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8 clue (Regional constraints only) puzzles http://www.rcbroughton.co.uk/sudoku/forum/viewtopic.php?f=13&t=753 |
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Author: | tarek [ Mon May 10, 2010 12:47 pm ] |
Post subject: | 8 clue (Regional constraints only) puzzles |
Restrained Sudoku puzzles are not new. The extra constraints usually makes it easy to require less clues for a unique solution. The minimum number of clues for 9x9 (regional constraints only) puzzles can't go below 8. I've introduced on the Players forum (RIP) several examples of such puzzles. The puzzle combination of Sudoku with X diagonals, Diamond diagonals, Disjoint groups & Disjoint groups diagonals is an example of a Restrained puzzle that allows this number of clues easily. This thread will be dedicated to such 8-clue Regional-constraints Restrained puzzles |
Author: | tarek [ Mon May 10, 2010 1:05 pm ] |
Post subject: | DD X DG DGD Sudoku puzzles |
The follwing is a combo (Sudoku, X, Disjoint Groups (DG), Diamond diagonals (DD) & DG diagonals (DGD)) with 42 "Declared" regional constraints. It is special because it starts with 68 consecutive empty cells & still achieves a single solution. It is beyond What many would consider humanly solvable so no need to attempt un-aided Here is the puzzle with the constraints explained: Solutin: & the above in text formats: Code: ....................................................................6..521.849..7
. . . | . . . | . . . . . . | . . . | . . . . . . | . . . | . . . ------+-------+------ . . . | . . . | . . . . . . | . . . | . . . . . . | . . . | . . . ------+-------+------ . . . | . . . | . . . . . . | . . 6 | . . 5 2 1 . | 8 4 9 | . . 7 124935876857261943693478521341687259572394618986152734768513492439726185215849367 1 2 4 | 9 3 5 | 8 7 6 8 5 7 | 2 6 1 | 9 4 3 6 9 3 | 4 7 8 | 5 2 1 ------+-------+------ 3 4 1 | 6 8 7 | 2 5 9 5 7 2 | 3 9 4 | 6 1 8 9 8 6 | 1 5 2 | 7 3 4 ------+-------+------ 7 6 8 | 5 1 3 | 4 9 2 4 3 9 | 7 2 6 | 1 8 5 2 1 5 | 8 4 9 | 3 6 7 |
Author: | tarek [ Fri May 14, 2010 7:33 pm ] |
Post subject: | Symmetric Solvable DD X DG DGD Sudokus |
Finally with the some programming, I've landed some nice symmetric examples. image to explain the constraints: The 1st is an 8 clue puzzle that requires advanced fish Code: ........438...9...................................................1...752........ . . . | . . . | . . 4 3 8 . | . . 9 | . . . . . . | . . . | . . . ------+-------+------ . . . | . . . | . . . . . . | . . . | . . . . . . | . . . | . . . ------+-------+------ . . . | . . . | . . . . . . | 1 . . | . 7 5 2 . . | . . . | . . . 162873594387459216945621738439215687521768943876394152758946321694132875213587469 The 2nd is a 9 clue puzzle that requires only "SUPERIOR" level techniques Code: ................6...1....4........5.....9.....8........3....7...2................ . . . | . . . | . . . . . . | . . . | . 6 . . . 1 | . . . | . 4 . ------+-------+------ . . . | . . . | . 5 . . . . | . 9 . | . . . . 8 . | . . . | . . . ------+-------+------ . 3 . | . . . | 7 . . . 2 . | . . . | . . . . . . | . . . | . . . 674589123358412967291736845912367458746895231583124679835241796129673584467958312 Walkthrough for 2nd puzzle: |
Author: | tarek [ Thu May 20, 2010 6:57 am ] |
Post subject: | Very difficult symmetric 8 clue Colver X |
Another example of a constrained puzzle is the Clover X (Sudoku, Windoku, Asterisk & X diagonals), here is a very very difficult 8 clue example: Code: .....9..........5..........2......7...........8......4..........3..........1..... . . . | . . 9 | . . . . . . | . . . | . 5 . . . . | . . . | . . . ------+-------+------ 2 . . | . . . | . 7 . . . . | . . . | . . . . 8 . | . . . | . . 4 ------+-------+------ . . . | . . . | . . . . 3 . | . . . | . . . . . . | 1 . . | . . . Solution: |
Author: | tarek [ Fri May 21, 2010 7:26 pm ] |
Post subject: | Anti-King Anti-Knight Symmetric 8-clue puzzles |
the Anti-King Anti-Knight Sudoku is another example where the 8-clue barrier can be easily reached. Here are 4 symmetrical examples of variable difficulties: This is an EASY Code: .............................3.974.............281.5............................. . . . | . . . | . . . . . . | . . . | . . . . . . | . . . | . . . ------+-------+------ . . 3 | . 9 7 | 4 . . . . . | . . . | . . . . . 2 | 8 1 . | 5 . . ------+-------+------ . . . | . . . | . . . . . . | . . . | . . . . . . | . . . | . . . Solution: This is a SUPERIOR Code: .........................5.2...9.......8.7.......1...4.3......................... . . . | . . . | . . . . . . | . . . | . . . . . . | . . . | . 5 . ------+-------+------ 2 . . | . 9 . | . . . . . . | 8 . 7 | . . . . . . | . 1 . | . . 4 ------+-------+------ . 3 . | . . . | . . . . . . | . . . | . . . . . . | . . . | . . . Solution: This is MILDLY ADVANCED Code: .........................5.2...9.7.............8.1...4.3......................... . . . | . . . | . . . . . . | . . . | . . . . . . | . . . | . 5 . ------+-------+------ 2 . . | . 9 . | 7 . . . . . | . . . | . . . . . 8 | . 1 . | . . 4 ------+-------+------ . 3 . | . . . | . . . . . . | . . . | . . . . . . | . . . | . . . Solution: And this is IMPOSSIBLE Code: ....97..4..................3.........................5..................2..81.... . . . | . 9 7 | . . 4 . . . | . . . | . . . . . . | . . . | . . . ------+-------+------ 3 . . | . . . | . . . . . . | . . . | . . . . . . | . . . | . . 5 ------+-------+------ . . . | . . . | . . . . . . | . . . | . . . 2 . . | 8 1 . | . . . Solution: Enjoy, tarek |
Author: | HATMAN [ Sat May 22, 2010 1:29 pm ] |
Post subject: | Re: 8 clue (Regional constraints only) puzzles |
tarek I enjoyed the AK-AN superior - thanks. Maurice |
Author: | tarek [ Sun May 23, 2010 8:49 am ] |
Post subject: | 8 clue symmetric Anti-Knight Wrapper |
Thanks Maurice, great puzzles ... hopefully Nikoli_Freak will re-surface again .... I managed to find a symmetric example with an Anti-Knight top-down Rt-Lt Wrap constraint. In this variant each cell has 8 cells which are a Knight's move away here is a demo with cells r1c1(red), r5c2(green) & r6c6(blue) highlighted The puzzle itself is very difficult so don't solve unaided Text format Code: .........................5.......7.4...1.9...2.8.......3......................... . . . | . . . | . . . . . . | . . . | . . . . . . | . . . | . 5 . ------+-------+------ . . . | . . . | 7 . 4 . . . | 1 . 9 | . . . 2 . 8 | . . . | . . . ------+-------+------ . 3 . | . . . | . . . . . . | . . . | . . . . . . | . . . | . . . Solution Code: 6 2 1 | 5 8 7 | 4 9 3 3 4 5 | 6 9 2 | 1 8 7 9 8 7 | 3 4 1 | 6 5 2 ------+-------+------ 1 9 3 | 2 5 8 | 7 6 4 7 5 4 | 1 6 9 | 2 3 8 2 6 8 | 7 3 4 | 5 1 9 ------+-------+------ 4 3 6 | 9 2 5 | 8 7 1 8 7 9 | 4 1 6 | 3 2 5 5 1 2 | 8 7 3 | 9 4 6 I have been posting these on the New Sudoku Forum ... I will try to stick to a unique topic per forum, the problem is that there are members here that are not members there and vice versa tarek |
Author: | tarek [ Sun May 23, 2010 10:54 pm ] |
Post subject: | Re: 8 clue (Regional constraints only) puzzles |
Hi Maurice, When you made the reference to OL X, did you mean that both puzzles can be solved using the HANDS groups ONLY, and that the solution grid is OL X compatible ? tarek |
Author: | HATMAN [ Mon May 24, 2010 8:02 am ] |
Post subject: | Re: 8 clue (Regional constraints only) puzzles |
That is correct for the first one but with the second I have not tried solving it without the X and OL. It does not mean it is not solvable that way though. |
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