## Investigation of 4 free boxes (square) patterns

Everything about Sudoku that doesn't fit in one of the other sections

### Re: Investigation of 4 free boxes (square) patterns

Hi, coloin!
coloin wrote:Your initial post was showing patterns with clues in B1245 which have puzzles. any less clues in B1245 will be a maximal pattern which doest have a puzzle.

Not quite true. Removing any clue (clues) in B1245 area will give us invalid pattern, not having valid puzzles, but that pattern may not be maximal.
For example, pattern
Code: Select all
`+-----+-----+-----+|. . .|. . .|x x x||. . .|. . .|x x x||. . .|. . .|x x x|+-----+-----+-----+|. . .|. . .|x x x||. . .|. . .|x x x||. . x|. . .|x x x|+-----+-----+-----+|x x x|x x x|x x x||x x x|x x x|x x x||x x x|x x x|x x x|+-----+-----+-----+`

is invalid, but not maximal, because we can add clue in r6c6 cell and get another invalid pattern.
Code: Select all
`+-----+-----+-----+|. . .|. . .|x x x||. . .|. . .|x x x||. . .|. . .|x x x|+-----+-----+-----+|. . .|. . .|x x x||. . .|. . .|x x x||. . x|. . x|x x x|+-----+-----+-----+|x x x|x x x|x x x||x x x|x x x|x x x||x x x|x x x|x x x|+-----+-----+-----+`

But maximal patterns are not expandable - adding 1 clue always convert maximal invalid pattern to valid pattern.
coloin wrote:... since 1 clue is needed in B124 we therefore need 2 clues in B1245 ...

2 clues in B1245 not alway guarantee validity of the pattern (see example above).

coloin wrote:Minimal patterns that have puzzles is now a new concept to me.... and indeed there is work that could be done.

Minimal patterns were introduced in the thread Minimal patterns. They have interesting property - to produce minimal puzzles only!
When we are talking about 18-clue patterns, the good examples of minimal 18-clue patterns are 18-clue vertically symmetrical patterns. (All 121 possible 18-clue vertically symmetrical patterns were found years ago.)

I should say, why I switched my attention from maximal patterns to minimal patterns. Both catalogues (of maximal/minimal patterns) are sufficient to describe classes of patterns. For example, all 6016 fully symmetrical patterns can be separated to valid/invalid patterns either by catalogue of maximal patterns (25 patterns) or by catalogue of minimal patterns (49 patterns). Filtering out invalid patterns can be done either by maximal patterns list (for example, by "40 maximal patterns list"), or by minimal patterns list, because any valid pattern must contain some minimal patterns as subsets. But I think catalogue of possible patterns is more suitable to use than catalogue of impossible patterns.

Of course, three 4-boxes partially minimal patterns (Q1, Q2 and Q3 published above in this thread) have very limited practical use. But I am planning to find 2-band (6-boxes) partially minimal patterns. 2-band patterns will be much more useful for filtering, etc.

Serg
Serg
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Location: Russia

### Re: Investigation of 4 free boxes (square) patterns

Yes that is all true, i overlooked that !
And as you say, patterns of clues can be either valid minimal or invalid [~proved impossible] maximal .

The valid minimals can be expanded with one or more clues, or expanded to a complete individual row,column or box to give various non-minimal valid patterns.
The invalid maximals can be reduced, but all the subsets will be invalid patterns

I think there may be a lot more valid minimal patterns [unfortunately] however ....
If the estimates are correct, there will be the 33,000 17C patterns, which would give approx 2M valid non-minimal 18C patterns
If there really are on average 50 puzzles per 18C pattern [40M patterns] - this would leave 38M 18C patterns which would be minimal....

Anyhow it was with great difficulty that I made these 20C puzzles ..... which almost certainly means the pattern will be minimal
Code: Select all
`........5......26.......31.......1.3.......7.84.5......8..14.....6.7....25.6....8........5......76.......31.......1.3.......2.84.5......3..14.....6.2....75.6....8........5......76.......31.......1.3.......2.84.5......3..14.....9.2....75.6....8........5......96.......31.......1.3.......2.47.5......3..14.....6.2....95.6....7........5......96.......31.......1.3.......2.48.5......3..14.....7.2....95.6....8`

Code: Select all
`+---+---+---+|...|...|..5||...|...|26.||...|...|31.|+---+---+---+|...|...|1.3||...|...|.7.||84.|5..|...|+---+---+---+|.8.|.14|...||..6|.7.|...||25.|6..|..8|+---+---+---+  20 Clues`

Code: Select all
`         Q2-A        +-----+-----+-----+ |. . .|. . .|. x x| |. . .|. . .|. x x| |. . .|. . .|. x x| +-----+-----+-----+ |. . .|. . .|x x x| |. . .|. . .|x x x| |. . x|. x x|x x x| +-----+-----+-----+ |x x x|x x x|x x x| |x x x|x x x|x x x| |x x x|x x x|x x x| +-----+-----+-----+ `

This might well therefore be a maximal invalid pattern ..?
coloin

Posts: 2004
Joined: 05 May 2005

### Re: Investigation of 4 free boxes (square) patterns

Hi, coloin!
coloin wrote:... it was with great difficulty that I made these 20C puzzles ..... which almost certainly means the pattern will be minimal
Code: Select all
`........5......26.......31.......1.3.......7.84.5......8..14.....6.7....25.6....8........5......76.......31.......1.3.......2.84.5......3..14.....6.2....75.6....8........5......76.......31.......1.3.......2.84.5......3..14.....9.2....75.6....8........5......96.......31.......1.3.......2.47.5......3..14.....6.2....95.6....7........5......96.......31.......1.3.......2.48.5......3..14.....7.2....95.6....8`

Code: Select all
`+---+---+---+|...|...|..5||...|...|26.||...|...|31.|+---+---+---+|...|...|1.3||...|...|.7.||84.|5..|...|+---+---+---+|.8.|.14|...||..6|.7.|...||25.|6..|..8|+---+---+---+  20 Clues`

Impressive work! The pattern looks like minimal, but I don't know exact answer. Now I only have a list of 26 (partially) minimal patterns of the following form.
Code: Select all
`+-----+-----+-----+|. . .|. . .|     ||. . .|. . .|  ?  ||. . .|. . .|     |+-----+-----+-----+|. . .|. . .|     ||. . .|. . x|  ?  ||. . x|. . .|     |+-----+-----+-----+|x x x|x x x|x x x||x x x|x x x|x x x||x x x|x x x|x x x|+-----+-----+-----+`

coloin wrote:
Code: Select all
`         Q2-A        +-----+-----+-----+ |. . .|. . .|. x x| |. . .|. . .|. x x| |. . .|. . .|. x x| +-----+-----+-----+ |. . .|. . .|x x x| |. . .|. . .|x x x| |. . x|. x x|x x x| +-----+-----+-----+ |x x x|x x x|x x x| |x x x|x x x|x x x| |x x x|x x x|x x x| +-----+-----+-----+ `

This might well therefore be a maximal invalid pattern ..?

I don't know at the moment - is it maximal (or even invalid) or no.

Serg
Serg
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Location: Russia

### Re: Investigation of 4 free boxes (square) patterns

"Sorry for missing the previous puzzle. This pattern is obviously valid.": Show
Could you check if this is invalid? I feel like this should be invalid.
And if this is invalid, then it's maximal.
Code: Select all
`+-----+-----+-----+|. . .|. . .|. x x||. . .|. . .|. x x||. . .|. . .|x x x|+-----+-----+-----+|. . .|. . .|x x x||. . .|. . .|x x x||x x x|x x x|x x x|+-----+-----+-----+|x x x|x x x|x x x||x x x|x x x|x x x||x x x|x x x|x x x|+-----+-----+-----+`

"a similar but valid pattern": Show
However, this pattern is valid.
Code: Select all
`+-----+-----+-----+|. . .|. . .|3 7 8||. . .|. . .|6 4 2||. . .|. . .|9 1 5|+-----+-----+-----+|. . .|. . .|. 8 9||. . .|. . .|. 2 3||1 2 3|7 8 9|4 5 6|+-----+-----+-----+|5 6 1|2 3 4|8 9 7||8 3 2|9 7 1|5 6 4||9 7 4|8 6 5|2 3 1|+-----+-----+-----+`

*I checked them using a simple generator NPGenerator, which could only make easy puzzles. I waited for 5 minutes and no output of puzzles.(there may still be easy puzzles though)
qiuyanzhe

Posts: 89
Joined: 21 August 2017
Location: China

### Re: Investigation of 4 free boxes (square) patterns

Hi, coloin and qiuyanzhe!
You asked me about particular patterns - are they maximal and minimal? I am now doing exhaustive search for partially minimal patterns having 9 clues in B7, B8 and B9 boxes (bands B123 and B456 are "free" - all box patterns configurations are permitted for these boxes). Unfortunately I have no completed program to do it, and even searching algorithm is not fixed. I am writing programs to perform search for minimal patterns for some box combinations. During such runs I usually find a bunch of patterns and go ahead. I have no possibility to check alone pattern - is it minimal or maximal. In some weeks (months) I hope to get full catalogue of "two-band free minimal patterns". Maybe some questions will be clear then. But I am not planning to search for maximal patterns now, because it could complicate the task twice.

I can advice you to do random search for interesting patterns. In my experience, it's enough to generate about 100 millions of puzzles to be sure about validity of given pattern. Found valid/invalid patterns (having filled B789 band) can help me in exhaustive search task.

The are some members of this forum having experience in checking validity of patterns - blue and Afmob. Maybe they can answer your questions about validity and miminamily/maximality of given patterns.

Serg
Serg
2018 Supporter

Posts: 742
Joined: 01 June 2010
Location: Russia

### Re: Investigation of 4 free boxes (square) patterns

For information, here are some valid puzzles:

Code: Select all
`+---+---+---+      +---+---+---+      +---+---+---+      +---+---+---+      +---+---+---+|...|...|...|      |...|...|...|      |...|...|...|      |...|...|...|      |...|.2.|...||...|...|2.1|      |...|...|8.7|      |...|...|6.8|      |...|.3.|1.7|      |...|...|3.4||...|...|978|      |...|...|345|      |...|.4.|591|      |...|...|924|      |...|...|861|+---+---+---+      +---+---+---+      +---+---+---+      +---+---+---+      +---+---+---+|...|...|812|      |...|...|236|      |...|...|452|      |...|...|571|      |...|...|537||...|...|7.5|      |...|.2.|7.8|      |...|...|8.9|      |...|...|8.3|      |...|...|4.2||8..|97.|643|      |3..|...|954|      |8..|...|316|      |8..|...|246|      |3..|...|618|+---+---+---+      +---+---+---+      +---+---+---+      +---+---+---+      +---+---+---+|418|293|...|      |736|985|...|      |326|157|...|      |687|392|...|      |732|948|...||3.2|7.4|...|      |1.8|4.2|...|      |1.8|3.6|...|      |2.1|4.6|...|      |6.5|3.1|...||759|861|...|      |452|371|...|      |759|428|...|      |439|185|...|      |194|652|...|+---+---+---+      +---+---+---+      +---+---+---+      +---+---+---+      +---+---+---+`

JPF
JPF
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### Re: Investigation of 4 free boxes (square) patterns

Serg wrote:Hi, coloin and qiuyanzhe!
I am now doing exhaustive search for partially minimal patterns having 9 clues in B7, B8 and B9 boxes ....Serg

I see, it is a nice choice to look at 9 clues in band 3 !
The puzzle which I gave you and its pattern [ with 20 clues] is as near as certain to be minimal as very much doubt it will hold 19C

To prove this I'm sure it would be possible to generate all combinations. Otherwise we would have to show that all of the 20 19 clue patterns do not have puzzles. Not sure which is easier !

I will continue to get more 20C patterns/puzzles for the Q2 case, and other exceptional patterns to test your resultant work.
It seems that Q1 and Q3 only have 21C puzzles [as all minimal so far], but all should have have 9 [or maybe 10] clues in one of their bands.
coloin

Posts: 2004
Joined: 05 May 2005

### Re: Investigation of 4 free boxes (square) patterns

Hi, people!
This is the first portion of patterns minimal in the two bands. All patterns are extensions of Q1 pattern to B3 and B6 boxes.
Code: Select all
`+-----+-----+-----+|. . .|. . .|     ||. . .|. . .|  ?  ||. . .|. . .|     |+-----+-----+-----+|. . .|. . .|     ||. . .|. . x|  ?  ||. . x|. . .|     |+-----+-----+-----+|x x x|x x x|x x x||x x x|x x x|x x x||x x x|x x x|x x x|+-----+-----+-----+`

This is full minimal patterns list (26 patterns).
Code: Select all
`         R1                      R2                      R3+-----+-----+-----+     +-----+-----+-----+     +-----+-----+-----+|. . .|. . .|. . .|     |. . .|. . .|. . .|     |. . .|. . .|. . .||. . .|. . .|. x x|     |. . .|. . .|. x x|     |. . .|. . .|. x x||. . .|. . .|x x x|     |. . .|. . .|x x x|     |. . .|. . .|x x x|+-----+-----+-----+     +-----+-----+-----+     +-----+-----+-----+|. . .|. . .|. . .|     |. . .|. . .|. . .|     |. . .|. . .|. . x||. . .|. . x|. . x|     |. . .|. . x|. x x|     |. . .|. . x|. . .||. . x|. . .|x x .|     |. . x|. . .|x . .|     |. . x|. . .|x x x|+-----+-----+-----+     +-----+-----+-----+     +-----+-----+-----+|x x x|x x x|x x x|     |x x x|x x x|x x x|     |x x x|x x x|x x x||x x x|x x x|x x x|     |x x x|x x x|x x x|     |x x x|x x x|x x x||x x x|x x x|x x x|     |x x x|x x x|x x x|     |x x x|x x x|x x x|+-----+-----+-----+     +-----+-----+-----+     +-----+-----+-----+         R4                      R5                      R6+-----+-----+-----+     +-----+-----+-----+     +-----+-----+-----+|. . .|. . .|. . .|     |. . .|. . .|. . x|     |. . .|. . .|. . x||. . .|. . .|. x x|     |. . .|. . .|. x .|     |. . .|. . .|. x .||. . .|. . .|x x x|     |. . .|. . .|x x x|     |. . .|. . .|x x x|+-----+-----+-----+     +-----+-----+-----+     +-----+-----+-----+|. . .|. . .|x . .|     |. . .|. . .|. . .|     |. . .|. . .|. . .||. . .|. . x|. . .|     |. . .|. . x|. . x|     |. . .|. . x|. x x||. . x|. . .|x x x|     |. . x|. . .|x x .|     |. . x|. . .|x . .|+-----+-----+-----+     +-----+-----+-----+     +-----+-----+-----+|x x x|x x x|x x x|     |x x x|x x x|x x x|     |x x x|x x x|x x x||x x x|x x x|x x x|     |x x x|x x x|x x x|     |x x x|x x x|x x x||x x x|x x x|x x x|     |x x x|x x x|x x x|     |x x x|x x x|x x x|+-----+-----+-----+     +-----+-----+-----+     +-----+-----+-----+         R7                      R8                      R9+-----+-----+-----+     +-----+-----+-----+     +-----+-----+-----+|. . .|. . .|. . x|     |. . .|. . .|. . x|     |. . .|. . .|. . x||. . .|. . .|. x .|     |. . .|. . .|. x .|     |. . .|. . .|. x x||. . .|. . .|x x x|     |. . .|. . .|x x x|     |. . .|. . .|x x .|+-----+-----+-----+     +-----+-----+-----+     +-----+-----+-----+|. . .|. . .|. . x|     |. . .|. . .|x . .|     |. . .|. . .|. . .||. . .|. . x|. . .|     |. . .|. . x|. . .|     |. . .|. . x|. . x||. . x|. . .|x x x|     |. . x|. . .|x x x|     |. . x|. . .|x x .|+-----+-----+-----+     +-----+-----+-----+     +-----+-----+-----+|x x x|x x x|x x x|     |x x x|x x x|x x x|     |x x x|x x x|x x x||x x x|x x x|x x x|     |x x x|x x x|x x x|     |x x x|x x x|x x x||x x x|x x x|x x x|     |x x x|x x x|x x x|     |x x x|x x x|x x x|+-----+-----+-----+     +-----+-----+-----+     +-----+-----+-----+        R10                     R11                     R12+-----+-----+-----+     +-----+-----+-----+     +-----+-----+-----+|. . .|. . .|. . x|     |. . .|. . .|. . x|     |. . .|. . .|. . x||. . .|. . .|. x x|     |. . .|. . .|. x x|     |. . .|. . .|. x x||. . .|. . .|x x .|     |. . .|. . .|x x .|     |. . .|. . .|x x .|+-----+-----+-----+     +-----+-----+-----+     +-----+-----+-----+|. . .|. . .|. . .|     |. . .|. . .|. . .|     |. . .|. . .|. . x||. . .|. . x|. x .|     |. . .|. . x|. x x|     |. . .|. . x|. . .||. . x|. . .|x . x|     |. . x|. . .|x . .|     |. . x|. . .|x x x|+-----+-----+-----+     +-----+-----+-----+     +-----+-----+-----+|x x x|x x x|x x x|     |x x x|x x x|x x x|     |x x x|x x x|x x x||x x x|x x x|x x x|     |x x x|x x x|x x x|     |x x x|x x x|x x x||x x x|x x x|x x x|     |x x x|x x x|x x x|     |x x x|x x x|x x x|+-----+-----+-----+     +-----+-----+-----+     +-----+-----+-----+        R13                     R14                     R15+-----+-----+-----+     +-----+-----+-----+     +-----+-----+-----+|. . .|. . .|. . x|     |. . .|. . .|. . x|     |. . .|. . .|. . x||. . .|. . .|. x x|     |. . .|. . .|. x x|     |. . .|. . .|x x .||. . .|. . .|x x .|     |. . .|. . .|x x .|     |. . .|. . .|x x .|+-----+-----+-----+     +-----+-----+-----+     +-----+-----+-----+|. . .|. . .|. x .|     |. . .|. . .|x . .|     |. . .|. . .|. . .||. . .|. . x|. . .|     |. . .|. . x|. . .|     |. . .|. . x|. . x||. . x|. . .|x x x|     |. . x|. . .|x x x|     |. . x|. . .|x x .|+-----+-----+-----+     +-----+-----+-----+     +-----+-----+-----+|x x x|x x x|x x x|     |x x x|x x x|x x x|     |x x x|x x x|x x x||x x x|x x x|x x x|     |x x x|x x x|x x x|     |x x x|x x x|x x x||x x x|x x x|x x x|     |x x x|x x x|x x x|     |x x x|x x x|x x x|+-----+-----+-----+     +-----+-----+-----+     +-----+-----+-----+        R16                     R17                     R18+-----+-----+-----+     +-----+-----+-----+     +-----+-----+-----+|. . .|. . .|. . x|     |. . .|. . .|. . x|     |. . .|. . .|. . x||. . .|. . .|x x .|     |. . .|. . .|x x .|     |. . .|. . .|x x .||. . .|. . .|x x .|     |. . .|. . .|x x .|     |. . .|. . .|x x .|+-----+-----+-----+     +-----+-----+-----+     +-----+-----+-----+|. . .|. . .|. . .|     |. . .|. . .|. . x|     |. . .|. . .|. x .||. . .|. . x|. x .|     |. . .|. . x|. . .|     |. . .|. . x|. . .||. . x|. . .|x . x|     |. . x|. . .|x x x|     |. . x|. . .|x x x|+-----+-----+-----+     +-----+-----+-----+     +-----+-----+-----+|x x x|x x x|x x x|     |x x x|x x x|x x x|     |x x x|x x x|x x x||x x x|x x x|x x x|     |x x x|x x x|x x x|     |x x x|x x x|x x x||x x x|x x x|x x x|     |x x x|x x x|x x x|     |x x x|x x x|x x x|+-----+-----+-----+     +-----+-----+-----+     +-----+-----+-----+        R19                     R20                     R21+-----+-----+-----+     +-----+-----+-----+     +-----+-----+-----+|. . .|. . .|. . .|     |. . .|. . .|. . .|     |. . .|. . .|. . x||. . .|. . .|x x x|     |. . .|. . .|x x x|     |. . .|. . .|x x .||. . .|. . .|x x x|     |. . .|. . .|x x x|     |. . .|. . .|x x x|+-----+-----+-----+     +-----+-----+-----+     +-----+-----+-----+|. . .|. . .|. . x|     |. . .|. . .|. . x|     |. . .|. . .|. . x||. . .|. . x|. . .|     |. . .|. . x|. x .|     |. . .|. . x|. . .||. . x|. . .|x x .|     |. . x|. . .|x . .|     |. . x|. . .|x x .|+-----+-----+-----+     +-----+-----+-----+     +-----+-----+-----+|x x x|x x x|x x x|     |x x x|x x x|x x x|     |x x x|x x x|x x x||x x x|x x x|x x x|     |x x x|x x x|x x x|     |x x x|x x x|x x x||x x x|x x x|x x x|     |x x x|x x x|x x x|     |x x x|x x x|x x x|+-----+-----+-----+     +-----+-----+-----+     +-----+-----+-----+        R22                     R23                     R24+-----+-----+-----+     +-----+-----+-----+     +-----+-----+-----+|. . .|. . .|. . x|     |. . .|. . .|. . x|     |. . .|. . .|. . x||. . .|. . .|x x .|     |. . .|. . .|x x .|     |. . .|. . .|x x .||. . .|. . .|x x x|     |. . .|. . .|x x x|     |. . .|. . .|x x x|+-----+-----+-----+     +-----+-----+-----+     +-----+-----+-----+|. . .|. . .|. . x|     |. . .|. . .|. x .|     |. . .|. . .|. x .||. . .|. . x|. x .|     |. . .|. . x|. . .|     |. . .|. . x|. . x||. . x|. . .|x . .|     |. . x|. . .|x . x|     |. . x|. . .|x . .|+-----+-----+-----+     +-----+-----+-----+     +-----+-----+-----+|x x x|x x x|x x x|     |x x x|x x x|x x x|     |x x x|x x x|x x x||x x x|x x x|x x x|     |x x x|x x x|x x x|     |x x x|x x x|x x x||x x x|x x x|x x x|     |x x x|x x x|x x x|     |x x x|x x x|x x x|+-----+-----+-----+     +-----+-----+-----+     +-----+-----+-----+        R25                     R26+-----+-----+-----+     +-----+-----+-----+|. . .|. . .|. x x|     |. . .|. . .|. x x||. . .|. . .|x . x|     |. . .|. . .|x . x||. . .|. . .|x x .|     |. . .|. . .|x x .|+-----+-----+-----+     +-----+-----+-----+|. . .|. . .|. . x|     |. . .|. . .|. . x||. . .|. . x|. . .|     |. . .|. . x|. x .||. . x|. . .|x x .|     |. . x|. . .|x . .|+-----+-----+-----+     +-----+-----+-----+|x x x|x x x|x x x|     |x x x|x x x|x x x||x x x|x x x|x x x|     |x x x|x x x|x x x||x x x|x x x|x x x|     |x x x|x x x|x x x|+-----+-----+-----+     +-----+-----+-----+`

I am sure I've done exhaustive search (all possible extensions of Q1 pattern are found). It would be nice to see cross-checking of this result.

Serg
Serg
2018 Supporter

Posts: 742
Joined: 01 June 2010
Location: Russia

### Re: Investigation of 4 free boxes (square) patterns

Code: Select all
`+---+---+---+|...|...|...||...|...|.12||...|...|345|+---+---+---+|...|...|..1||...|6..|7..||5..|...|.23|+---+---+---+|.8.|..3|6..||27.|.4.|...||1.9|.5.|...|+---+---+---+  20 clues`

It looks like this gets through the filter, although I only just made it to 20 clues ......
With 3 clues in B1B2B4B5 I have found a few 18s, [14], and i believe there is a 17C with 4 clues in B1B2B4B5 ..
coloin

Posts: 2004
Joined: 05 May 2005

### Re: Investigation of 4 free boxes (square) patterns

And further searching .....with the pattern
Code: Select all
`+---+---+---+|...|...|...||...|...|...||...|x..|...|+---+---+---+|...|...|...||...|...|...||x..|...|...|+---+---+---+|...|...|...||...|...|...||...|...|...|+---+---+---+`

around 2600 21C puzzles ... but no 20C puzzle puzzle found !

but with 3 clues in the 4 boxes .... more than 150 18C
with 4 clues [one in each box] in the 4 boxes - > 5000 18C and 10 17C [none new]
coloin

Posts: 2004
Joined: 05 May 2005

### Re: Investigation of 4 free boxes (square) patterns

coloin wrote:
Code: Select all
`+---+---+---+|...|...|...||...|...|.12||...|...|345|+---+---+---+|...|...|..1||...|6..|7..||5..|...|.23|+---+---+---+|.8.|..3|6..||27.|.4.|...||1.9|.5.|...|+---+---+---+  20 clues`

It looks like this gets through the filter, ...

What do you mean ? Looks like pattern R2 with an additional clue (swap stacks 12 and rows 56).
eleven

Posts: 2478
Joined: 10 February 2008

### Re: Investigation of 4 free boxes (square) patterns

eleven wrote:...What do you mean ? Looks like pattern R2 with an additional clue (swap stacks 12 and rows 56).

Ah ... I meant that it passes the filter as being a valid pattern .. ie its not filtered out ..... it was a poor choice of words !
coloin

Posts: 2004
Joined: 05 May 2005

### Re: Investigation of 4 free boxes (square) patterns

Code: Select all
`+---+---+---+     +---+---+---+|...|...|.37|     |...|...|.18||...|...|182|     |...|...|672||...|5..|...|     |...|9..|...|+---+---+---+     +---+---+---+|...|...|9.8|     |...|...|.96||...|...|45.|     |...|...|53.||2..|...|..1|     |8..|...|..7|+---+---+---+     +---+---+---+|.51|.2.|...|     |.35|..1|...||.49|6..|...|     |.49|6..|3..||.6.|.71|...|     |.6.|..2|...|+---+---+---+     +---+---+---+   21C puzzles with this structure can be valid`

but I am unable to get a 20C with the diagonal 2C pattern
it seems these clues-in-box patterns are precluded ...
Code: Select all
`015    015     015    015     014104 or 104 or  104 or 104 and 104540    450     531    351     442`
coloin

Posts: 2004
Joined: 05 May 2005

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