The New Sudoku Players' Forum

[Borneq]

In thonky are described Naked and Hidden sets for n=2,3,4; in planetsudoku is for n=5;
theoretically n can be for 1 to 8, but n>4 are useless like N-fish degree > 4?

[pjb]

Code: Select all

 3469    6789    347    | 4789   4579   1      | 368    35689  2     
 169     2       17     | 789    3      578    | 4      5689   15689 
 1349    189     5      | 6      2      48     | 138    7      189   
------------------------+----------------------+---------------------
 12459   159     6      | 124789 4579   24578  | 78     58     3     
 459     3       8      | 479    45679  4567   | 2      1      4567   
 7       15      124    | 12348  456    234568 | 9      568    4568   
------------------------+----------------------+---------------------
 1236    4       1237   | 237    8      9      | 5      236    167   
 2356    567     9      | 237    1      2367   | 3678   4      678   
 8       167     1237   | 5      467    23467  | 1367   2369   1679   

.....1..2.2..3.4....562..7...6.....3.38...21.7.....9...4..895....9.1..4.8..5.....


These higher level sets can be occasionally very useful. Consider above (Champagne, pattern game 0161) There is the naked quin of 45679 at r4c5, r5c456, r6c5, and the complementary hidden quads of 1238 at r46c46 (=> -479 r4c4, -457 r4c6, -4 r6c4 and -456 r6c6) .

Phil

[Borneq]

This complementarity is always or only in this case? For example http://planetsudoku.com/how-to/sudoku-naked-quint.html has no complementary hidden quad? But in the opposite direction: hidden sets are stronger and each naked set has complementary hidden set?

[eleven]

This complementarity is always or only in this case?

Always, it's just a different way of looking at the same thing. If you have a naked set, you can eliminate these digits from the other/complementary - not resolved - cells of this unit. This means, that you have a hidden set with the complementary digits there. Vice versa: if you have a hidden set, these digits cannot be in the complementary cells, thus there is a naked set of the other (not resolved) digits.

For example http://planetsudoku.com/how-to/sudoku-naked-quint.html has no complementary hidden quad?

Since two cells in the box are resoved, the complementary set is the hidden pair 23 (theoretically you also can call 2379 a hidden quad). The 23 pair is easy to spot, if you look at row 6 and column 8, which both have 2 and 3 outside the box 6.