Well ,,, great analysis ... and so 1 % have less than 30 19s ... and we are less likely to get these of course.....
suppose same analysis on the found 19C grids we need to see ? [ am worried now]
We wont easily find the grids with only one 19 ... and the 250k grids without 19Cs these will be in the mix too
The 1 in 7 grids which have an 18C - these will be in the top half of the distribution ... making it more skewed presumably ...
Low/Hi Clue Thresholds
Re: Low/Hi Clue Thresholds
by coloin » Sat Aug 31, 2019 8:43 pm
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Re: Low/Hi Clue Thresholds
by coloin » Sun Sep 01, 2019 2:00 pm
Excellent !
indeed but we still have what we suspected and feared ...
im no expert in stats ... but the median tells the same story
that last count will be heading downwards the more plethoric grids which we find and we will continue to find these ones preferentially .....
we wont have this problem in the 18C though, as the 18C are more likely to be found in the grids with more 19C....
... they will have at least 63 non minimal 19C plus a good few minimal {-1+2} within the same grid......
... maybe thats why we found so many 18C when we did the {-2+1} on the found C19s
... perhaps its a good idea to save all the 19C generated [ I have] and perform a non-minimality check on them all when the time comes .... if it comes
blue wrote:Fewer than I expected, but not too bad.
indeed but we still have what we suspected and feared ...
im no expert in stats ... but the median tells the same story
- Code: Select all
median no of 19C in random grids 904
median no of 19C in grids which we have found a 19C 1936
median no of 19C in grids not yet determined 619
that last count will be heading downwards the more plethoric grids which we find and we will continue to find these ones preferentially .....
we wont have this problem in the 18C though, as the 18C are more likely to be found in the grids with more 19C....
... they will have at least 63 non minimal 19C plus a good few minimal {-1+2} within the same grid......
... maybe thats why we found so many 18C when we did the {-2+1} on the found C19s
... perhaps its a good idea to save all the 19C generated [ I have] and perform a non-minimality check on them all when the time comes .... if it comes
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Re: Low/Hi Clue Thresholds
by coloin » Thu Oct 10, 2019 10:49 pm
blue wrote:It looks like the "relative yield" -- (% yield)/(% unresolved) -- has stabilized at ~30%.
That's good !
Updated Blue19 :
Yes ... because its as predicted 250-300k will be no 19C grids ....
and the new 19C finder will surely be an improvement too !
The no 19C grid solutions will be known soon.
Regarding the 18C - i wonder what proportion of 18C puzzles are "untouchable" ? [ no non-isomorphic puzzles within {-1+1} ] - these wont be found as easily as the rest !!!
I found an untouchable 21C some time ago - which might be rare - or maybe just flukey
here i posted - "new " challenges !!!
- Code: Select all
+---+---+---+
|...|...|...|
|12.|3..|8..|
|34.|12.|...|
+---+---+---+
|...|.6.|..7|
|..9|..7|..8|
|6..|...|5..|
+---+---+---+
|..5|..3|..4|
|.1.|...|...|
|...|8..|.9.|
+---+---+---+ untouchable 21C
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Re: Low/Hi Clue Thresholds
by coloin » Thu Oct 31, 2019 3:05 pm
Great progress
So the super computor will indeed deliver the 20C grids ....in a couple of weeks !.
And from the peudo-random 19Cs which I have many batches will probably tend to give even more pseudo-random 18Cs ! - maybe most ways that you make 18C puzzles you will tend to generate the non-remote puzzles.
At any rate the workers are on the case !!!!
The big file of 18C which is a closed group of around 1 Billion - and probably we will get most of them in the end with a blunderbust {-1+1} with the gen18c
As dobrichev says a +2 but keeping the same pattern can be pretty efficient and this may give us a source of remote puzzles.
I have numerous collections of {-2+2} 18C which may well be good in terms of yield too
So we will see how the yield changes with time , hopefully identyfing the new puzzles [ if this is possible - not easy !] and {-1+1} will extend the collection
total number of 18C by subset analysis by Afmob with only a 2% error
so 0.35 x 5.47e9 = 1.91 x 10 ^9 18C puzzles total
The master blue did the analysis on 100,000 random grids we should marvel at again
These are some of the results that can be calculated, based on the hidden table: (with 95% confidence levels for the error estimates)
This agrees with Afmob's work above from here
So the super computor will indeed deliver the 20C grids ....in a couple of weeks !.
And from the peudo-random 19Cs which I have many batches will probably tend to give even more pseudo-random 18Cs ! - maybe most ways that you make 18C puzzles you will tend to generate the non-remote puzzles.
At any rate the workers are on the case !!!!
The big file of 18C which is a closed group of around 1 Billion - and probably we will get most of them in the end with a blunderbust {-1+1} with the gen18c
As dobrichev says a +2 but keeping the same pattern can be pretty efficient and this may give us a source of remote puzzles.
I have numerous collections of {-2+2} 18C which may well be good in terms of yield too
So we will see how the yield changes with time , hopefully identyfing the new puzzles [ if this is possible - not easy !] and {-1+1} will extend the collection
total number of 18C by subset analysis by Afmob with only a 2% error
- Code: Select all
Computation time: 31x17 days
1,310,492 samples
1,310,492 size 3 subsets
4,386 valid minimal puzzles
+----+-------+------------+----------------+
| Cl | Count | E(nr/grid) | E(rel err)*100 |
+----+-------+------------+----------------+
| 18 | 4386 | 3.499e-01 | 2.177e+00 |
so 0.35 x 5.47e9 = 1.91 x 10 ^9 18C puzzles total
The master blue did the analysis on 100,000 random grids we should marvel at again
Hidden Text: Show
These are some of the results that can be calculated, based on the hidden table: (with 95% confidence levels for the error estimates)
- Code: Select all
Avg. Puzzles per grid: 0.3534 +/- 0.0086
Total puzzles : (1.9340 +/- 0.0468) * 10^9
Probablility(grid has 18): (17.69 +/- 0.24)%
Total grids with an 18 : (0.9683 +/- 0.0129) * 10^9
Avg. Puzzles per "grid with an 18": 1.9972 +/- 0.0403
This agrees with Afmob's work above from here
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Re: Low/Hi Clue Thresholds
by coloin » Thu Nov 07, 2019 2:10 pm
Great progress..... and noting that the projection is decreasing based on your processing bands systematically.
blue did predict on random grids it would be in the 234-280K range. On course for that perhaps then.
blue did predict on random grids it would be in the 234-280K range. On course for that perhaps then.
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Re: Low/Hi Clue Thresholds
by coloin » Thu Feb 06, 2020 7:12 pm
Pretty good ....we are half way !!
An excellent effort I think !!
But the fast gen19c continues for now on my PC ...
Interesting that some of the yields are up [24% wow !] , and i suppose that when you get into "non-remote / already found" territory thats when the yield will plummet....
I mentioned that perhaps a selective selective {-1,-1+2}might be the way.
When one removes the best [least sol] clue of the 18 - the number of sols determines the remoteness to an extent .
Instead of trying to process every seed - if we are selective and only process those seeds which have a highish eg 100 sol - maybe this will tend to keep us out of the non-remote/already found territory.
There wont be so many puzzles made however ...
An excellent effort I think !!
But the fast gen19c continues for now on my PC ...
Interesting that some of the yields are up [24% wow !] , and i suppose that when you get into "non-remote / already found" territory thats when the yield will plummet....
I mentioned that perhaps a selective selective {-1,-1+2}might be the way.
When one removes the best [least sol] clue of the 18 - the number of sols determines the remoteness to an extent .
Instead of trying to process every seed - if we are selective and only process those seeds which have a highish eg 100 sol - maybe this will tend to keep us out of the non-remote/already found territory.
There wont be so many puzzles made however ...
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Re: Low/Hi Clue Thresholds
by coloin » Fri Feb 07, 2020 3:29 pm
Well that is progress !!!
Is each batch from a single 17C subpuzzle ?
Is each batch from a single 17C subpuzzle ?
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Re: Low/Hi Clue Thresholds
by coloin » Wed Feb 12, 2020 10:26 pm
Well it seems you have confirmed the E18 grid number - even though taking 1000 solution grids from each band wasn’t actually a random selection !!
I am not aware of the total band counts for all 6 bands in all of the 5e9 solution grids.... but I would guess that those bands needing 5 or 6 clues would be less likely to have an 18C
I am not aware of the total band counts for all 6 bands in all of the 5e9 solution grids.... but I would guess that those bands needing 5 or 6 clues would be less likely to have an 18C
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Re: Low/Hi Clue Thresholds
by coloin » Thu Feb 13, 2020 9:07 pm
Great ... with all the mini tests we have done , im hopeful that searching the new puzzles/grids is/will be the way to improve the yield.
As time goes the Gen18H yield inherently will tail .
The increased time and reduced rate of puzzle making will be made up by finding the more remote puzzles - the puzzles a random search inherently again tends to miss.
Will also do a run continuation of a large batch of which 10% will be new C18s by searching {-1+2} the high sol count subpuzzles [300 sol plus] , and then complete with a final {-1+1} to bump up the numbers, and then calculate the NPH.
As time goes the Gen18H yield inherently will tail .
The increased time and reduced rate of puzzle making will be made up by finding the more remote puzzles - the puzzles a random search inherently again tends to miss.
Will also do a run continuation of a large batch of which 10% will be new C18s by searching {-1+2} the high sol count subpuzzles [300 sol plus] , and then complete with a final {-1+1} to bump up the numbers, and then calculate the NPH.
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Re: Low/Hi Clue Thresholds
by coloin » Wed Feb 26, 2020 9:29 am
Thanks to Mathimagics for that program, and indeed I think we are getting to understand a bit more about the 18C sudoku space.
Given that we have probably found now over 50% of the grids with an 18C , our yields [ with "random" generation] are and have always been significantly less ... now 10%.
We have 2 ways of making 19Cs.
Bluemagic gives us puzzle which are all from different unrelated grids.
Gen19c gives us 19Cs from different grids - but made by repeated {-1+1} morphing.
There is significantly more non-minimal 19Cs [therefore 18Cs] in the puzzles made by Gen19c.
The fact that performing a {-1+1} gives you more puzzles is balanced by the fact that these are from the already found and likely less remote grids [which have more 18s].
Any puzzle found by {-1+1} is also quite likely to be from the original grid. So we will always find preferentially 18C which are non-remote, hence the yields are what they are.
With the advances in performing our partial {-2+2} , I have been able to do this to 18C which have no other puzzles within {-1+1} {previously coined untouchable puzzles }.
Newly found untouchable 18C are then treated with a partial {-2+2} and the process is slowly expansive.
I'm sure that the yield with this technique will be higher, as its also pretty likely that a new puzzle is from a different grid from the original.
Performing this only on newly found puzzles must be a similar process .... but identifying the new puzzles requires indexing the puzzles and is not trivial ! The recent advances by Mathimagics are encouraging.
Given that we have probably found now over 50% of the grids with an 18C , our yields [ with "random" generation] are and have always been significantly less ... now 10%.
We have 2 ways of making 19Cs.
Bluemagic gives us puzzle which are all from different unrelated grids.
Gen19c gives us 19Cs from different grids - but made by repeated {-1+1} morphing.
There is significantly more non-minimal 19Cs [therefore 18Cs] in the puzzles made by Gen19c.
The fact that performing a {-1+1} gives you more puzzles is balanced by the fact that these are from the already found and likely less remote grids [which have more 18s].
Any puzzle found by {-1+1} is also quite likely to be from the original grid. So we will always find preferentially 18C which are non-remote, hence the yields are what they are.
With the advances in performing our partial {-2+2} , I have been able to do this to 18C which have no other puzzles within {-1+1} {previously coined untouchable puzzles }.
Newly found untouchable 18C are then treated with a partial {-2+2} and the process is slowly expansive.
I'm sure that the yield with this technique will be higher, as its also pretty likely that a new puzzle is from a different grid from the original.
Performing this only on newly found puzzles must be a similar process .... but identifying the new puzzles requires indexing the puzzles and is not trivial ! The recent advances by Mathimagics are encouraging.
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Re: Low/Hi Clue Thresholds
by coloin » Thu Mar 12, 2020 4:44 pm
The generation continues , and perhaps its reassuring that new puzzles are found just as easily within {-2+2} of many already found puzzles ....
I am continuing to generate 18C, at better yields it seems. [17%]
Taking a random grid, find the first 19C. Perform a {-1+1}and then a partial {-2+1} to get 18C
However from a few of the non-minimal 19s made from random grids [1 non-minimal 19 - per ~ 8000 minimal puzzles] [which fits Afmobs figures][Average 0.35 18C per grid and 2666 19C per grid]1:7617]
I was able to disern that remote 18s are also common ...
This 18C puzzle is remote to level 1
in a small series , 1 in 4 of these "random" 18C were remote to level 1
It wasnt difficult to find 18C puzzles which were remote to level 2 [no non-trivial isomorph 18C puzzles within {-2+2}] !
the numbers in brackets are the number of other 18C puzzles within {3+3} [range 8-97 for these 5 puzzles]
The approximate incidence was 1 in 11 of 1-remote 18C puzzles are 2-remote.
Which implies 1 in 44 18C puzzles are 2-remote
A previous experiment , searching only remote /untouchable level 1 18C puzzles with a partial {-2+2} gave yields of 28%, thanks to Mathimagics's database.
This may reflect finding more of the level 1 remote puzzles, as they wont be found with the previously used {-1+1} process at the 18C level.
The puzzles which are remote at the level 2 wont be found by a {-2+2}. At least they are findable from non-minimal and minimal 19C...
.... working from 18C to 19C a {-1+2} on 2 of the puzzles from above ...
I am continuing to generate 18C, at better yields it seems. [17%]
Taking a random grid, find the first 19C. Perform a {-1+1}and then a partial {-2+1} to get 18C
However from a few of the non-minimal 19s made from random grids [1 non-minimal 19 - per ~ 8000 minimal puzzles] [which fits Afmobs figures][Average 0.35 18C per grid and 2666 19C per grid]1:7617]
I was able to disern that remote 18s are also common ...
This 18C puzzle is remote to level 1
- Code: Select all
....5.7.....1...36..8....4.23...........9..58.....4.....9...8.1........2.....3...
in a small series , 1 in 4 of these "random" 18C were remote to level 1
It wasnt difficult to find 18C puzzles which were remote to level 2 [no non-trivial isomorph 18C puzzles within {-2+2}] !
- Code: Select all
.2...6...4.......3.891....621.......5....3........7...3.....4...6..........5..2.. #001 [8]
......78.........3..91.2....315.............2......67.....7.9..6.2.....4.......5. #001 [97]
...45........89...7......6.2..6...5.......43......4.....8...9......13....4.5..... #001 [28]
1...5.7....6.8.1..7.....46......7....39...........4...........85.......2.4...3... #001 [23]
..3.5.7..4.........9......6.3.9.....68....4.1.................85.7.4......26..... #001 [16]
.23.......5...91..7..........5...9..6...7.....1.......3.......8......67...4.32... #001
......7.......9.....92....6.7..4..9......5.1..4.86........7...........2..3..14... #001
1.............9........1..4..56...........92...8.......675...9......3..1..28..6.. #001
.2....78.4.6..9...............6..59.37...........2....5............7.4..982...... #001
1....67..4...8..36.9.....1.......9......2...48...............48.72..1............ #001
..3.....9.5.1........7.....2...3..1..7.....6.9.4.......895............7...2.....3 #001
...4.6....5.....3.....7..1..6..........912...78...........2......239..........6.5 #001
the numbers in brackets are the number of other 18C puzzles within {3+3} [range 8-97 for these 5 puzzles]
The approximate incidence was 1 in 11 of 1-remote 18C puzzles are 2-remote.
Which implies 1 in 44 18C puzzles are 2-remote
- Code: Select all
.2...6...4.......3.891....621.......5....3........7...3.....4...6..........5..2..
.....6...4...2...3.891....621......7...9.3............3.....4...6..........5..2..
.2..............73.891....6.12......5....3.......67...3.....4...6..........5..2..
.2..............73.891....6.14......5....3.......67...3.....4...6..........5..2..
.2.......4.......3.891....671............3.9......7...3.....4...6.........15..2..
.2.......4.......3.891....6.1...4........35.......7..83.....4...6..........5..2..
.2.......4.......3.891....6.1..9...85....3............3.....4...6..........5.42..
.2.4.6...4.......3..91....6.1.......5............37...3.7...4...6..........5..2..
.2...6...4.......3.891....6.1.......5....3........7..83.....4...6..........8..9..
A previous experiment , searching only remote /untouchable level 1 18C puzzles with a partial {-2+2} gave yields of 28%, thanks to Mathimagics's database.
This may reflect finding more of the level 1 remote puzzles, as they wont be found with the previously used {-1+1} process at the 18C level.
The puzzles which are remote at the level 2 wont be found by a {-2+2}. At least they are findable from non-minimal and minimal 19C...
.... working from 18C to 19C a {-1+2} on 2 of the puzzles from above ...
- Code: Select all
....5.7.....1...36..8....4.23...........9..58.....4.....9...8.1........2.....3...
- Code: Select all
.2...6...4.......3.891....621.......5....3........7...3.....4...6..........5..2..
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Re: Low/Hi Clue Thresholds
by coloin » Tue Jun 02, 2020 11:26 am
Indeed ... progress .... and predictable slowing down !
This 18 has a transversal 1-9 ..... approx one in 20000 18C have this and consequently I have slowly found a little over 100000 [? 95%] of these !
Inspection of the puzzles reveals that each puzzle has at least 36 isomorphs with the 1-9 transversal
This observation might help in finding the puzzles but isolated puzzles not in the {-2+2} are not found easily....
Removing the 3 clues of the 9 with the lowest individual sol count and doing a {+3} might be a way ... or 2 clues and performing a {-1+3} which would take a bit longer ....
This illustrates the global 18 problem where the remote 18C puzzles, and their grids, which are less likely to be found by chance .....
- Code: Select all
+---+---+---+
|1..|...|...|
|...|2..|...|
|...|...|3..|
+---+---+---+
|.4.|...|...|
|...|.5.|...|
|...|...|.6.|
+---+---+---+
|..7|...|...|
|...|..8|...|
|...|...|..9|
+---+---+---+
+---+---+---+
|1..|..4|...|
|...|29.|..5|
|..6|...|3..|
+---+---+---+
|.4.|...|...|
|2..|.5.|1..|
|8..|...|.6.|
+---+---+---+
|..7|...|..4|
|...|..8|...|
|.5.|...|..9|
+---+---+---+ 18C puzzle [quite hard]
1....4......29...5..6...3...4.......2...5.1..8......6...7.....4.....8....5......9
This 18 has a transversal 1-9 ..... approx one in 20000 18C have this and consequently I have slowly found a little over 100000 [? 95%] of these !
Inspection of the puzzles reveals that each puzzle has at least 36 isomorphs with the 1-9 transversal
This observation might help in finding the puzzles but isolated puzzles not in the {-2+2} are not found easily....
Removing the 3 clues of the 9 with the lowest individual sol count and doing a {+3} might be a way ... or 2 clues and performing a {-1+3} which would take a bit longer ....
This illustrates the global 18 problem where the remote 18C puzzles, and their grids, which are less likely to be found by chance .....
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Re: Low/Hi Clue Thresholds
by coloin » Wed Jun 17, 2020 1:15 pm
Very good again..presumably you are adding 3 clues .... what inspired it was this .. from What is most solved cells with "n" clues?
Adding 2 clues does not give a 17C
Adding 3 clues gives us 1093 minimal 18C - although many from the same grid solution
and this 15 clue [one clue different] has 2715 grid solutions
Adding 2 clues gives one 17C [ thats how Gordon found it, I suppose]
Adding 3 clues gives us 1150 minimal 18C - which are different but again probably many from the same grid solution
I admit that it is highly likely that all these solution grids are known, and presumably remote 18C wont necessarily have a 15C subpuzzle with a low sol count / extra solved clues ....
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+---+---+---+
|...|3.1|...|
|2.4|...|...|
|...|...|...|
+---+---+---+
|8..|52.|...|
|...|...|9.1|
|...|...|3..|
+---+---+---+
|...|.4.|.5.|
|91.|...|...|
|.3.|...|...|
+---+---+---+ this 15C found by G Royle has only 576 sol
solves to
+---+---+---+
|5.9|3.1|...|
|2.4|.95|13.|
|1.3|...|59.|
+---+---+---+
|891|523|...|
|35.|...|9.1|
|.4.|91.|3.5|
+---+---+---+
|.2.|149|.53|
|915|.3.|...|
|43.|.5.|.19|
+---+---+---+ which has 29 more solved clues ! [still 576 sol]
Adding 2 clues does not give a 17C
Adding 3 clues gives us 1093 minimal 18C - although many from the same grid solution
1093.txt- (87.53 KiB) Downloaded 261 times
and this 15 clue [one clue different] has 2715 grid solutions
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+---+---+---+
|...|3.1|...|
|2.4|...|...|
|...|...|...|
+---+---+---+
|8..|52.|...|
|...|...|9.1|
|...|...|3..|
+---+---+---+
|...|.4.|.5.|
|71.|...|...|
|.3.|...|...|
+---+---+---+
Adding 2 clues gives one 17C [ thats how Gordon found it, I suppose]
Adding 3 clues gives us 1150 minimal 18C - which are different but again probably many from the same grid solution
I admit that it is highly likely that all these solution grids are known, and presumably remote 18C wont necessarily have a 15C subpuzzle with a low sol count / extra solved clues ....
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Minimum clues in a double band [DB]
by coloin » Sat Jan 22, 2022 3:07 am
Jus wondering what progress if any has been made !
Generating ever reducing yields with random search [it seems it needs to be better than a +2 to find some 18C] has made it difficult to see how it could ever be completed.
However... ... been reading through this thread and maybe some /many solution grids can be excluded from the search
On page 4
The proposal that I have ... is that we have this very incomplete table
Double bands have got 54 clues and they have been shown to be only 4 which complete in 7 clues ....
I am not aware of any DB been shown to need 13 clues and I guess it might be a big if ... ... but I suspect our 4 grids which need 21 clues would be highly likely to have a contribution there.,..
Now the point is if we exclude all DBs which complete in 12 and below, we would be left with the remaining DB which could be presumably tested quickly for their minimum no of clues for a completion. We have a very large supply of puzzles with 12 clues in their DB ---- so progress could be made quickly !!
If we get DB which cant be solved in 12, ie need 13, we would have grids which could be tested individually [or by gangster] to see whether the third band[s] cannot be completed by adding 4 then 5 clues, then this would exclude a 17 and 18 clues in the full grid[s].
I guess it all depends on the absolute numbers of DB needing 13 clues as to how much this will contribute.
On a side note - I have been experimenting generating 18C keeping the clues in box pattern [ in particular patterns with max 6 clues in a band]...... and this seems to be a fast way of generating them .. more on this...
Perhaps is relevant ...Generating 18C with 6 clues per band both ways will give us 6 DB per puzzle which will all have 12 clues in the 6 DBs ...
Generating ever reducing yields with random search [it seems it needs to be better than a +2 to find some 18C] has made it difficult to see how it could ever be completed.
However... ... been reading through this thread and maybe some /many solution grids can be excluded from the search
On page 4
blue wrote:There are 983,959,110 ED double bands.
The 44 classes that you have in mind, can be partitioned into 913,393 smaller classes too
The proposal that I have ... is that we have this very incomplete table
Double bands have got 54 clues and they have been shown to be only 4 which complete in 7 clues ....
- Code: Select all
Clues to complete number
7 4
8 ?1000
9 ?
10 ?
11 ?
12 ?
13 any ?
--------------------------------
983,959,110
I am not aware of any DB been shown to need 13 clues and I guess it might be a big if ... ... but I suspect our 4 grids which need 21 clues would be highly likely to have a contribution there.,..
Now the point is if we exclude all DBs which complete in 12 and below, we would be left with the remaining DB which could be presumably tested quickly for their minimum no of clues for a completion. We have a very large supply of puzzles with 12 clues in their DB ---- so progress could be made quickly !!
If we get DB which cant be solved in 12, ie need 13, we would have grids which could be tested individually [or by gangster] to see whether the third band[s] cannot be completed by adding 4 then 5 clues, then this would exclude a 17 and 18 clues in the full grid[s].
I guess it all depends on the absolute numbers of DB needing 13 clues as to how much this will contribute.
On a side note - I have been experimenting generating 18C keeping the clues in box pattern [ in particular patterns with max 6 clues in a band]...... and this seems to be a fast way of generating them .. more on this...
Perhaps is relevant ...Generating 18C with 6 clues per band both ways will give us 6 DB per puzzle which will all have 12 clues in the 6 DBs ...
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Minimum clues per DB
by coloin » Sat Jan 22, 2022 5:01 am
Taking the first grid of the 4 without a 21...,
here is 13 clues completing the DB .... and a 12 clue wasnt found at (-3+2) within the grid...
Taking a few ED DB from the 4 grids without a 20C .... probably these are representatives of 6 of the 44 classes ....
I have checked this several times ..... and the first DB here cant be completed with 5 clues, and this applies to
- all the grid solutions of the DB
- all the DB which have that class of gangster in band 3
Aside from this fortunate revelation...
We also know all the single bands which need 6 clues per se - so we actually do know which DB combined with whichever SB need 6 clues [for that SB] at a stroke
here is 13 clues completing the DB .... and a 12 clue wasnt found at (-3+2) within the grid...
- Code: Select all
......789
.........
.8.1.3.5.
.1.8.....
..5......
....6.2.4
541632978
632978541
978541632
Taking a few ED DB from the 4 grids without a 20C .... probably these are representatives of 6 of the 44 classes ....
- Code: Select all
...........................123456789456789123789123456214897365365214897897365214 - none are solvable with 5
...........................123456789456789123789132465218967534564213978937548216 - some are solved in 4
...........................123456789457189326689327154214965873375814962968273415 - some are solved in 4
...........................123456789457189326689327154216534897745891632938672541 - some are solved in 4
...........................123456789457189326689327154216573948574918263938264517 - some are solved in 4
...........................123456789457189326689327154218634597745891632936572841 - some are solved in 4
I have checked this several times ..... and the first DB here cant be completed with 5 clues, and this applies to
- all the grid solutions of the DB
- all the DB which have that class of gangster in band 3
Aside from this fortunate revelation...
We also know all the single bands which need 6 clues per se - so we actually do know which DB combined with whichever SB need 6 clues [for that SB] at a stroke
- coloin
- Posts: 2556
- Joined: 05 May 2005
- Location: Devon
