits {2,1,7,9}
T4-delete: digit 2 template 5839 cannot form Template[4] with digits {2,1,7,9}
T4-delete: digit 2 template 5851 cannot form Template[4] with digits {2,1,5,7}
T4-delete: digit 2 template 5970 cannot form Template[4] with digits {2,1,5,8}
T4-delete: digit 2 template 5971 cannot form Template[4] with digits {2,1,5,8}
T4-delete: digit 2 template 7854 cannot form Template[4] with digits {2,1,5,7}
T4-delete: digit 2 template 7855 cannot form Template[4] with digits {2,1,5,7}
T4-delete: digit 2 template 7866 cannot form Template[4] with digits {2,1,5,7}
T4-delete: digit 2 template 7867 cannot form Template[4] with digits {2,1,5,7}
T4-delete: digit 2 template 8142 cannot form Template[4] with digits {2,1,5,8}
T4-delete: digit 2 template 8154 cannot form Template[4] with digits {2,5,7,9}
T4-delete: digit 2 template 16750 cannot form Template[4] with digits {2,4,8,9}
T4-delete: digit 2 template 16751 cannot form Template[4] with digits {2,1,3,5}
T4-delete: digit 2 template 16782 cannot form Template[4] with digits {2,1,4,5}
T4-delete: digit 2 template 16795 cannot form Template[4] with digits {2,1,3,9}
T4-delete: digit 2 template 16914 cannot form Template[4] with digits {2,1,3,5}
T4-delete: digit 2 template 16915 cannot form Template[4] with digits {2,1,3,5}
T4-delete: digit 2 template 17039 cannot form Template[4] with digits {2,1,7,9}
T4-delete: digit 2 template 17070 cannot form Template[4] with digits {2,1,5,7}
T4-delete: digit 2 template 17071 cannot form Template[4] with digits {2,1,5,7}
T4-delete: digit 2 template 17083 cannot form Template[4] with digits {2,1,5,7}
T4-delete: digit 2 template 17202 cannot form Template[4] with digits {2,1,3,5}
T4-delete: digit 2 template 17203 cannot form Template[4] with digits {2,1,3,5}
T4-delete: digit 2 template 17598 cannot form Template[4] with digits {2,1,3,4}
T4-delete: digit 2 template 17611 cannot form Template[4] with digits {2,1,3,4}
T4-delete: digit 2 template 17614 cannot form Template[4] with digits {2,1,3,5}
T4-delete: digit 2 template 17615 cannot form Template[4] with digits {2,1,3,5}
T4-delete: digit 2 template 17766 cannot form Template[4] with digits {2,1,5,8}
T4-delete: digit 2 template 17767 cannot form Template[4] with digits {2,1,3,5}
T4-delete: digit 2 template 17778 cannot form Template[4] with digits {2,1,5,8}
T4-delete: digit 2 template 17886 cannot form Template[4] with digits {2,1,3,5}
T4-delete: digit 2 template 17887 cannot form Template[4] with digits {2,1,3,5}
T4-delete: digit 2 template 17899 cannot form Template[4] with digits {2,1,3,5}
T4-delete: digit 2 template 17902 cannot form Template[4] with digits {2,1,3,5}
T4-delete: digit 2 template 17903 cannot form Template[4] with digits {2,1,3,5}
T4-delete: digit 2 template 18054 cannot form Template[4] with digits {2,1,5,8}
T4-delete: digit 2 template 18055 cannot form Template[4] with digits {2,1,3,9}
T4-delete: digit 2 template 18510 cannot form Template[4] with digits {2,1,5,7}
T4-delete: digit 2 template 18511 cannot form Template[4] with digits {2,1,5,7}
T4-delete: digit 2 template 18522 cannot form Template[4] with digits {2,1,5,7}
T4-delete: digit 2 template 18523 cannot form Template[4] with digits {2,1,5,7}
T4-delete: digit 2 template 21920 cannot form Template[4] with digits {2,1,5,7}
T4-delete: digit 2 template 21966 cannot form Template[4] with digits {2,1,5,7}
T4-delete: digit 2 template 22098 cannot form Template[4] with digits {2,1,3,5}
T4-delete: digit 2 template 22208 cannot form Template[4] with digits {2,1,5,7}
T4-delete: digit 2 template 22209 cannot form Template[4] with digits {2,1,5,7}
T4-delete: digit 2 template 22254 cannot form Template[4] with digits {2,1,5,7}
T4-delete: digit 2 template 22386 cannot form Template[4] with digits {2,1,3,5}
T4-delete: digit 2 template 22782 cannot form Template[4] with digits {2,1,3,5}
T4-delete: digit 2 template 22799 cannot form Template[4] with digits {2,1,3,5}
T4-delete: digit 2 template 22950 cannot form Template[4] with digits {2,1,3,5}
T4-delete: digit 2 template 22952 cannot form Template[4] with digits {2,1,3,5}
T4-delete: digit 2 template 23070 cannot form Template[4] with digits {2,1,3,5}
T4-delete: digit 2 template 23072 cannot form Template[4] with digits {2,1,3,5}
T4-delete: digit 2 template 23238 cannot form Template[4] with digits {2,1,3,5}
T4-delete: digit 2 template 23240 cannot form Template[4] with digits {2,1,3,9}
T4-delete: digit 2 template 23241 cannot form Template[4] with digits {2,1,3,5}
T4-delete: digit 2 template 23406 cannot form Template[4] with digits {2,1,5,7}
T4-delete: digit 2 template 23408 cannot form Template[4] with digits {2,3,5,9}
T4-delete: digit 2 template 23418 cannot form Template[4] with digits {2,1,5,7}
T4-delete: digit 2 template 23420 cannot form Template[4] with digits {2,1,3,5}
T4-delete: digit 2 template 23421 cannot form Template[4] with digits {2,1,3,5}
T4-delete: digit 2 template 23694 cannot form Template[4] with digits {2,1,5,7}
T4-delete: digit 2 template 23706 cannot form Template[4] with digits {2,1,5,7}
T4-delete: digit 2 template 32046 cannot form Template[4] with digits {2,1,5,7}
T4-delete: digit 2 template 32047 cannot form Template[4] with digits {2,1,4,8}
T4-delete: digit 2 template 32058 cannot form Template[4] with digits {2,1,5,7}
T4-delete: digit 2 template 32059 cannot form Template[4] with digits {2,1,5,7}
T4-delete: digit 2 template 32289 cannot form Template[4] with digits {2,1,5,7}
T4-delete: digit 2 template 32334 cannot form Template[4] with digits {2,1,5,7}
T4-delete: digit 2 template 32346 cannot form Template[4] with digits {2,1,5,7}
T4-delete: digit 2 template 32862 cannot form Template[4] with digits {2,1,3,5}
T4-delete: digit 2 template 32863 cannot form Template[4] with digits {2,1,3,4}
T4-delete: digit 2 template 32874 cannot form Template[4] with digits {2,1,3,4}
T4-delete: digit 2 template 32875 cannot form Template[4] with digits {2,1,3,5}
T4-delete: digit 2 template 33150 cannot form Template[4] with digits {2,1,3,5}
T4-delete: digit 2 template 33152 cannot form Template[4] with digits {2,1,3,9}
T4-delete: digit 2 template 33162 cannot form Template[4] with digits {2,1,3,5}
T4-delete: digit 2 template 33164 cannot form Template[4] with digits {2,1,3,5}
T4-delete: digit 2 template 33165 cannot form Template[4] with digits {2,1,3,5}
T4-delete: digit 2 template 33775 cannot form Template[4] with digits {2,1,5,7}
T4-delete: digit 2 template 34062 cannot form Template[4] with digits {2,1,7,9}
T4-delete: digit 2 template 34063 cannot form Template[4] with digits {2,1,4,8}
T4-delete: digit 2 template 34074 cannot form Template[4] with digits {2,1,5,7}
T4-delete: digit 2 template 34075 cannot form Template[4] with digits {2,1,7,9}
T4-delete: digit 2 template 37198 cannot form Template[4] with digits {2,4,8,9}
T4-delete: digit 2 template 37199 cannot form Template[4] with digits {2,1,3,5}
T4-delete: digit 2 template 37230 cannot form Template[4] with digits {2,1,4,7}
T4-delete: digit 2 template 37243 cannot form Template[4] with digits {2,1,3,7}
T4-delete: digit 2 template 37363 cannot form Template[4] with digits {2,1,3,5}
T4-delete: digit 2 template 37472 cannot form Template[4] with digits {2,1,5,7}
T4-delete: digit 2 template 37518 cannot form Template[4] with digits {2,1,5,7}
T4-delete: digit 2 template 37640 cannot form Template[4] with digits {2,1,3,9}
T4-delete: digit 2 template 37650 cannot form Template[4] with digits {2,1,3,5}
T4-delete: digit 2 template 38046 cannot form Template[4] with digits {2,1,3,4}
T4-delete: digit 2 template 38062 cannot form Template[4] with digits {2,1,3,5}
T4-delete: digit 2 template 38214 cannot form Template[4] with digits {2,1,3,9}
T4-delete: digit 2 template 38215 cannot form Template[4] with digits {2,1,3,4}
T4-delete: digit 2 template 38226 cannot form Template[4] with digits {2,1,5,8}
T4-delete: digit 2 template 38334 cannot form Template[4] with digits {2,1,3,5}
T4-delete: digit 2 template 38351 cannot form Template[4] with digits {2,1,3,5}
T4-delete: digit 2 template 38502 cannot form Template[4] with digits {2,1,5,8}
T4-delete: digit 2 template 38504 cannot form Template[4] with digits {2,1,3,9}
T4-delete: digit 2 template 38958 cannot form Template[4] with digits {2,1,5,7}
T4-delete: digit 2 template 39378 cannot form Template[4] with digits {2,1,5,8}
T4-delete: digit 2 template 39379 cannot form Template[4] with digits {2,1,5,8}
T4-delete: digit 2 template 42383 cannot form Template[4] with digits {2,1,7,9}
T4-delete: digit 2 template 42414 cannot form Template[4] with digits {2,1,5,7}
T4-delete: digit 2 template 42415 cannot form Template[4] with digits {2,1,5,7}
T4-delete: digit 2 template 42427 cannot form Template[4] with digits {2,1,5,7}
T4-delete: digit 2 template 42546 cannot form Template[4] with digits {2,1,3,5}
T4-delete: digit 2 template 42547 cannot form Template[4] with digits {2,1,3,5}
T4-delete: digit 2 template 42656 cannot form Template[4] with digits {2,1,5,7}
T4-delete: digit 2 template 42657 cannot form Template[4] with digits {2,1,5,7}
T4-delete: digit 2 template 42702 cannot form Template[4] with digits {2,1,5,7}
T4-delete: digit 2 template 42834 cannot form Template[4] with digits {2,1,3,5}
T4-delete: digit 2 template 43230 cannot form Template[4] with digits {2,1,3,5}
T4-delete: digit 2 template 43231 cannot form Template[4] with digits {2,1,3,5}
T4-delete: digit 2 template 43243 cannot form Template[4] with digits {2,1,3,5}
T4-delete: digit 2 template 43246 cannot form Template[4] with digits {2,1,3,5}
T4-delete: digit 2 template 43398 cannot form Template[4] with digits {2,1,3,9}
T4-delete: digit 2 template 43399 cannot form Template[4] with digits {2,1,3,9}
T4-delete: digit 2 template 43518 cannot form Template[4] with digits {2,1,3,5}
T4-delete: digit 2 template 43520 cannot form Template[4] with digits {2,1,3,5}
T4-delete: digit 2 template 43521 cannot form Template[4] with digits {2,1,3,5}
T4-delete: digit 2 template 43535 cannot form Template[4] with digits {2,1,3,5}
T4-delete: digit 2 template 43686 cannot form Template[4] with digits {2,1,5,8}
T4-delete: digit 2 template 43688 cannot form Template[4] with digits {2,1,3,9}
T4-delete: digit 2 template 43689 cannot form Template[4] with digits {2,1,3,9}
T4-delete: digit 2 template 44398 cannot form Template[4] with digits {2,5,7,9}
T4-delete: digit 2 template 44399 cannot form Template[4] with digits {2,1,5,7}
T4-delete: digit 2 template 44430 cannot form Template[4] with digits {2,1,7,9}
T4-delete: digit 2 template 44431 cannot form Template[4] with digits {2,1,7,9}
T4-delete: digit 2 template 44443 cannot form Template[4] with digits {2,1,7,9}
T4-delete: digit 2 template 44562 cannot form Template[4] with digits {2,1,5,8}
T4-delete: digit 2 template 44563 cannot form Template[4] with digits {2,1,5,8}
T4-delete: digit 3 template 14355 cannot form Template[4] with digits {3,1,5,9}
T4-delete: digit 3 template 14641 cannot form Template[4] with digits {3,1,2,9}
T4-delete: digit 3 template 14645 cannot form Template[4] with digits {3,1,5,9}
T4-delete: digit 4 template 31116 cannot form Template[4] with digits {4,3,6,8}
T4-delete: digit 5 template 344 cannot form Template[4] with digits {5,1,7,9}
T4-delete: digit 5 template 2084 cannot form Template[4] with digits {5,1,2,7}
T4-delete: digit 5 template 5480 cannot form Template[4] with digits {5,1,2,3}
T4-delete: digit 5 template 5526 cannot form Template[4] with digits {5,2,7,9}
T4-delete: digit 5 template 5538 cannot form Template[4] with digits {5,2,7,9}
T4-delete: digit 5 template 7220 cannot form Template[4] with digits {5,1,3,9}
T4-delete: digit 5 template 7266 cannot form Template[4] with digits {5,2,7,9}
T4-delete: digit 5 template 16758 cannot form Template[4] with digits {5,1,2,7}
T4-delete: digit 5 template 16770 cannot form Template[4] with digits {5,1,2,7}
T4-delete: digit 5 template 16866 cannot form Template[4] with digits {5,1,7,9}
T4-delete: digit 5 template 17574 cannot form Template[4] with digits {5,1,2,3}
T4-delete: digit 5 template 17576 cannot form Template[4] with digits {5,2,3,9}
T4-delete: digit 5 template 17586 cannot form Template[4] with digits {5,1,2,3}
T4-delete: digit 5 template 21908 cannot form Template[4] with digits {5,1,2,7}
T4-delete: digit 5 template 21954 cannot form Template[4] with digits {5,1,2,3}
T4-delete: digit 5 template 22002 cannot form Template[4] with digits {5,1,7,9}
T4-delete: digit 5 template 22050 cannot form Template[4] with digits {5,1,7,9}
T4-delete: digit 5 template 22770 cannot form Template[4] with digits {5,1,2,3}
T4-delete: digit 5 template 27092 cannot form Template[4] with digits {5,1,2,7}
T4-delete: digit 5 template 27138 cannot form Template[4] with digits {5,1,2,7}
T4-delete: digit 5 template 27186 cannot form Template[4] with digits {5,1,7,9}
T4-delete: digit 5 template 27954 cannot form Template[4] with digits {5,1,2,3}
T4-delete: digit 5 template 27956 cannot form Template[4] with digits {5,1,2,7}
T4-delete: digit 5 template 28038 cannot form Template[4] with digits {5,1,2,7}
T4-delete: digit 5 template 37206 cannot form Template[4] with digits {5,1,2,7}
T4-delete: digit 5 template 37218 cannot form Template[4] with digits {5,1,2,7}
T4-delete: digit 5 template 37314 cannot form Template[4] with digits {5,1,7,9}
T4-delete: digit 5 template 37506 cannot form Template[4] with digits {5,1,2,3}
T4-delete: digit 5 template 37554 cannot form Template[4] with digits {5,1,7,9}
T4-delete: digit 5 template 37602 cannot form Template[4] with digits {5,1,7,9}
T4-delete: digit 5 template 37748 cannot form Template[4] with digits {5,1,2,7}
T4-delete: digit 5 template 37794 cannot form Template[4] with digits {5,1,2,7}
T4-delete: digit 5 template 37842 cannot form Template[4] with digits {5,1,3,9}
T4-delete: digit 5 template 38022 cannot form Template[4] with digits {5,1,2,3}
T4-delete: digit 5 template 38024 cannot form Template[4] with digits {5,1,3,9}
T4-delete: digit 5 template 38034 cannot form Template[4] with digits {5,1,2,3}
T4-delete: digit 5 template 38322 cannot form Template[4] with digits {5,1,2,3}
T4-delete: digit 5 template 38324 cannot form Template[4] with digits {5,1,2,3}
T4-delete: digit 5 template 38406 cannot form Template[4] with digits {5,2,8,9}
T4-delete: digit 5 template 38610 cannot form Template[4] with digits {5,1,2,3}
T4-delete: digit 5 template 38612 cannot form Template[4] with digits {5,1,2,7}
T4-delete: digit 5 template 38694 cannot form Template[4] with digits {5,1,2,7}
T4-delete: digit 5 template 38936 cannot form Template[4] with digits {5,1,7,9}
T4-delete: digit 5 template 39176 cannot form Template[4] with digits {5,1,2,3}
T4-delete: digit 5 template 39222 cannot form Template[4] with digits {5,2,7,9}
T4-delete: digit 5 template 39234 cannot form Template[4] with digits {5,2,7,9}
T4-delete: digit 5 template 40676 cannot form Template[4] with digits {5,1,2,7}
T4-delete: digit 5 template 40916 cannot form Template[4] with digits {5,1,3,9}
T4-delete: digit 5 template 40962 cannot form Template[4] with digits {5,2,7,9}
T4-delete: digit 7 template 17277 cannot form Template[4] with digits {7,1,2,5}
T4-delete: digit 7 template 27615 cannot form Template[4] with digits {7,1,2,9}
T4-delete: digit 7 template 32205 cannot form Template[4] with digits {7,1,2,5}
T4-delete: digit 7 template 32751 cannot form Template[4] with digits {7,1,2,9}
T4-delete: digit 7 template 42621 cannot form Template[4] with digits {7,1,2,5}
T4-delete: digit 7 template 43167 cannot form Template[4] with digits {7,1,2,9}
T4-delete: digit 8 template 35164 cannot form Template[4] with digits {8,1,2,9}
T4-delete: digit 8 template 40348 cannot form Template[4] with digits {8,1,2,9}
T4-delete: digit 8 template 40516 cannot form Template[4] with digits {8,1,2,9}
T4-delete: digit 9 template 2353 cannot form Template[4] with digits {9,4,7,8}
T4-delete: digit 9 template 3216 cannot form Template[4] with digits {9,2,5,7}
T4-delete: digit 9 template 3217 cannot form Template[4] with digits {9,2,5,7}
T4-delete: digit 9 template 7248 cannot form Template[4] with digits {9,1,2,7}
T4-delete: digit 9 template 7422 cannot form Template[4] with digits {9,1,5,8}
T4-delete: digit 9 template 7423 cannot form Template[4] with digits {9,1,2,5}
T4-delete: digit 9 template 7498 cannot form Template[4] with digits {9,1,5,7}
T4-delete: digit 9 template 7499 cannot form Template[4] with digits {9,1,5,7}
T4-delete: digit 9 template 7536 cannot form Template[4] with digits {9,1,2,7}
T4-delete: digit 9 template 7537 cannot form Template[4] with digits {9,1,2,7}
T4-delete: digit 9 template 7543 cannot form Template[4] with digits {9,1,2,7}
T4-delete: digit 9 template 7710 cannot form Template[4] with digits {9,1,5,8}
T4-delete: digit 9 template 7711 cannot form Template[4] with digits {9,1,5,8}
T4-delete: digit 9 template 8112 cannot form Template[4] with digits {9,1,2,8}
T4-delete: digit 9 template 8113 cannot form Template[4] with digits {9,2,5,7}
T4-delete: digit 9 template 8400 cannot form Template[4] with digits {9,1,5,7}
T4-delete: digit 9 template 8401 cannot form Template[4] with digits {9,1,5,7}
T4-delete: digit 9 template 21890 cannot form Template[4] with digits {9,1,2,7}
T4-delete: digit 9 template 21936 cannot form Template[4] with digits {9,1,2,7}
T4-delete: digit 9 template 22110 cannot form Template[4] with digits {9,1,3,5}
T4-delete: digit 9 template 22111 cannot form Template[4] with digits {9,1,2,3}
T4-delete: digit 9 template 22178 cannot form Template[4] with digits {9,1,2,7}
T4-delete: digit 9 template 22179 cannot form Template[4] with digits {9,1,2,7}
T4-delete: digit 9 template 22186 cannot form Template[4] with digits {9,1,2,3}
T4-delete: digit 9 template 22224 cannot form Template[4] with digits {9,1,2,7}
T4-delete: digit 9 template 22225 cannot form Template[4] with digits {9,1,2,3}
T4-delete: digit 9 template 22231 cannot form Template[4] with digits {9,1,2,3}
T4-delete: digit 9 template 22398 cannot form Template[4] with digits {9,1,3,5}
T4-delete: digit 9 template 22399 cannot form Template[4] with digits {9,1,2,3}
T4-delete: digit 9 template 22752 cannot form Template[4] with digits {9,1,2,3}
T4-delete: digit 9 template 22968 cannot form Template[4] with digits {9,1,5,8}
T4-delete: digit 9 template 22975 cannot form Template[4] with digits {9,1,5,7}
T4-delete: digit 9 template 23040 cannot form Template[4] with digits {9,1,2,3}
T4-delete: digit 9 template 23041 cannot form Template[4] with digits {9,1,2,3}
T4-delete: digit 9 template 23042 cannot form Template[4] with digits {9,1,2,3}
T4-delete: digit 9 template 23043 cannot form Template[4] with digits {9,1,2,3}
T4-delete: digit 9 template 23050 cannot form Template[4] with digits {9,1,2,3}
T4-delete: digit 9 template 23051 cannot form Template[4] with digits {9,1,2,3}
T4-delete: digit 9 template 23256 cannot form Template[4] with digits {9,1,5,8}
T4-delete: digit 9 template 23257 cannot form Template[4] with digits {9,1,5,8}
T4-delete: digit 9 template 23378 cannot form Template[4] with digits {9,2,3,5}
T4-delete: digit 9 template 23664 cannot form Template[4] with digits {9,2,5,8}
T4-delete: digit 9 template 23665 cannot form Template[4] with digits {9,2,5,8}
T4-delete: digit 9 template 27120 cannot form Template[4] with digits {9,1,2,7}
T4-delete: digit 9 template 27294 cannot form Template[4] with digits {9,1,2,7}
T4-delete: digit 9 template 27295 cannot form Template[4] with digits {9,1,3,5}
T4-delete: digit 9 template 27371 cannot form Template[4] with digits {9,1,2,7}
T4-delete: digit 9 template 27408 cannot form Template[4] with digits {9,1,2,7}
T4-delete: digit 9 template 27409 cannot form Template[4] with digits {9,1,2,7}
T4-delete: digit 9 template 27415 cannot form Template[4] with digits {9,1,2,7}
T4-delete: digit 9 template 27582 cannot form Template[4] with digits {9,1,2,7}
T4-delete: digit 9 template 27583 cannot form Template[4] with digits {9,1,3,5}
T4-delete: digit 9 template 27936 cannot form Template[4] with digits {9,1,2,3}
T4-delete: digit 9 template 28152 cannot form Template[4] with digits {9,1,2,3}
T4-delete: digit 9 template 28153 cannot form Template[4] with digits {9,1,2,3}
T4-delete: digit 9 template 28158 cannot form Template[4] with digits {9,1,2,7}
T4-delete: digit 9 template 28224 cannot form Template[4] with digits {9,1,2,3}
T4-delete: digit 9 template 28225 cannot form Template[4] with digits {9,1,2,3}
T4-delete: digit 9 template 28231 cannot form Template[4] with digits {9,1,2,3}
T4-delete: digit 9 template 28234 cannot form Template[4] with digits {9,1,2,3}
T4-delete: digit 9 template 28235 cannot form Template[4] with digits {9,1,2,3}
T4-delete: digit 9 template 28440 cannot form Template[4] with digits {9,1,2,3}
T4-delete: digit 9 template 28441 cannot form Template[4] with digits {9,1,5,7}
T4-delete: digit 9 template 28560 cannot form Template[4] with digits {9,1,5,7}
T4-delete: digit 9 template 28561 cannot form Template[4] with digits {9,1,5,7}
T4-delete: digit 9 template 28848 cannot form Template[4] with digits {9,1,5,7}
T4-delete: digit 9 template 28849 cannot form Template[4] with digits {9,1,5,7}
T4-delete: digit 9 template 32259 cannot form Template[4] with digits {9,1,5,7}
T4-delete: digit 9 template 32304 cannot form Template[4] with digits {9,1,2,7}
T4-delete: digit 9 template 32305 cannot form Template[4] with digits {9,1,2,3}
T4-delete: digit 9 template 32592 cannot form Template[4] with digits {9,1,2,7}
T4-delete: digit 9 template 32593 cannot form Template[4] with digits {9,1,2,7}
T4-delete: digit 9 template 33120 cannot form Template[4] with digits {9,1,2,3}
T4-delete: digit 9 template 33122 cannot form Template[4] with digits {9,1,2,3}
T4-delete: digit 9 template 33408 cannot form Template[4] with digits {9,1,2,3}
T4-delete: digit 9 template 33409 cannot form Template[4] with digits {9,1,2,3}
T4-delete: digit 9 template 35473 cannot form Template[4] with digits {9,2,5,7}
T4-delete: digit 9 template 35760 cannot form Template[4] with digits {9,1,2,7}
T4-delete: digit 9 template 35761 cannot form Template[4] with digits {9,1,2,5}
T4-delete: digit 9 template 37442 cannot form Template[4] with digits {9,1,2,7}
T4-delete: digit 9 template 37488 cannot form Template[4] with digits {9,1,2,7}
T4-delete: digit 9 template 37662 cannot form Template[4] with digits {9,1,3,5}
T4-delete: digit 9 template 37663 cannot form Template[4] with digits {9,1,2,3}
T4-delete: digit 9 template 37950 cannot form Template[4] with digits {9,1,2,7}
T4-delete: digit 9 template 37951 cannot form Template[4] with digits {9,1,3,5}
T4-delete: digit 9 template 38304 cannot form Template[4] with digits {9,1,2,3}
T4-delete: digit 9 template 38520 cannot form Template[4] with digits {9,1,5,8}
T4-delete: digit 9 template 38527 cannot form Template[4] with digits {9,1,5,7}
T4-delete: digit 9 template 38808 cannot form Template[4] with digits {9,1,2,7}
T4-delete: digit 9 template 38809 cannot form Template[4] with digits {9,1,2,3}
T4-delete: digit 9 template 38814 cannot form Template[4] with digits {9,1,2,7}
T4-delete: digit 9 template 38815 cannot form Template[4] with digits {9,1,5,7}
T4-delete: digit 9 template 40656 cannot form Template[4] with digits {9,1,5,7}
T4-delete: digit 9 template 41118 cannot form Template[4] with digits {9,1,5,8}
T4-delete: digit 9 template 41119 cannot form Template[4] with digits {9,1,2,5}
T4-delete: digit 9 template 42626 cannot form Template[4] with digits {9,1,2,7}
T4-delete: digit 9 template 42627 cannot form Template[4] with digits {9,1,2,7}
T4-delete: digit 9 template 42634 cannot form Template[4] with digits {9,1,2,3}
T4-delete: digit 9 template 42672 cannot form Template[4] with digits {9,1,2,7}
T4-delete: digit 9 template 42673 cannot form Template[4] with digits {9,1,2,3}
T4-delete: digit 9 template 42679 cannot form Template[4] with digits {9,1,2,3}
T4-delete: digit 9 template 42846 cannot form Template[4] with digits {9,1,3,5}
T4-delete: digit 9 template 42847 cannot form Template[4] with digits {9,1,2,3}
T4-delete: digit 9 template 42922 cannot form Template[4] with digits {9,2,5,7}
T4-delete: digit 9 template 42923 cannot form Template[4] with digits {9,1,2,7}
T4-delete: digit 9 template 42960 cannot form Template[4] with digits {9,1,2,7}
T4-delete: digit 9 template 42961 cannot form Template[4] with digits {9,1,2,7}
T4-delete: digit 9 template 42967 cannot form Template[4] with digits {9,1,2,7}
T4-delete: digit 9 template 43134 cannot form Template[4] with digits {9,1,2,7}
T4-delete: digit 9 template 43135 cannot form Template[4] with digits {9,1,3,5}
T4-delete: digit 9 template 43488 cannot form Template[4] with digits {9,1,2,3}
T4-delete: digit 9 template 43489 cannot form Template[4] with digits {9,1,2,3}
T4-delete: digit 9 template 43490 cannot form Template[4] with digits {9,1,2,3}
T4-delete: digit 9 template 43491 cannot form Template[4] with digits {9,1,2,3}
T4-delete: digit 9 template 43498 cannot form Template[4] with digits {9,1,2,3}
T4-delete: digit 9 template 43499 cannot form Template[4] with digits {9,1,2,3}
T4-delete: digit 9 template 43704 cannot form Template[4] with digits {9,1,5,8}
T4-delete: digit 9 template 43705 cannot form Template[4] with digits {9,1,5,8}
T4-delete: digit 9 template 43776 cannot form Template[4] with digits {9,1,2,3}
T4-delete: digit 9 template 43777 cannot form Template[4] with digits {9,1,2,3}
T4-delete: digit 9 template 43786 cannot form Template[4] with digits {9,1,2,3}
T4-delete: digit 9 template 43992 cannot form Template[4] with digits {9,1,2,7}
T4-delete: digit 9 template 43993 cannot form Template[4] with digits {9,1,5,7}
T4-delete: digit 9 template 46090 cannot form Template[4] with digits {9,2,5,7}
T4-delete: digit 9 template 46091 cannot form Template[4] with digits {9,1,5,7}
T4-delete: digit 9 template 46128 cannot form Template[4] with digits {9,1,2,7}
T4-delete: digit 9 template 46129 cannot form Template[4] with digits {9,1,2,7}
T4-delete: digit 9 template 46135 cannot form Template[4] with digits {9,1,2,7}
T4-delete: digit 9 template 46302 cannot form Template[4] with digits {9,1,5,8}
T4-delete: digit 9 template 46303 cannot form Template[4] with digits {9,1,5,8}
T3-delete: digit 1 template 156 cannot form Template[3] with digits {1,2,8}
T3-delete: digit 1 template 1836 cannot form Template[3] with digits {1,5,7}
T3-delete: digit 1 template 1837 cannot form Template[3] with digits {1,2,7}
T3-delete: digit 1 template 1854 cannot form Template[3] with digits {1,2,7}
T3-delete: digit 1 template 1855 cannot form Template[3] with digits {1,2,5}
T3-delete: digit 1 template 17461 cannot form Template[3] with digits {1,3,9}
T3-delete: digit 1 template 22608 cannot form Template[3] with digits {1,3,5}
T3-delete: digit 1 template 22632 cannot form Template[3] with digits {1,2,5}
T3-delete: digit 1 template 27768 cannot form Template[3] with digits {1,2,8}
T3-delete: digit 1 template 27780 cannot form Template[3] with digits {1,5,9}
T3-delete: digit 2 template 498 cannot form Template[3] with digits {2,1,7}
T3-delete: digit 2 template 499 cannot form Template[3] with digits {2,1,5}
T3-delete: digit 2 template 786 cannot form Template[3] with digits {2,1,7}
T3-delete: digit 2 template 787 cannot form Template[3] with digits {2,1,7}
T3-delete: digit 2 template 8108 cannot form Template[3] with digits {2,5,7}
T3-delete: digit 2 template 33786 cannot form Template[3] with digits {2,1,5}
T3-delete: digit 2 template 38227 cannot form Template[3] with digits {2,1,9}
T3-delete: digit 2 template 39090 cannot form Template[3] with digits {2,1,7}
T3-delete: digit 2 template 39091 cannot form Template[3] with digits {2,1,5}
T3-delete: digit 2 template 44274 cannot form Template[3] with digits {2,1,7}
T3-delete: digit 2 template 44275 cannot form Template[3] with digits {2,1,7}
T3-delete: digit 5 template 22902 cannot form Template[3] with digits {5,1,9}
T3-delete: digit 5 template 38166 cannot form Template[3] with digits {5,1,2}
T3-delete: digit 5 template 38454 cannot form Template[3] with digits {5,1,2}
T3-delete: digit 9 template 2238 cannot form Template[3] with digits {9,1,7}
T3-delete: digit 9 template 2239 cannot form Template[3] with digits {9,1,5}
T3-delete: digit 9 template 2526 cannot form Template[3] with digits {9,1,7}
T3-delete: digit 9 template 23259 cannot form Template[3] with digits {9,3,5}
T3-delete: digit 9 template 23376 cannot form Template[3] with digits {9,1,5}
T3-delete: digit 9 template 23377 cannot form Template[3] with digits {9,2,5}
T3-delete: digit 9 template 27370 cannot form Template[3] with digits {9,1,5}
T3-delete: digit 9 template 28446 cannot form Template[3] with digits {9,1,2}
T3-delete: digit 9 template 40830 cannot form Template[3] with digits {9,1,7}
T3-delete: digit 9 template 40831 cannot form Template[3] with digits {9,1,5}
T3-delete: digit 9 template 46014 cannot form Template[3] with digits {9,1,7}
T3-delete: digit 1 template 22572 cannot form Template[3] with digits {1,2,5}
T3-delete: digit 1 template 22591 cannot form Template[3] with digits {1,2,5}
T3-delete: digit 2 template 2958 cannot form Template[3] with digits {2,1,5}
T3-delete: digit 2 template 2970 cannot form Template[3] with digits {2,1,5}
T3-delete: digit 9 template 2363 cannot form Template[3] with digits {9,1,5}
T4-delete: digit 1 template 48 cannot form Template[4] with digits {1,2,5,7}
T4-delete: digit 1 template 49 cannot form Template[4] with digits {1,2,3,5}
T4-delete: digit 1 template 61 cannot form Template[4] with digits {1,2,3,9}
T4-delete: digit 1 template 73 cannot form Template[4] with digits {1,2,3,9}
T4-delete: digit 1 template 175 cannot form Template[4] with digits {1,2,3,9}
T4-delete: digit 1 template 186 cannot form Template[4] with digits {1,2,3,7}
T4-delete: digit 1 template 187 cannot form Template[4] with digits {1,2,3,9}
T4-delete: digit 1 template 1801 cannot form Template[4] with digits {1,2,3,9}
T4-delete: digit 1 template 1866 cannot form Template[4] with digits {1,2,3,9}
T4-delete: digit 1 template 1867 cannot form Template[4] with digits {1,2,3,9}
T4-delete: digit 1 template 5340 cannot form Template[4] with digits {1,2,3,9}
T4-delete: digit 1 template 5359 cannot form Template[4] with digits {1,2,3,9}
T4-delete: digit 1 template 5370 cannot form Template[4] with digits {1,2,7,9}
T4-delete: digit 1 template 5371 cannot form Template[4] with digits {1,5,6,9}
T4-delete: digit 1 template 7038 cannot form Template[4] with digits {1,2,3,9}
T4-delete: digit 1 template 7050 cannot form Template[4] with digits {1,2,3,9}
T4-delete: digit 1 template 7051 cannot form Template[4] with digits {1,2,3,9}
T4-delete: digit 1 template 16442 cannot form Template[4] with digits {1,2,3,9}
T4-delete: digit 1 template 16454 cannot form Template[4] with digits {1,2,3,9}
T4-delete: digit 1 template 16455 cannot form Template[4] with digits {1,2,3,9}
T4-delete: digit 1 template 17436 cannot form Template[4] with digits {1,2,5,6}
T4-delete: digit 1 template 17437 cannot form Template[4] with digits {1,2,5,6}
T4-delete: digit 1 template 17454 cannot form Template[4] with digits {1,2,6,9}
T4-delete: digit 1 template 17455 cannot form Template[4] with digits {1,2,5,6}
T4-delete: digit 1 template 17466 cannot form Template[4] with digits {1,2,6,9}
T4-delete: digit 1 template 21638 cannot form Template[4] with digits {1,2,3,9}
T4-delete: digit 1 template 21639 cannot form Template[4] with digits {1,2,3,9}
T4-delete: digit 1 template 21698 cannot form Template[4] with digits {1,2,3,4}
T4-delete: digit 1 template 21734 cannot form Template[4] with digits {1,2,3,4}
T4-delete: digit 1 template 21746 cannot form Template[4] with digits {1,2,3,9}
T4-delete: digit 1 template 21770 cannot form Template[4] with digits {1,2,3,9}
T4-delete: digit 1 template 21782 cannot form Template[4] with digits {1,2,3,9}
T4-delete: digit 1 template 22586 cannot form Template[4] with digits {1,2,3,5}
T4-delete: digit 1 template 22590 cannot form Template[4] with digits {1,2,3,5}
T4-delete: digit 1 template 22598 cannot form Template[4] with digits {1,2,3,5}
T4-delete: digit 1 template 22602 cannot form Template[4] with digits {1,2,3,5}
T4-delete: digit 1 template 22603 cannot form Template[4] with digits {1,2,3,5}
T4-delete: digit 1 template 22620 cannot form Template[4] with digits {1,2,3,5}
T4-delete: digit 1 template 22634 cannot form Template[4] with digits {1,2,3,5}
T4-delete: digit 1 template 22638 cannot form Template[4] with digits {1,2,3,5}
T4-delete: digit 1 template 22644 cannot form Template[4] with digits {1,2,3,5}
T4-delete: digit 1 template 22646 cannot form Template[4] with digits {1,2,3,5}
T4-delete: digit 1 template 22650 cannot form Template[4] with digits {1,2,3,5}
T4-delete: digit 1 template 27774 cannot form Template[4] with digits {1,2,6,9}
T4-delete: digit 1 template 27775 cannot form Template[4] with digits {1,2,3,9}
T4-delete: digit 1 template 27786 cannot form Template[4] with digits {1,2,6,9}
T4-delete: digit 1 template 27787 cannot form Template[4] with digits {1,2,7,9}
T4-delete: digit 2 template 366 cannot form Template[4] with digits {2,1,7,9}
T4-delete: digit 2 template 379 cannot form Template[4] with digits {2,1,3,9}
T4-delete: digit 2 template 382 cannot form Template[4] with digits {2,1,3,9}
T4-delete: digit 2 template 383 cannot form Template[4] with digits {2,1,3,5}
T4-delete: digit 2 template 654 cannot form Template[4] with digits {2,1,3,9}
T4-delete: digit 2 template 655 cannot form Template[4] with digits {2,1,3,9}
T4-delete: digit 2 template 667 cannot form Template[4] with digits {2,1,3,9}
T4-delete: digit 2 template 670 cannot form Template[4] with digits {2,1,5,7}
T4-delete: digit 2 template 671 cannot form Template[4] with digits {2,1,3,5}
T4-delete: digit 2 template 2670 cannot form Template[4] with digits {2,1,3,5}
T4-delete: digit 2 template 2671 cannot form Template[4] with digits {2,1,3,5}
T4-delete: digit 2 template 2682 cannot form Template[4] with digits {2,1,3,5}
T4-delete: digit 2 template 2683 cannot form Template[4] with digits {2,1,3,9}
T4-delete: digit 2 template 2960 cannot form Template[4] with digits {2,1,3,5}
T4-delete: digit 2 template 8097 cannot form Template[4] with digits {2,3,5,9}
T4-delete: digit 2 template 17038 cannot form Template[4] with digits {2,1,5,7}
T4-delete: digit 2 template 17779 cannot form Template[4] with digits {2,1,3,9}
T4-delete: digit 2 template 18066 cannot form Template[4] with digits {2,1,5,8}
T4-delete: digit 2 template 18067 cannot form Template[4] with digits {2,5,6,9}
T4-delete: digit 2 template 18222 cannot form Template[4] with digits {2,1,3,5}
T4-delete: digit 2 template 18223 cannot form Template[4] with digits {2,1,3,5}
T4-delete: digit 2 template 18234 cannot form Template[4] with digits {2,1,3,5}
T4-delete: digit 2 template 18235 cannot form Template[4] with digits {2,1,3,9}
T4-delete: digit 2 template 21933 cannot form Template[4] with digits {2,1,3,9}
T4-delete: digit 2 template 21935 cannot form Template[4] with digits {2,1,3,5}
T4-delete: digit 2 template 22088 cannot form Template[4] with digits {2,1,3,9}
T4-delete: digit 2 template 22089 cannot form Template[4] with digits {2,1,3,9}
T4-delete: digit 2 template 22221 cannot form Template[4] with digits {2,1,5,7}
T4-delete: digit 2 template 22223 cannot form Template[4] with digits {2,1,5,7}
T4-delete: digit 2 template 22376 cannot form Template[4] with digits {2,1,3,9}
T4-delete: digit 2 template 22377 cannot form Template[4] with digits {2,1,3,9}
T4-delete: digit 2 template 22962 cannot form Template[4] with digits {2,1,3,9}
T4-delete: digit 2 template 23250 cannot form Template[4] with digits {2,1,3,9}
T4-delete: digit 2 template 23648 cannot form Template[4] with digits {2,1,3,9}
T4-delete: digit 2 template 23649 cannot form Template[4] with digits {2,1,5,6}
T4-delete: digit 2 template 23660 cannot form Template[4] with digits {2,1,3,9}
T4-delete: digit 2 template 23661 cannot form Template[4] with digits {2,1,5,7}
T4-delete: digit 2 template 32288 cannot form Template[4] with digits {2,1,5,7}
T4-delete: digit 2 template 32300 cannot form Template[4] with digits {2,1,3,5}
T4-delete: digit 2 template 32301 cannot form Template[4] with digits {2,1,3,9}
T4-delete: digit 2 template 33774 cannot form Template[4] with digits {2,1,7,9}
T4-delete: digit 2 template 33787 cannot form Template[4] with digits {2,3,5,9}
T4-delete: digit 2 template 37485 cannot form Template[4] with digits {2,1,3,9}
T4-delete: digit 2 template 37487 cannot form Template[4] with digits {2,1,3,5}
T4-delete: digit 2 template 37641 cannot form Template[4] with digits {2,1,3,9}
T4-delete: digit 2 template 38514 cannot form Template[4] with digits {2,1,3,9}
T4-delete: digit 2 template 38971 cannot form Template[4] with digits {2,1,3,9}
T4-delete: digit 2 template 38974 cannot form Template[4] with digits {2,1,3,9}
T4-delete: digit 2 template 38975 cannot form Template[4] with digits {2,1,3,5}
T4-delete: digit 2 template 42382 cannot form Template[4] with digits {2,1,4,8}
T4-delete: digit 2 template 42669 cannot form Template[4] with digits {2,1,5,7}
T4-delete: digit 2 template 42671 cannot form Template[4] with digits {2,1,5,7}
T4-delete: digit 2 template 42824 cannot form Template[4] with digits {2,1,3,9}
T4-delete: digit 2 template 42825 cannot form Template[4] with digits {2,1,3,9}
T4-delete: digit 2 template 43410 cannot form Template[4] with digits {2,1,3,9}
T4-delete: digit 2 template 43411 cannot form Template[4] with digits {2,1,3,5}
T4-delete: digit 2 template 43698 cannot form Template[4] with digits {2,1,3,9}
T4-delete: digit 2 template 44142 cannot form Template[4] with digits {2,1,7,9}
T4-delete: digit 2 template 44143 cannot form Template[4] with digits {2,3,5,9}
T4-delete: digit 2 template 44155 cannot form Template[4] with digits {2,1,3,9}
T4-delete: digit 2 template 44159 cannot form Template[4] with digits {2,1,3,5}
T4-delete: digit 3 template 14065 cannot form Template[4] with digits {3,1,2,9}
T4-delete: digit 3 template 14067 cannot form Template[4] with digits {3,1,2,9}
T4-delete: digit 3 template 14068 cannot form Template[4] with digits {3,1,2,9}
T4-delete: digit 3 template 14069 cannot form Template[4] with digits {3,1,2,9}
T4-delete: digit 3 template 14089 cannot form Template[4] with digits {3,2,5,9}
T4-delete: digit 3 template 14091 cannot form Template[4] with digits {3,1,2,9}
T4-delete: digit 3 template 14092 cannot form Template[4] with digits {3,2,5,9}
T4-delete: digit 3 template 14093 cannot form Template[4] with digits {3,1,2,5}
T4-delete: digit 3 template 14101 cannot form Template[4] with digits {3,1,2,5}
T4-delete: digit 3 template 14105 cannot form Template[4] with digits {3,1,2,5}
T4-delete: digit 3 template 14107 cannot form Template[4] with digits {3,1,2,5}
T4-delete: digit 3 template 14353 cannot form Template[4] with digits {3,1,2,5}
T4-delete: digit 3 template 14356 cannot form Template[4] with digits {3,1,2,5}
T4-delete: digit 3 template 14357 cannot form Template[4] with digits {3,1,2,5}
T4-delete: digit 3 template 14365 cannot form Template[4] with digits {3,1,2,5}
T4-delete: digit 3 template 14391 cannot form Template[4] with digits {3,1,2,9}
T4-delete: digit 3 template 14393 cannot form Template[4] with digits {3,1,2,5}
T4-delete: digit 3 template 14644 cannot form Template[4] with digits {3,1,2,9}
T4-delete: digit 3 template 14649 cannot form Template[4] with digits {3,1,2,9}
T4-delete: digit 3 template 14651 cannot form Template[4] with digits {3,1,2,9}
T4-delete: digit 3 template 14653 cannot form Template[4] with digits {3,1,2,5}
T4-delete: digit 3 template 14679 cannot form Template[4] with digits {3,1,5,9}
T4-delete: digit 3 template 14681 cannot form Template[4] with digits {3,1,2,5}
T4-delete: digit 4 template 15877 cannot form Template[4] with digits {4,2,3,9}
T4-delete: digit 4 template 16140 cannot form Template[4] with digits {4,1,2,9}
T4-delete: digit 4 template 21036 cannot form Template[4] with digits {4,1,2,5}
T4-delete: digit 4 template 21048 cannot form Template[4] with digits {4,1,5,9}
T4-delete: digit 4 template 21324 cannot form Template[4] with digits {4,1,5,9}
T4-delete: digit 4 template 26245 cannot form Template[4] with digits {4,1,2,9}
T4-delete: digit 4 template 26520 cannot form Template[4] with digits {4,1,2,9}
T4-delete: digit 4 template 31117 cannot form Template[4] with digits {4,3,5,6}
T4-delete: digit 4 template 31416 cannot form Template[4] with digits {4,1,2,9}
T4-delete: digit 4 template 31428 cannot form Template[4] with digits {4,1,2,9}
T4-delete: digit 4 template 36300 cannot form Template[4] with digits {4,1,3,9}
T4-delete: digit 4 template 36588 cannot form Template[4] with digits {4,1,2,5}
T4-delete: digit 4 template 36876 cannot form Template[4] with digits {4,2,7,8}
T4-delete: digit 4 template 41473 cannot form Template[4] with digits {4,2,7,8}
T4-delete: digit 4 template 41772 cannot form Template[4] with digits {4,1,2,5}
T4-delete: digit 4 template 41784 cannot form Template[4] with digits {4,1,5,9}
T4-delete: digit 4 template 42072 cannot form Template[4] with digits {4,1,2,9}
T4-delete: digit 5 template 450 cannot form Template[4] with digits {5,1,3,7}
T4-delete: digit 5 template 2130 cannot form Template[4] with digits {5,1,3,7}
T4-delete: digit 5 template 5634 cannot form Template[4] with digits {5,1,6,9}
T4-delete: digit 5 template 7314 cannot form Template[4] with digits {5,1,6,9}
T4-delete: digit 5 template 16712 cannot form Template[4] with digits {5,1,7,9}
T4-delete: digit 5 template 17718 cannot form Template[4] with digits {5,1,2,3}
T4-delete: digit 5 template 17730 cannot form Template[4] with digits {5,2,6,9}
T4-delete: digit 5 template 22040 cannot form Template[4] with digits {5,1,7,9}
T4-delete: digit 5 template 22854 cannot form Template[4] with digits {5,1,2,3}
T4-delete: digit 5 template 22856 cannot form Template[4] with digits {5,1,2,6}
T4-delete: digit 5 template 22866 cannot form Template[4] with digits {5,1,2,3}
T4-delete: digit 5 template 22904 cannot form Template[4] with digits {5,1,2,3}
T4-delete: digit 5 template 22914 cannot form Template[4] with digits {5,1,2,3}
T4-delete: digit 5 template 28050 cannot form Template[4] with digits {5,2,3,9}
T4-delete: digit 5 template 37160 cannot form Template[4] with digits {5,1,2,7}
T4-delete: digit 5 template 37460 cannot form Template[4] with digits {5,1,7,9}
T4-delete: digit 5 template 37544 cannot form Template[4] with digits {5,1,2,3}
T4-delete: digit 5 template 37592 cannot form Template[4] with digits {5,1,7,9}
T4-delete: digit 5 template 38178 cannot form Template[4] with digits {5,2,6,9}
T4-delete: digit 5 template 38408 cannot form Template[4] with digits {5,1,2,3}
T4-delete: digit 5 template 38418 cannot form Template[4] with digits {5,1,2,3}
T4-delete: digit 5 template 38456 cannot form Template[4] with digits {5,1,2,3}
T4-delete: digit 5 template 38466 cannot form Template[4] with digits {5,1,2,3}
T4-delete: digit 5 template 38706 cannot form Template[4] with digits {5,2,6,9}
T4-delete: digit 5 template 39042 cannot form Template[4] with digits {5,1,2,7}
T4-delete: digit 5 template 39330 cannot form Template[4] with digits {5,1,6,9}
T4-delete: digit 5 template 40722 cannot form Template[4] with digits {5,1,2,7}
T4-delete: digit 5 template 41010 cannot form Template[4] with digits {5,1,2,9}
T4-delete: digit 7 template 6045 cannot form Template[4] with digits {7,2,5,9}
T4-delete: digit 7 template 7743 cannot form Template[4] with digits {7,1,2,9}
T4-delete: digit 7 template 8013 cannot form Template[4] with digits {7,1,2,5}
T4-delete: digit 7 template 8559 cannot form Template[4] with digits {7,1,2,9}
T4-delete: digit 7 template 18669 cannot form Template[4] with digits {7,1,2,5}
T4-delete: digit 7 template 29007 cannot form Template[4] with digits {7,1,2,9}
T4-delete: digit 7 template 34221 cannot form Template[4] with digits {7,2,5,9}
T4-delete: digit 7 template 35919 cannot form Template[4] with digits {7,1,2,9}
T4-delete: digit 7 template 44637 cannot form Template[4] with digits {7,2,5,9}
T4-delete: digit 7 template 46335 cannot form Template[4] with digits {7,1,2,9}
T4-delete: digit 8 template 40349 cannot form Template[4] with digits {8,1,5,9}
T4-delete: digit 9 template 2064 cannot form Template[4] with digits {9,1,2,4}
T4-delete: digit 9 template 2352 cannot form Template[4] with digits {9,1,2,6}
T4-delete: digit 9 template 2359 cannot form Template[4] with digits {9,1,5,8}
T4-delete: digit 9 template 2527 cannot form Template[4] with digits {9,1,2,3}
T4-delete: digit 9 template 2928 cannot form Template[4] with digits {9,1,2,7}
T4-delete: digit 9 template 2929 cannot form Template[4] with digits {9,1,2,3}
T4-delete: digit 9 template 2930 cannot form Template[4] with digits {9,1,2,3}
T4-delete: digit 9 template 8067 cannot form Template[4] with digits {9,2,5,7}
T4-delete: digit 9 template 22106 cannot form Template[4] with digits {9,1,2,3}
T4-delete: digit 9 template 22107 cannot form Template[4] with digits {9,1,2,3}
T4-delete: digit 9 template 22185 cannot form Template[4] with digits {9,1,2,3}
T4-delete: digit 9 template 22187 cannot form Template[4] with digits {9,1,2,5}
T4-delete: digit 9 template 22394 cannot form Template[4] with digits {9,1,2,3}
T4-delete: digit 9 template 22395 cannot form Template[4] with digits {9,1,2,3}
T4-delete: digit 9 template 22970 cannot form Template[4] with digits {9,1,2,3}
T4-delete: digit 9 template 22974 cannot form Template[4] with digits {9,1,2,3}
T4-delete: digit 9 template 23258 cannot form Template[4] with digits {9,1,2,3}
T4-delete: digit 9 template 23262 cannot form Template[4] with digits {9,1,2,3}
T4-delete: digit 9 template 23263 cannot form Template[4] with digits {9,1,2,3}
T4-delete: digit 9 template 23618 cannot form Template[4] with digits {9,1,2,3}
T4-delete: digit 9 template 23619 cannot form Template[4] with digits {9,1,5,7}
T4-delete: digit 9 template 28159 cannot form Template[4] with digits {9,2,3,5}
T4-delete: digit 9 template 28447 cannot form Template[4] with digits {9,1,2,3}
T4-delete: digit 9 template 32258 cannot form Template[4] with digits {9,1,2,3}
T4-delete: digit 9 template 35472 cannot form Template[4] with digits {9,1,2,7}
T4-delete: digit 9 template 37658 cannot form Template[4] with digits {9,1,2,3}
T4-delete: digit 9 template 37659 cannot form Template[4] with digits {9,1,2,3}
T4-delete: digit 9 template 38522 cannot form Template[4] with digits {9,1,2,3}
T4-delete: digit 9 template 38526 cannot form Template[4] with digits {9,1,2,3}
T4-delete: digit 9 template 42633 cannot form Template[4] with digits {9,1,2,3}
T4-delete: digit 9 template 42635 cannot form Template[4] with digits {9,1,2,4}
T4-delete: digit 9 template 42842 cannot form Template[4] with digits {9,1,2,3}
T4-delete: digit 9 template 42843 cannot form Template[4] with digits {9,1,2,3}
T4-delete: digit 9 template 43706 cannot form Template[4] with digits {9,1,2,3}
T4-delete: digit 9 template 43707 cannot form Template[4] with digits {9,1,2,3}
T4-delete: digit 9 template 43710 cannot form Template[4] with digits {9,1,2,3}
T4-delete: digit 9 template 43711 cannot form Template[4] with digits {9,1,2,3}
T4-delete: digit 9 template 43998 cannot form Template[4] with digits {9,1,2,6}
T4-delete: digit 9 template 43999 cannot form Template[4] with digits {9,1,2,3}
T4-delete: digit 9 template 45840 cannot form Template[4] with digits {9,1,2,5}
T4-delete: digit 9 template 45841 cannot form Template[4] with digits {9,1,5,8}
T4-delete: digit 9 template 45847 cannot form Template[4] with digits {9,1,5,8}
T4-delete: digit 9 template 45851 cannot form Template[4] with digits {9,1,2,3}
T4-delete: digit 9 template 46015 cannot form Template[4] with digits {9,1,2,3}
FOUND HIDDEN-SUBSET: digits=3 cells=r3c4 sector=19 size=1
  -> eliminate digit 4 templates={31104, 31105, 31128, 31129, 31140, 31141, 36288, 36289, 36301, 36312, 36313, 41472, 41484, 41485, 41496, 41497}
  -> eliminate digit 7 templates={33069, 43485}
FOUND HIDDEN-SUBSET: digits=7 cells=r2c3 sector=18 size=1
  -> eliminate digit 1 templates={17467}
FOUND HIDDEN-SUBSET: digits=9 cells=r6c8 sector=23 size=1
  -> eliminate digit 4 templates={16135, 16147, 31404, 31692}
  -> eliminate digit 8 templates={35153, 35236, 35237, 35285}
FOUND HIDDEN-SUBSET: digits=1,2 cells=r5c89 sector=23 size=2
  -> eliminate digit 4 templates={16165, 26533, 31704, 31705, 31710, 31716, 31717, 31722}
  -> eliminate digit 8 templates={35165, 35260, 35261, 35309}
FOUND HIDDEN-SUBSET: digits=2,9 cells=r18c2 sector=10 size=2
  -> eliminate digit 3 templates={14104}
  -> eliminate digit 6 templates={10240, 10258}
  -> eliminate digit 8 templates={40420, 40444}
FOUND HIDDEN-SUBSET: digits=2,9 cells=r39c5 sector=13 size=2
  -> eliminate digit 1 templates={1813}
  -> eliminate digit 4 templates={15853, 16141, 26233, 26521, 36600, 36889, 42073}
FOUND HIDDEN-SUBSET: digits=2,9 cells=r4c13 sector=21 size=2
  -> eliminate digit 1 templates={72, 84, 85, 1806, 1818}
  -> eliminate digit 5 templates={342, 354, 2082, 38934, 38946, 40674}
FOUND HIDDEN-SUBSET: digits=3,5 cells=r3c48 sector=2 size=2
  -> eliminate digit 4 templates={15840, 15841, 15852, 15864, 15865, 26220, 26232, 26238}
FOUND HIDDEN-SUBSET: digits=3,5 cells=r7c16 sector=6 size=2
  -> eliminate digit 1 templates={21722, 21735}
  -> eliminate digit 9 templates={8066}
FOUND HIDDEN-SUBSET: digits=3,5 cells=r8c37 sector=7 size=2
  -> eliminate digit 2 templates={8096}
  -> eliminate digit 7 templates={18141, 28479, 44031}
FOUND HIDDEN-SUBSET: digits=3,5 cells=r57c1 sector=9 size=2
  -> eliminate digit 8 templates={40421, 40469, 40517}
FOUND HIDDEN-SUBSET: digits=3,5 cells=r34c4 sector=12 size=2
  -> eliminate digit 8 templates={40445}
FOUND HIDDEN-SUBSET: digits=3,5 cells=b2p27 sector=19 size=2
  -> eliminate digit 1 templates={21783}
  -> eliminate digit 4 templates={21336}
FOUND HIDDEN-SUBSET: digits=3,5 cells=r79c6 sector=25 size=2
  -> eliminate digit 4 templates={16129, 16153}
FOUND HIDDEN-SUBSET: digits=3,6 cells=r19c6 sector=14 size=2
  -> eliminate digit 4 templates={26508, 26526}
FOUND HIDDEN-SUBSET: digits=3,7 cells=r5c25 sector=4 size=2
  -> eliminate digit 4 templates={16128, 42060}
FOUND HIDDEN-SUBSET: digits=3,7 cells=r36c4 sector=12 size=2
  -> eliminate digit 4 templates={36888}
FOUND HIDDEN-SUBSET: digits=3,7 cells=r39c6 sector=14 size=2
  -> eliminate digit 4 templates={36894, 42078}
FOUND HIDDEN-SUBSET: digits=3,9 cells=r7c17 sector=6 size=2
  -> eliminate digit 2 templates={44158}
FOUND HIDDEN-SUBSET: digits=4,5 cells=r5c17 sector=4 size=2
  -> eliminate digit 6 templates={30706}
  -> eliminate digit 8 templates={40493}
FOUND HIDDEN-SUBSET: digits=4,5 cells=r16c5 sector=13 size=2
  -> eliminate digit 3 templates={14077}
FOUND HIDDEN-SUBSET: digits=4,5 cells=r3c89 sector=20 size=2
  -> eliminate digit 9 templates={2362}
 POM:  (10409.3377ms):

[denis_berthier]

OK, so "Subset" does mean "Subset". As Subsets are totally irrelevant here, I had some doubts.

..3......4...8..36..8...1...4..6..73...9..........2..5..4.7..686........7..6..5..
a hand full of the "t3" grids like this one report as t4.

I confirm this puzzle is in T3 (regardless of using Subsets or not).
This shows your code is not correct.
If this can help, here's a small part of my solution. I can't publish the full details: like any T&E-ish solution, it's very long.

Code: Select all

entering level T1 with <Fact-3723>
candidate in no template[1] for digit 8 ==> r6c2≠8
candidate in no template[1] for digit 6 ==> r6c2≠6
candidate in no template[1] for digit 8 ==> r5c2≠8
candidate in no template[1] for digit 6 ==> r5c2≠6
The 4 can be replaced by whips[1].

entering level T2 with <Fact-4697>
entering level T3 with <Fact-145330>
retracting template[2]: (n7c962834571, n9c176348259) incompatible with all the templates[1] for digit 6
retracting template[2]: (n7c962834571, n9c176348295) incompatible with all the templates[1] for digit 6
retracting template[2]: (n4c419267358, n9c176348295) incompatible with all the templates[1] for digit 7
retracting template[2]: (n4c519267348, n9c176348295) incompatible with all the templates[1] for digit 7
retracting template[2]: (n7c962834571, n9c275148639) incompatible with all the templates[1] for digit 6
retracting template[2]: (n7c962834571, n9c275148693) incompatible with all the templates[1] for digit 6
retracting template[2]: (n7c962834571, n9c275348169) incompatible with all the templates[1] for digit 6
lots of other templates[2] get retracted before anything happens to another template[1]:
...
retracting template[2]: (n4c916284375, n9c861347259) incompatible with all the templates[1] for digit 6
retracting template[2]: (n4c916284375, n6c692537814) incompatible with all the templates[1] for digit 7
retracting template[1]: (n4c916284375) incompatible with all the templates[1] for digit 6
...

.

[StrmCkr]

thanks, "thinking out loud here"

i believe my bug is subtle:

if this is how it should operate:

T1 list : {a,b}
T2{x}-> T1{a} union T{b} : check if T2(x) { a,b} if it has 1 representation for each combination set for [0,1,2,3,4,5,6,7,8] - [A,B] = pass | fail
T2{y}-> T1{a} union T{c} : check if T2(y) { a,c} if it has 1 representation for each combination set for [0,1,2,3,4,5,6,7,8] - [A,C] = pass | fail

T2 list: {x,y}
T3{z}-> union of T2{x} union T2{y} check if T3{ a,b,c} if it has 1 representation for each combination set for [0,1,2,3,4,5,6,7,8] - [A,B,C] = pass | fail

my actual code :
takes digits T{3}: {a,b,c} : if it has 1 representation for each combination set for [0,1,2,3,4,5,6,7,8] - [A,B,C] = pass |fail

which doesn't account for the fact T2{x,y} x | y could have failed on its own ... eg x invalidated as digit C has no representation. ... or y is invalid as digit B has no representation.
this check would skip checking digits A,B,C as it is "one" representation of the three digits. {false positive}

--- logical ? .. probably not...