The source is in this thread
http://forum.enjoysudoku.com/challenging-puzzle-2602-2-t46664.html
From my last update of the file of potential hardest puzzles, this expanded puzzle
.2.45..894...8923..89.3...42..34..98.9..1842..48.9.3...3.8..9.28.29.3.4.97..2.8.3
2889161802 QEUMCpopAAjLJ5 42 111
had a surprisingly high rating for 42 clues.
In fact, the digits 1567 have only 3 clues and are responsible for most of the rating.
In this thread, we study the solution grid to see how we can find directly such patterns and puzzles with high ratings.
This search uses intensively unavoidable sets (UA).
The minimum to have a puzzle with 3 given for 4 digits is that each pair of the 4 digits has only one UA of size 18.
In the solution grid 2889161802
123456789457189236689732154261347598395618427748295361534861972812973645976524813
this is possible for digits 1567 and 1579. Both will be studied, but we start with 1567, the digits of our example.
My UAs builder DLL finds 1833 UAs as start for the solution grid
Potential n digits end in solution grid 2889161802
18 posts
• Page 1 of 2 • 1, 2
Potential n digits end in solution grid 2889161802
by champagne » Thu Mar 19, 2026 10:42 am
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Potential hardest status for the solution grid
by champagne » Thu Mar 19, 2026 10:45 am
In the update 2603 of the potential hardest, we have 6942 records for the solution grid.
All have the 1567 4 digits pattern, and all are rating skfr 11.1
5 1 7
...45....4....92...8.......2..34...8.9..1.42...8...3.....8..9....29.3.4.97....8.3
All have the same 3 clues for the 1567 digits.
More will come here later if something of interest comes
All have the 1567 4 digits pattern, and all are rating skfr 11.1
5 1 7
...45....4....92...8.......2..34...8.9..1.42...8...3.....8..9....29.3.4.97....8.3
All have the same 3 clues for the 1567 digits.
More will come here later if something of interest comes
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Pattern 1567
by champagne » Thu Mar 19, 2026 10:51 am
For these 4 digits, we find the 6 UAs of the minimal condition
In the process the UAs (1833 at the start) are spilt in three tables
Field the UA is a subset of “field UA”
Infield the UA has a hit in “field UA”
Outfield the UA has no hit in “field UA”
May be a key point to explain what comes later, in this 1567 pattern, the first table contains only the 6 compulsory UAs.
The first step of the process, in the mood of the strategy “divide and conquer” of “blue”, is to find the 3 clues.
This gives 4*9*9*9 =2916 possibilities.
The first test is to see if adding all clues “outfield” we have a valid puzzle. This is always 45+3= 48 clues.
The 2916 solution are valid, So we don’t need any additional UA. This is far from the standard. In the 5 digit example, we will finish with more than 2000 "field" UAs.
The skfr rating of the 48 clues puzzles goes from ‘very easy’ 1.5 to ‘still very hard’ 10.1.
For the puzzles of the potential hardest file, all have the same expanded 48 clues skfr 9.5/9.5/2.8
The significant number of puzzles having a high 48 clues rating pushed me to test a big sample of minimal puzzles.
I got an amazing 50 million puzzles rating 10.2 10.3, but never above. The “good 3 clues” was not in my sample.
The next test will be done in the vicinity of the existing 11.1 set. Likely a common property explains the higher rating, but this has to be understood.
- Code: Select all
123456789457189236689732154261347598395618427748295361534861972812973645976524813
1...1.....1.1...........11...1...1....1.1.........1..11....1....1......1...1...1. 0
1....1......1....11.....1...11.........11...........11....11....1....1....1....1. 1
1.....1....11........1..1....1..1.......1...11.......1.....1.1..1..1.....1.....1. 2
....11....1......11......1..1....1....11..........1.1.1...1..........1.1..11..... 3
....1.1...11.........1...1......11....1.....11....1...1......1.....1...1.1.1..... 4
.....11....1.....11..1......1...1......1....11......1.....1..1.....1.1...11...... 5
Giving a full UA for the 4 digits
1...111...111....11..1..11..11..11....111...11....1.111...11.1..1..1.1.1.111...1. “field UA”
In the process the UAs (1833 at the start) are spilt in three tables
Field the UA is a subset of “field UA”
Infield the UA has a hit in “field UA”
Outfield the UA has no hit in “field UA”
May be a key point to explain what comes later, in this 1567 pattern, the first table contains only the 6 compulsory UAs.
The first step of the process, in the mood of the strategy “divide and conquer” of “blue”, is to find the 3 clues.
This gives 4*9*9*9 =2916 possibilities.
The first test is to see if adding all clues “outfield” we have a valid puzzle. This is always 45+3= 48 clues.
The 2916 solution are valid, So we don’t need any additional UA. This is far from the standard. In the 5 digit example, we will finish with more than 2000 "field" UAs.
The skfr rating of the 48 clues puzzles goes from ‘very easy’ 1.5 to ‘still very hard’ 10.1.
For the puzzles of the potential hardest file, all have the same expanded 48 clues skfr 9.5/9.5/2.8
The significant number of puzzles having a high 48 clues rating pushed me to test a big sample of minimal puzzles.
I got an amazing 50 million puzzles rating 10.2 10.3, but never above. The “good 3 clues” was not in my sample.
The next test will be done in the vicinity of the existing 11.1 set. Likely a common property explains the higher rating, but this has to be understood.
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Where can be seen this pattern.
by champagne » Thu Mar 19, 2026 4:14 pm
This is a side point, but interesting to consider. With the TH threat, it seems that the vicinity can produce plenty of solution grids.
I wanted to see if this would be true with a vicinity keeping untouched the 4 digits pattern. If such a solution grid exists, it must be (or can be morphed) in the min lexical catalog.
As it is a min lexical solution grid. In other grids of the catalog, the pattern will share these cells
The first band can only one of four
“12345678945” +
57 "7189236689723154",
62 "7189236689732154",
86 "7189236698723154",
90 "7189236698732154",
The four bands have common cells,
We also have some constraints in column 1 -> r5c1=3 r89c1=89
so the common ED pattern in the solution grids is
with a single 3r7c2
for each of the four valid band 1, we have a smal number of possible fills
eg, with our band1 1 62 index 61
we can not expect many valid fils with such a pattern.
Anecdotic, but...
the next solution grid 2889161803 has also a high rating 1567 in the database
but the pattern 1567 is not the same
I wanted to see if this would be true with a vicinity keeping untouched the 4 digits pattern. If such a solution grid exists, it must be (or can be morphed) in the min lexical catalog.
As it is a min lexical solution grid. In other grids of the catalog, the pattern will share these cells
- Code: Select all
123456789
457189..6
6..7..15.
261..75..
..561...7
7....5.61
5...61.7.
.1..7.6.5
.765...1.
The first band can only one of four
“12345678945” +
57 "7189236689723154",
62 "7189236689732154",
86 "7189236698723154",
90 "7189236698732154",
The four bands have common cells,
We also have some constraints in column 1 -> r5c1=3 r89c1=89
so the common ED pattern in the solution grids is
- Code: Select all
123 456 789
457 189 236
6.. 7.. 154
261 ..7 5..
3.5 61. ..7
7.. ..5 .61
5.. .61 .7.
81. .7. 6.5
976 5.. .1.
with a single 3r7c2
for each of the four valid band 1, we have a smal number of possible fills
eg, with our band1 1 62 index 61
- Code: Select all
123 456 789
457 189 236
689 732 154
261 ..7 5..
3.5 61. .27
7.8 ..5 .61
53. .61 .7.
81. .7. 6.5
976 5.. .1.
we can not expect many valid fils with such a pattern.
Anecdotic, but...
the next solution grid 2889161803 has also a high rating 1567 in the database
- Code: Select all
123 456 789
457 189 236
689 732 154
261 347 598
395 618 427
748 295 361
534 961 872
876 524 913
912 873 645 1...111.. has 6 pairs
but the pattern 1567 is not the same
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infield assignments
by champagne » Fri Mar 20, 2026 7:26 am
Once the three digit of the field assigned, all UAs "infield" are reduced to the "outfield digits".
We must clear first all UAs hit by the 3 digits, so, the list is different for each triplet.
To see what can happen, here is the table "in field" reduced to the other digits and limited to the UAs with no subset.
the infield table has here most of the UAs 1748 out of 1833. The reduced table has only 142 UAs with no subset, the biggest with 10 cells.
Many UAs have now 2/3 cells as we can see with the first UAs of the table
such UAs will be assigned first, but this remains likely above 1 million possibilities per triplet if the target is 23/26 cells.
As we don't look for an exhaustive search, triplet having a low potential (easy to solve with 48 clues) can be ignored.
The last table, "out field" has only UAs >=4 clues. It can be merged with this one if a reordering is done after 10 assignments.
I am drafting the code to do that, with a priority to get results in the vicinity of the known area. The nex post on the 1567 4 digits pattern is expected next week;
We must clear first all UAs hit by the 3 digits, so, the list is different for each triplet.
To see what can happen, here is the table "in field" reduced to the other digits and limited to the UAs with no subset.
the infield table has here most of the UAs 1748 out of 1833. The reduced table has only 142 UAs with no subset, the biggest with 10 cells.
Many UAs have now 2/3 cells as we can see with the first UAs of the table
Hidden Text: Show
such UAs will be assigned first, but this remains likely above 1 million possibilities per triplet if the target is 23/26 cells.
As we don't look for an exhaustive search, triplet having a low potential (easy to solve with 48 clues) can be ignored.
The last table, "out field" has only UAs >=4 clues. It can be merged with this one if a reordering is done after 10 assignments.
I am drafting the code to do that, with a priority to get results in the vicinity of the known area. The nex post on the 1567 4 digits pattern is expected next week;
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Re: Potential n digits end in solution grid 2889161802
by champagne » Tue Mar 24, 2026 1:53 pm
I checked the results from about one third of the puzzles in the output of the UAs expansion with the pattern of known high ratings.
I got plenty of puzzles rating skfr 10.5 or 11.1
No other rating so far with the cutoff of the potential hardest database.
Most of the puzzles are not minimal, and all minimal rating 11.1 are known.
The 10.5/1.2/1.2 rating was out of the the cutoff for the old database, so we can think that the known puzzles have been seen long ago.
I continue the rating of the output for this test, but it is clear that I have to clear all non minimal puzzle from the output.
I got plenty of puzzles rating skfr 10.5 or 11.1
No other rating so far with the cutoff of the potential hardest database.
Most of the puzzles are not minimal, and all minimal rating 11.1 are known.
The 10.5/1.2/1.2 rating was out of the the cutoff for the old database, so we can think that the known puzzles have been seen long ago.
I continue the rating of the output for this test, but it is clear that I have to clear all non minimal puzzle from the output.
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Re: Potential n digits end in solution grid 2889161802
by coloin » Wed Mar 25, 2026 5:10 pm
My crude way of confirming the scale of the exercise !
there were 2590 ED ways to fill in 3 clues ....
of which these were top
taking the first expanded puzzle , non-TH [?] as the 3 extra clues are in more than one box
there were 507143 ED minimal puzzles [ all ED=10.1 or better]
expanding these gave only 6 puzzles .... non spectacular though
I am not sure how similar your process is ....and maybe there is scope to process somehow the 2590 ways to insert the 3 clues...
- Code: Select all
5 1 7
.2.4...894...8923..89.3...42..34..9839...842..4829.3...348..9.28.29.3.4.9...248.3
+---+---+---+
|.2.|4..|.89|
|4..|.89|23.|
|.89|.3.|..4|
+---+---+---+
|2..|34.|.98|
|39.|..8|42.|
|.48|29.|3..|
+---+---+---+
|.34|8..|9.2|
|8.2|9.3|.4.|
|9..|.24|8.3|
+---+---+---+ the 5-template 23489
has 24 solutions /// 1 ED solution [24 [4*3*2*1] ways to have 1567] [1=5=6=7]
there were 2590 ED ways to fill in 3 clues ....
of which these were top
- Code: Select all
.2.45..894...8923..8913...42.734..9839...842..4829.3...348..9.28.29.3.4.9...248.3 ED=10.1/1.2/1.2
.2.45..894...8923..89.3...42..34..9839..1842..4829.3...3487.9.28.29.3.4.9...248.3 ED=10.1/1.0/1.0
.2.45..894...8923..89.3...42..34..9839..1842..4829.3...348..9.28.2973.4.9...248.3 ED=10.1/1.0/1.0
.2.45..894...8923..89.3...42..34..9839...842..4829.3...3481.9.28.2973.4.9...248.3 ED=10.1/1.0/1.0
.2.4...894...8923..89.3...42..34..9839..1842..4829.3...3485.9.28.2973.4.9...248.3 ED=10.1/1.0/1.0
.2.4...894...8923..89.3...42..34..9839...842..4829.3.1.348..9.28.29.3.4.957.248.3 ED=9.5/1.2/1.2
.2.45..894...8923..89.3...42..34..9839..1842..4829.3...348..9.28.29.3.4.97..248.3 ED=9.5/1.2/1.2 ## original puzzle
.2.45..894...8923..89.3...42..34..9839...842..4829.3.1.348..9.28.29.3.4.97..248.3 ED=9.3/1.2/1.2
.2.45..894...8923..89.3...42..34..9839...842..4829.3...3481.9728.29.3.4.9...248.3 ED=9.3/1.2/1.2
.2.45..894...8923..89.3...42..34..9839...842..4829.3...3481.9.28.29.3.4.97..248.3 ED=9.3/1.2/1.2
.2.4...8941..8923..89.3...42..34..9839...842..4829.3...348579.28.29.3.4.9...248.3 ED=9.3/1.2/1.2
.2.4...8941..8923..89.3...42..34..9839...842..4829.3...3485.9728.29.3.4.9...248.3 ED=9.3/1.2/1.2
.2.4...8941..8923..89.3...42..34..9839...842..4829.3...348.59728.29.3.4.9...248.3 ED=9.3/1.2/1.2
.2.4...894...8923..89.3..142.534..9839...842..4829.3...348..9728.29.3.4.9...248.3 ED=9.3/1.2/1.2
.2.4...894...8923..89.3..142..34..9839...842..4829.35..348..9.28729.3.4.9...248.3 ED=9.3/1.2/1.2
.2.4...894...8923..89.3..142..34..9839...842..4829.35..348..9.28.2973.4.9...248.3 ED=9.3/1.2/1.2
.2.4...894...8923..89.3..142..34..9839...842..4829.35..348..9.28.29.3.4.9...24873 ED=9.3/1.0/1.0
.2.4...894...8923..89.3..142..34..9839...842..4829.3...348..9.2852973.4.9...248.3 ED=9.3/1.2/1.2
.2.4...894...8923..89.3...42.134..9839...842..4829.3...3485.9728.29.3.4.9...248.3 ED=9.3/1.2/1.2
.2.4...894...8923..89.3...42..34..9839...842..4829.35..348..9128.29.3.4.9...24873 ED=9.3/1.0/1.0
.2.4...894...8923..89.3...42..34..9839...842..4829.35..348..9.2812973.4.9...248.3 ED=9.3/1.2/1.2
.2.4...894...8923..89.3...42..34..9839...842..4829.3..1348579.28.29.3.4.9...248.3 ED=9.3/1.0/1.0
.2.4...894...8923..89.3...42..34..9839...842..4829.3..13485.9728.29.3.4.9...248.3 ED=9.3/1.0/1.0
.2.4...894...8923..89.3...42..34..9839...842..4829.3..1348.59728.29.3.4.9...248.3 ED=9.3/1.0/1.0
taking the first expanded puzzle , non-TH [?] as the 3 extra clues are in more than one box
- Code: Select all
.2.45..894...8923..8913...42.734..9839...842..4829.3...348..9.28.29.3.4.9...248.3 ED=10.1/1.2/1.2
there were 507143 ED minimal puzzles [ all ED=10.1 or better]
expanding these gave only 6 puzzles .... non spectacular though
- Code: Select all
.2345..894...8923..89132..42.734..9839...842..4829.3...3.8..9.28.29.3.4.9...2.8.3 ED=10.2/10.2/8.0
.2345..894...8923..89132..42.734..9839...842..4829.3...348..9.28.29.3.4.9...248.3 ED=10.1/10.1/7.8
.2345..894...8923..89132..42.734..9839...842..4829.3...3.8..9..8..9.3.4.9...2.8.3 ED=10.2/10.2/7.8
.2.45..894...8923..89132..42.734..98.9...842..4829.3...348..9.28.29.3.4.9...248.3 ED=10.2/10.2/7.9
.2.45..894...8923..89132..42.734..98.9...842..4829.3...3.8..9.28.29.3.4.9...2.8.3 ED=10.2/10.2/8.0
.2345..894...8923..891....42.734..9839...842..4829.3...348..9..8.29...4.9....48.. ED=10.2/10.2/3.0
I am not sure how similar your process is ....and maybe there is scope to process somehow the 2590 ways to insert the 3 clues...
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Re: Potential n digits end in solution grid 2889161802
by champagne » Thu Mar 26, 2026 7:41 am
Hi coloin,
some comments on your last post.
First, to clarify, my reference in the thread is this start
with this 45+3 clues corresponding puzzle (skfr rating)
_____________________________
For sure, this solution grid is special.
In theory, with only 6 UAs in the 1567 field, we have all ways valid to fill the PM
4x9x9x9 = 2916 clues.
I got all of them valid with a rating from very easy (1.5) to hard (10.1)
As my code is based on UAs expansion, I got them doing it in the set of UAs having only the digits 1567.
I am missing here the start of the expansion several rows here have more than 4 missing clues...
.2345..89
4...8923.
.89132..4
2.734..98
39...842.
.4829.3..
.3.8..9.2
8.29.3.4.
9...2.8.3 ED=10.2/10.2/8.0
so I skip this point
In fact, I would like to see if this amazing pattern can be seen in other solution grids.
The rating 11.1 seems on come with the triplet 167 of the example and the database apparently has all the 11.1, what I am trying to establish.
From my estimate, 70% of the solution grids have a potential for a 4 digits pattern and 8% a potential for a 5 digits pattern.
In my draft, I first build all the UAs table delivered by My DLL. This is about 150-180 milliseconds oper solution grid.
In fact, to see if we have a potential and check the 2916 triplets, we only need UAs of all pairs of digits, what is done in some microseconds.
Another quick way to start the search is to use the 320K minimal of the potential hardest data base showing a potential for a 4 digits end, but I would like to search new areas.
Any way, I have first to finish my draft of code. Is missing the filter for non minimal puzzles.
BTW, with a list of UAs, a puzzle is minimal if each clue is the only hit on one UA of the list. This is a fast way to check it when you have the list of UAs
some comments on your last post.
First, to clarify, my reference in the thread is this start
- Code: Select all
.2.45..894...8923.........42..34........18.2...8.......3....9.28..9.3.4.97..2...3;2889161802;QEU0C3mY02DLJ4;29;111;0;0;1567
with this 45+3 clues corresponding puzzle (skfr rating)
- Code: Select all
.2345..894...8923..89.32..42..34..9839..1842..4829.3...348..9.28.29.3.4.97..248.3 ED=9.5/9.5/2.8
_____________________________
For sure, this solution grid is special.
coloin wrote:My crude way of confirming the scale of the exercise !
there were 2590 ED ways to fill in 3 clues ....
In theory, with only 6 UAs in the 1567 field, we have all ways valid to fill the PM
4x9x9x9 = 2916 clues.
I got all of them valid with a rating from very easy (1.5) to hard (10.1)
As my code is based on UAs expansion, I got them doing it in the set of UAs having only the digits 1567.
coloin wrote:expanding these gave only 6 puzzles .... non spectacular though
.2345..894...8923..89132..42.734..9839...842..4829.3...3.8..9.28.29.3.4.9...2.8.3 ED=10.2/10.2/8.0
I am missing here the start of the expansion several rows here have more than 4 missing clues...
.2345..89
4...8923.
.89132..4
2.734..98
39...842.
.4829.3..
.3.8..9.2
8.29.3.4.
9...2.8.3 ED=10.2/10.2/8.0
so I skip this point
coloin wrote:I am not sure how similar your process is ....and maybe there is scope to process somehow the 2590 ways to insert the 3 clues...
In fact, I would like to see if this amazing pattern can be seen in other solution grids.
The rating 11.1 seems on come with the triplet 167 of the example and the database apparently has all the 11.1, what I am trying to establish.
From my estimate, 70% of the solution grids have a potential for a 4 digits pattern and 8% a potential for a 5 digits pattern.
In my draft, I first build all the UAs table delivered by My DLL. This is about 150-180 milliseconds oper solution grid.
In fact, to see if we have a potential and check the 2916 triplets, we only need UAs of all pairs of digits, what is done in some microseconds.
Another quick way to start the search is to use the 320K minimal of the potential hardest data base showing a potential for a 4 digits end, but I would like to search new areas.
Any way, I have first to finish my draft of code. Is missing the filter for non minimal puzzles.
BTW, with a list of UAs, a puzzle is minimal if each clue is the only hit on one UA of the list. This is a fast way to check it when you have the list of UAs
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Re: Potential n digits end in solution grid 2889161802
by coloin » Thu Mar 26, 2026 11:16 am
yeah .. I didnt start the process with the full 45 plus 3 clues....however on repeat I got 2519 ways to add the 3 clues .. which means that my program misses a few !!
the figure 2916 looks correct ... 36 x 27 x 18 / 6 .... all ways to add 3 different clues hits all the UAs / solves the puzzle.
What surprized me was that all the 0.5M+ minimal puzzles tend to expand to nearly the 45plus3 clues... except for the ? few which dont and have the 11.1 rating...
Of note about 12.6% of all 4-templates solve with 3 clues ..... would have to check a few to see how common the 1 ED completion [as here] is ....
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Re: Potential n digits end in solution grid 2889161802
by blue » Thu Mar 26, 2026 10:08 pm
coloin wrote:Of note about 12.6% of all 4-templates solve with 3 clues .....
And >99.8% of grids have at least one such 4-template.
This one has seven: 1259, 1567, 1579, 2348, 2349, 3678, and 4579.
coloin wrote:would have to check a few to see how common the 1 ED completion [as here] is ....
"1 ED completion" ?
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Re: Potential n digits end in solution grid 2889161802
by coloin » Thu Mar 26, 2026 11:35 pm
blue wrote:"1 ED completion" ?
Good to see you on this..
- Code: Select all
+---+---+---+
|.23|4..|.89|
|4..|.89|23.|
|.89|.32|..4|
+---+---+---+
|2..|34.|.98|
|39.|..8|42.|
|.48|29.|3..|
+---+---+---+
|.34|8..|9.2|
|8.2|9.3|.4.|
|9..|.24|8.3|
+---+---+---+ 24 sol.
The 5-template here with the associated 4-template spaces... is solved with 3 clues.
The 5-template sub puzzle has 24 sol [4*3*2*1] .... but only 1 ED solution ....
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- Joined: 05 May 2005
- Location: Devon
Re: Potential n digits end in solution grid 2889161802
by coloin » Fri Mar 27, 2026 12:06 am
Semi-random 5-template... with associated 4-rookery spaces [?]
- Code: Select all
+---+---+---+
|.21|.56|.8.|
|.5.|18.|2.6|
|86.|2..|.15|
+---+---+---+
|28.|.15|.6.|
|...|862|5.1|
|615|...|82.|
+---+---+---+
|5.2|6.8|1..|
|..6|.21|.58|
|1.8|5..|6.2|
+---+---+---+ 1104 sol
- Code: Select all
421.56.8..5.18.2.686.2...1528..15.6...38625.1615.7.82.5.26.81....6.21.581.85..6.2
421.56.8..5.18.2.686.2...1528..15.6...38625.1615...82.5.26.81....6.21.581785..6.2
.21356.8..5.18.2.686.2...1528..15.6....8625.1615..482.5.26.81.7..6.21.581.85..6.2
.21.56.8.35.18.2.686.2...15284.15.6....8625.1615.7.82.5.26.81....6.21.581.85..6.2
.21.56.8.35.18.2.686.2...15284.15.6....8625.1615...82.5.26.81....6.21.581785..6.2
.21.56.8.35.18.2.686.2...1528..15.6....862541615.7.82.5.26.81....6.21.581.85..6.2
.21.56.8.35.18.2.686.2...1528..15.6....862541615...82.5.26.81....6.21.581785..6.2
.21.56.8..5.18.2.686.23..1528..15.6....8625.1615...82.5.26.81.4..6.21.581.85.76.2
.21.56.8..5.18.2.686.2...1528..15.6...38625.1615...82.5426.81....6.217581.85..6.2
.21.56.8..5.18.2.686.2...1528..15.6...38625.1615...82.5.26481....6.21.581.85..672
.21.56.8..5.18.2.686.2...1528..15.6...38625.1615...82.5.26.81....6421.581785..6.2
.21.56.8..5.18.2.686.2...1528..15.6....8625.1615.4.82.5.26.81.3..6721.581.85..6.2
- coloin
- Posts: 2670
- Joined: 05 May 2005
- Location: Devon
Re: Potential n digits end in solution grid 2889161802
by blue » Fri Mar 27, 2026 6:04 am
coloin wrote:blue wrote:"1 ED completion" ?
Good to see you on this..
- Code: Select all
+---+---+---+
|.23|4..|.89|
|4..|.89|23.|
|.89|.32|..4|
+---+---+---+
|2..|34.|.98|
|39.|..8|42.|
|.48|29.|3..|
+---+---+---+
|.34|8..|9.2|
|8.2|9.3|.4.|
|9..|.24|8.3|
+---+---+---+ 24 sol.
The 5-template here with the associated 4-template spaces... is solved with 3 clues.
The 5-template sub puzzle has 24 sol [4*3*2*1] .... but only 1 ED solution ....
I see.
Of note about 12.6% of all 4-templates solve with 3 clues ..... would have to check a few to see how common the 1 ED completion [as here] is ....
There are only 759 of them -- 4-rookeries with 24 "1234" solutions, differing by relabelling only.
- blue
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- Joined: 11 March 2013
Re: Potential n digits end in solution grid 2889161802
by champagne » Fri Mar 27, 2026 6:45 am
blue wrote:coloin wrote:Of note about 12.6% of all 4-templates solve with 3 clues .....
And >99.8% of grids have at least one such 4-template.
This one has seven: 1259, 1567, 1579, 2348, 2349, 3678, and 4579.
Hi "blue",
With my constraint to have all pairs of digits with only one UA, I have only 2 of the seven (1567 1579) and my estimate was about 70% of the grids with such a pattern.
Do you have high ratings with a "45 + 3 clues" puzzle with other 4 digits?
note : my estimate for a 5 digits with the same constraint is that it can be seen in about 8% of the solution grids.
As this is a 'software' chapter, I'll post my last attempt to have a 'n' loops code performing well derived from an old code that you shared with me long ago.
- champagne
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Re: Potential n digits end in solution grid 2889161802
by champagne » Fri Mar 27, 2026 8:29 am
Here is the code used here to expand 10 clues (10 imbricated loops) after the digits of the n digits pattern.
The table of UAs has at this point plenty of very short UAs and no chance to get short in UAs.
This code is far to be optimal (no vectore ot speed up the search of the next UA ....) but seems for me easy to code, open to local special process and performing well.
This is derived of a process shared by 'blue' long ago. I tested several variants of the code in various projects, using for example the preprocessor, this seems to me better for the UA expansion.
The table of UAs has at this point plenty of very short UAs and no chance to get short in UAs.
This code is far to be optimal (no vectore ot speed up the search of the next UA ....) but seems for me easy to code, open to local special process and performing well.
This is derived of a process shared by 'blue' long ago. I tested several variants of the code in various projects, using for example the preprocessor, this seems to me better for the UA expansion.
- Code: Select all
struct SPFX2 {// getting clues in floor
BF128 ua, dead, ass;
int cell, iua, fl, fl2;
inline int Getcell() {
if (ua.isEmpty())return 0;
cell = ua.getFirstCell();
ua.Clear_c(cell);
dead.Set_c(cell);
return (this + 1)->GetinNext();
}
inline int GetinNext() {
*this = *(this - 1);
ass.Set_c(cell);
iua++;
for (iua; iua < ntnofl; iua++) {
ua = tnofl[iua];
if ((ass & ua).isNotEmpty()) continue;
ua -= dead;
return ua.isNotEmpty();
}
return 0;// no more ua should never be here
}
int NotOnPath();
}spfx2[12];
void ExpandFX2(SPFX& s) {// add 10 forced infield
register int ir;
{
assspfx= s.ass;
nasspfx = s.ass.Count();
SPFX2& s0 = spfx2[0];
memset(&s0, 0, sizeof s0);
s0.ua = tnofl[0];
}
gcl1: if (!spfx2[0].Getcell()) { return; }
gcl2: if (!(ir = spfx2[1].Getcell()))goto gcl1;
gcl3: if (!(ir = spfx2[2].Getcell()))goto gcl2;
gcl4: if (!(ir = spfx2[3].Getcell()))goto gcl3;
gcl5: if (!(ir = spfx2[4].Getcell()))goto gcl4;
gcl6: if (!(ir = spfx2[5].Getcell()))goto gcl5;
gcl7: if (!(ir = spfx2[6].Getcell()))goto gcl6;
gcl8: if (!(ir = spfx2[7].Getcell()))goto gcl7;
gcl9: if (!(ir = spfx2[8].Getcell()))goto gcl8;
gcl10: if (!(ir = spfx2[9].Getcell()))goto gcl9;
if(!IsMinimal(spfx2[10].ass))goto gcl10;
ExpandFX2B();
goto gcl10;
}
- champagne
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