coloin wrote: Here are their incidence in 100000 grids .. one per grid
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........1........2........3........4........5........6........7........8123478569 [#1] 4363
........1........2........3........4........5........6........7........8124378569 [#2] 13315
........1........2........3........4........5........6........7........8124578369 [#3] 48617
........1........2........3........4........5........6........7........8127458369 [#4] 11140
........1........2........3........4........5........6........7........8147258369 [#5] 22565
100000
........1........2........3........4........5........6........7........81....8.69 constant clues
Taking the most common of these there will be only a few grids which do not have this in one of their 81
I took a large number of ED random solution grids.
Using gsfs program to verify if pattern [#3] was present
In 1000 grids pattern [#3] was found in all 1000
In 10000 grids pattern [#3] was found in all 10000
In 50000 grids pattern [#3] was found in all 50000
program still running and will update when 100000 is passed
Which means that there are indeed a select few grids which do not have this clue combination equivalent in the 81 instances of the pattern in the grid.
5e9/5e4 ~ 100000 grids is an upper bound perhaps
Jim would have a field day !
Im sure he would be the first to suggest that the automorphic grids are probably the most likely place to find solution grids without the pattern ...
... this is indeed the case.
Im guessing that the number of grids not having this pattern is a lot smaller ...
So...... out of 140,000 solution grids ...2 did not have the common L- pattern [#3]
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similarity 15
........1........2........3........4........5........6........7........8124578369
472936581963185472518247693185369724639472815247851936851693247396724158724518369
similarity 15
........1........2........3........4........5........6........7........8124578369
257341698341869572869257413692735184418926735573184926985613247736492851124578369
despite this apparent rareity there may well be 50000-100000 !
In any case all the crossing bands in these puzzles dont have the L-pattern ...and there are 11 ED out of 18
