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kNight Rules http://www.rcbroughton.co.uk/sudoku/forum/viewtopic.php?f=13&t=95 |
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Author: | HATMAN [ Tue Jun 03, 2008 11:23 pm ] |
Post subject: | Re: kNight Rules |
OK Matt: You Win I was just about to post a Ferz NC & Camel NC which has a classic 72 solutions. But with 8 you've got it dead-on; and unbeatable. When I came up with the kNight NC idea (boast), I new it would very "restrained" - but the idea of doubling it is magic!!! HATMAN {Restrained - copyright Ruud: for sudoku puzzle structures with very limited solution sets (i.e. before the givens/cages are introduced} |
Author: | udosuk [ Wed Jun 04, 2008 4:52 am ] |
Post subject: | Re: kNight Rules |
To get 8 solutions one would need the NC property with {19} not considered consecutive. Also one probably need an end-to-end leaper (one leaping across opposite edges, e.g. Ostrich on a 6x6 board). Note with 9x9 NC AK X you can add the NC property of an (8,8) leaper (i.e. opposite corner leaper) to get 8 solutions. Interesting find in FNC CNC having 9x8 solutions. Will explore that! PS: Note NNC+AC also has 9x8 solutions. NNC with 15x8 solutions is probably the best you can do in 9x9 with one variant rule. PPS: Your FNC CNC has a one-to-one mapping from FNC AK AN with the following transformations: If FNC AK AN has r123456789, then r123897456 is FNC CNC. -or- If FNC AK AN has n123456789, then n123897456 is FNC CNC. |
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