Hi Serg,
Thank you !
Ask for patterns that they dont have puzzles 2
Re: Ask for patterns that they dont have puzzles 2
by blue » Tue Jun 20, 2023 3:47 am
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Re: Ask for patterns that they dont have puzzles 2
by coloin » Tue Jun 20, 2023 9:57 am
Yes, good work confriming the invalid patterns ...
when I produced the valid anticorner puzzles above I added 4 clues to a random selection of 36 clue 4-corner pattern of clues
With a more intensive directed search I failed to find any more valid patterns .....
maybe the details of this more intensive search will be of use
here is an anticorner pattern
Going back to gangster days I realized that one could attempt[*] to classify the anticorner patterns according to their solution count
I was able to generate 5680 different solution counts [ though maybe a couple more exist]
However I do believe that some different classes have identical clue counts [*}
So..... to an exemplar of each I was able to add 4 clues .... and no new valid patterns emerged
I have tried to estimate the upper bound of these 4-corner gangster classes as 7400 ... so a few are doubled up
when I produced the valid anticorner puzzles above I added 4 clues to a random selection of 36 clue 4-corner pattern of clues
With a more intensive directed search I failed to find any more valid patterns .....
maybe the details of this more intensive search will be of use
here is an anticorner pattern
- Code: Select all
+---+---+---+ +---+---+---+
|...|...|...| |...|...|..9|
|...|...|...| |...|...|..6|
|...|...|...| |...|...|..5|
+---+---+---+ +---+---+---+
|...|...|698| |...|...|698|
|...|...|371| |...|...|371|
|...|...|542| |...|...|542|
+---+---+---+ +---+---+---+
|385|761|924| |385|761|924|
|712|945|863| |712|945|863|
|964|823|157| |964|823|157|
+---+---+---+ +---+---+---+ 82180 sols
Going back to gangster days I realized that one could attempt[*] to classify the anticorner patterns according to their solution count
- Code: Select all
........9........6........5......698......371......542385761924712945863964823157 ## 82180 sol #0001
........9........6........5......968......374......512372865491641923857985714623 ## 83048 sol #0002
........
........1........3........4......315......982......476561749238327568149498213567 ## 94436 sol #200x
........
........9........3........5......978......452......631371948526542361897968572314 ## 141016 sol #5679
........9........6........4......891......362......475394862517572391648861547923 ## 148536 sol #5680
I was able to generate 5680 different solution counts [ though maybe a couple more exist]
However I do believe that some different classes have identical clue counts [*}
So..... to an exemplar of each I was able to add 4 clues .... and no new valid patterns emerged
I have tried to estimate the upper bound of these 4-corner gangster classes as 7400 ... so a few are doubled up
- coloin
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- Location: Devon
Re: Ask for patterns that they dont have puzzles 2
by coloin » Thu Jun 22, 2023 1:46 pm
here is blue's puzzle and more expanded puzzles can be produced form the 4-corner pattern gangsters - all have the same inverse 5-corner solution solved with 4 clues.
here are the 222 puzzle extrapolations for blue's puzzle
- Code: Select all
1.....6.....8..............6.....315......982......476561749238327568149498213567 blue's puzzle
185472693234896751976135824642987315713654982859321476561749238327568149498213567 solutiom grid
........1........3........4......315......982......476561749238327568149498213567 4-corner with 94436 sol
185472693234896751976135824642987...713654...859321.............................. inverse "5-corner" which solves with 4 clues
185472693234896751976135824642987...713654...859321...3........4........5........ 222 [x6] all different solutions of this
here are the 222 puzzle extrapolations for blue's puzzle
Hidden Text: Show
- coloin
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Re: Ask for patterns that they dont have puzzles 2
by coloin » Thu Jun 22, 2023 7:04 pm
Here is a perhaps suitably "fruitless" table with some unpresented data and attempted classifications ....which would clearly need verification !
The B1245 and B12347 are from blue
The B159 is from JPF
The B123456 is from champagne
The B123456789 is from red ed
Am pretty sure that the 56675 3-corner value is correct
I have estimated the 4-corner and 5-corner possibilities
The B1245 and B12347 are from blue
The B159 is from JPF
The B123456 is from champagne
The B123456789 is from red ed
Am pretty sure that the 56675 3-corner value is correct
- Code: Select all
+---+---+---+
|...|...|...|
|...|...|...|
|...|...|...|
+---+---+---+
|...|...|123|
|...|...|456|
|...|...|789|
+---+---+---+
|...|617|548|
|...|328|917|
|...|954|362|
+---+---+---+ Exanple of 3-corner - 56675 ED possibilities
I have estimated the 4-corner and 5-corner possibilities
- Code: Select all
Boxes ED combinations classes Acceptable label
B1 1 Box
B12 43 2 classes [minirow repeat] BoxPair
B123 416 44 classes/gangsters Band/Chute
B124 56675 ? classes 3-corner
B1234 ? 2,032,889 ? 7392 classes with 5680 diff sol counts 4-corner
B12345 ? ~ 100,000,000 ? 7392 classes with ? diff sol counts 5-corner
B123456 983,959,110 44 classes DoubleBand
B1234567 ~ 45,000,000,000 43 classes
B12345678 ~ 45,000,000,000
B123456789 5,472,730,538 416 classes by minimum band Solution Grid
B15 124 15 classes [5x5] 2-Diagonal Box
B159 237,083 3-Diagonal Box
B1245 5,699,915 2865 classes 4-Square
B12459 4-Squareplusbox
B12347 18,296,007 2865 classes CrossingBand
- coloin
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Re: Ask for patterns that they dont have puzzles 2
by blue » Fri Jun 23, 2023 3:24 am
Hi Colin,
This is what I get for 3, 4 & 5-corner numbers:
My 3-corner "ED" count is one higher than what you listed. Typo ?
P.S. (Edited) Two more "ED combinations" numbers:
This is what I get for 3, 4 & 5-corner numbers:
- Code: Select all
B124 56,676 7869 classes 3-corner
B1234 2,032,854 8923 classes with 5704 diff sol counts 4-corner
B12345 737,910,756 8923 classes with 139 diff sol counts 5-corner
My 3-corner "ED" count is one higher than what you listed. Typo ?
P.S. (Edited) Two more "ED combinations" numbers:
- Code: Select all
B1234567 60,335,485,357
B12345678 49,252,605,137
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Re: Ask for patterns that they dont have puzzles 2
by coloin » Sun Jun 25, 2023 6:41 pm
Many thanks for producing those numbers ....
3-corner .. yes ..i was one short ...56676 is correct - but would be interested how you classed them
4-corner .... excellent - NB - almost 4/36 = 1/9 of the B12347 number
also wondering how you differentiated between the 4-corners with the same sol counts !
5-corner .... quite a large total ! glad the 8923 classes is the same as the 4-corner classes
Maybe serg can employ the 4-corner to run throuh the patterns ? or maybe it been completed ?
3-corner .. yes ..i was one short ...56676 is correct - but would be interested how you classed them
4-corner .... excellent - NB - almost 4/36 = 1/9 of the B12347 number
also wondering how you differentiated between the 4-corners with the same sol counts !
5-corner .... quite a large total ! glad the 8923 classes is the same as the 4-corner classes
Maybe serg can employ the 4-corner to run throuh the patterns ? or maybe it been completed ?
Last edited by coloin on Wed Jun 28, 2023 11:26 pm, edited 1 time in total.
- coloin
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- Joined: 05 May 2005
- Location: Devon
Re: Ask for patterns that they dont have puzzles 2
by blue » Sun Jun 25, 2023 10:19 pm
Hi Colin,
After generating the ED cases, including getting them into a canonical form, I did this:
3-corner .. hmmm ...I'm still one short ! and would be interested how you classed them too
After generating the ED cases, including getting them into a canonical form, I did this:
- Flag each case as "class unknown".
- Loop the list, skipping cases where the class is known
- As each "unknown" case, is encountered:
- Tally one new class
- Extend it to a complete grid, and make a puzzle by removing clues from B124
- For each solution to the puzzle:
- Get the B124 part into canonical form
- Find it in the list
- Flag it as "class known" (if it isn't already flagged)
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