- Code: Select all
*** ***
*** ***
**2*2**
***
**2*2**
*** ***
*** ***
where each character represents a 3x3 box, and a digit the number of puzzles that share that box if geater than one.
The whole is on a 21x21 grid, with 4x2x9 = 72 unused cells.
One could also imagine within that grid the following arrangement of four overlapping puzzles:
- Code: Select all
***
***
**2*2**
*** ***
**2*2**
***
***
I don't recall ever seeing such a plus-sign layout, but I may be wrong. Maybe it's just not so interesting.
However, what might be of interest is a layout which is the sum of the two shown above, namely
- Code: Select all
**2*2**
**2*2**
224*422
*******
224*422
**2*2**
**2*2**
Let's call that a SamuraiPlus. (I don't recall ever seeing such a layout, but I could be wrong.)
Here is such a puzzle consisting of nine 9x9 sudokus overlapping as show above.
- Code: Select all
. . . 7 . 9 . . . 5 . . . . . 1 . . . . .
7 8 . . . . 4 . . . . 9 1 3 . . . . . . .
. . 3 . . . . . . 3 . . . . . . 8 . 1 . 6
. 6 . . . 7 . 4 . 6 . . 5 7 . . . 4 . . 3
. . 4 . . . . . . 8 . . . . 6 . . . . 4 .
. 9 . 5 . . . . . . . 5 9 4 . . . 7 . 2 1
5 4 . . . . . . . . . . . . . . 3 1 . . 5
. 3 . . 1 . . . . . . . . . . 6 . . . . .
. . . 2 . 4 . . . . . . . . . . . . . . .
1 . 3 . . . . . . . . . . . . 1 5 3 . . .
. . . . . . . . . . . . . . . . . . . . .
. . . 1 5 2 . . . . . . . . . . . . 2 . 6
. . . . . . . . . . . . . . . 3 . 5 . . .
. . . . . 1 . . . . . . . . . . 1 . . 4 .
2 . . 3 8 . . . . . . . . . . . . . . 2 1
1 2 . 8 . . . 4 5 7 . . . . . . . 6 . 7 .
. 5 . . . . 7 . . . . 3 . . . . . . 1 . .
8 . . 4 . . . 1 2 . . 6 . 9 . 1 . . . 5 .
6 . 2 . 1 . . . . . . 7 . . . . . . 9 . .
. . . . . . . 5 6 2 . . . . 4 . . . . 6 5
. . . . . 8 . . . . . 4 . . . 5 . 7 . . . Number of clues 100, symmetric, middle puzzle empty, easy
and a Word file of the same puzzle is attached below.
The large number of constraints allows us to construct patterns such as this doughnut:
- Code: Select all
. . . . . . . . . . . . . . . . . . . . .
. . . . 2 . 4 . . . . . 1 . 7 4 5 . . 8 .
. . . 4 . 6 . . . . 6 1 . 5 . . . 9 1 . .
. . 5 8 . . 3 . . . . 2 . 7 . 2 . . . . .
. . . . . . . 9 . 8 . . . . . . . 5 . 4 .
. . . 5 . 1 . 8 . . 7 . . . 3 8 . . . 2 .
. 4 . . 7 . . . . . . . . . . 9 . . . 7 .
. . . . . 5 . . . . . . . . . . . . . . .
. 7 . 2 3 . . . . . . . . . . . . . 3 . .
. . . . 6 . . . . . . . . . . 1 . . . . .
. . . . . 3 . . . . . . . . . . 8 . . . .
. . . 1 5 2 . . . . . . . . . . . 7 . . .
. 1 . 7 . . . . . . . . . . . 3 2 . . 9 .
. 8 6 . . 1 . . . . . . . . . . . . . . .
. . . 3 8 . . . . . . . . . . 7 . 4 . . .
. . 7 . . . . . . . . 9 . . . . . 6 8 . .
. 5 . 1 . 2 . 8 9 . 2 . . 4 . . . . 1 . .
. . . . . . . . 2 . 5 . 7 . 8 1 . . . 5 .
. . . 9 . . . . 4 . . . 2 5 . . . 3 . . .
. . 8 . . . 1 5 . . . 8 9 . . . . . . . .
. . . . . . . . . . . . . . . . . . . . . Number of clues 88, doughnut, very hard
or one with a large, empty, central square (14x14):
- Code: Select all
. . . 7 . 9 2 1 . 5 . . 8 . . 1 . . . . .
. 8 . 1 . . 4 6 . . . 9 . 3 7 4 . 6 . . .
. . . 4 . 6 9 . 8 3 6 . . 5 2 . 8 9 . 3 .
. . 5 . . . . . . . . . . . . . . . 6 . 3
. 1 . . . . . . . . . . . . . . . . 7 4 .
. . . . . . . . . . . . . . . . . . 5 . .
5 . . . . . . . . . . . . . . . . 1 . . 5
6 3 8 . . . . . . . . . . . . . . . . 1 .
. . 1 . . . . . . . . . . . . . . . 3 . .
1 . 3 . . . . . . . . . . . . . . 3 4 . 9
. 5 . . . . . . . . . . . . . . . . 1 5 7
8 6 . . . . . . . . . . . . . . . . . . .
3 . . . . . . . . . . . . . . . . 5 . . 8
7 8 6 . . . . . . . . . . . . . . 9 . . 3
. 9 4 . . . . . . . . . . . . . . . 5 . .
. . . . . . . . . . . . . . . . . . 8 . .
. . . . . . . . . . . . . . . . . . . 3 2
. 6 9 4 . 7 . . . . 5 6 . . . 1 . 2 . 5 .
. . 2 9 . . . . 4 9 . . 2 . . 6 . . . . 7
. . . 2 . . 1 5 . . . 8 9 . 4 2 . . . . .
5 . . . 3 8 . 2 7 . . . 3 . 6 . . . . . . Number of clues 98, very hard
which remind us of the black hole puzzles of a few years ago.
Comments welcome,
Mike
