- Code: Select all
+---+---+---+
|168|924|573|
|924|573|168|
|573|168|924|
+---+---+---+
|816|492|357|
|492|357|816|
|357|816|492|
+---+---+---+
|681|249|735|
|249|735|681|
|735|681|249|
+---+---+---+
1. The middle block (nonet 5) is the 3x3 magic square.
2. All mini-rows and mini-columns sum to 15.
3. 6 of the mini-diagonals sum to 15.
4. It is a Diagonal Sudoku (Sudoku X): the 2 main diagonals contain 1..9.
5. Besides, 4 more "broken diagonals" contain 1..9.
6. It is an "Emerald": symmetrical pairs of cells across the centre always sum to 10.
7. It is a "Disjoint Sets" Sudoku: all the 9 "spots" (same-positioned cells) within each block (e.g. r147c147, r258c258) contain 1..9.
8. Besides, if you make the "Disjoint Sets" conversion (i.e. nonets become rows and spots become columns), the resulting grid is also a Diagonal Sudoku: r159c159 and r357c357 both contain 1..9. (In fact, the resulting grid is just identical to the original grid.)
9. There are many other "3x3 rectangles" across the grid containing 1..9:
r147c159, r258c159, r369c159, r159c147, r159c258, r159c369
r147c357, r258c357, r369c357, r357c147, r357c258, r357c369
10. The grid is isomorphic to the "most canonical grid" (one of its 648 isomorphisms).
Now, what's left is just to design a puzzle that makes use of all these properties...
